TY - JOUR
AU - Muhammad, Khan
AB - Abstract The ant colony optimization algorithm is a classical swarm intelligence algorithm, but it cannot be used for continuous class optimization problems. A continuous ant colony optimization algorithm (ACOR) is proposed to overcome this difficulty. Still, some problems exist, such as quickly falling into local optimum, slow convergence speed, and low convergence accuracy. To solve these problems, this paper proposes a modified version of ACOR called ADNOLACO. There is an opposition-based learning mechanism introduced into ACOR to effectively improve the convergence speed of ACOR. All-dimension neighborhood mechanism is also introduced into ACOR to further enhance the ability of ACOR to avoid getting trapped in the local optimum. To strongly demonstrate these core advantages of ADNOLACO, with the 30 benchmark functions of IEEE CEC2017 as the basis, a detailed analysis of ADNOLACO and ACOR is not only qualitatively performed, but also a comparison experiment is conducted between ADNOLACO and its peers. The results fully proved that ADNOLACO has accelerated the convergence speed and improved the convergence accuracy. The ability to find a balance between local and globally optimal solutions is improved. Also, to show that ADNOLACO has some practical value in real applications, it deals with four engineering problems. The simulation results also illustrate that ADNOLACO can improve the accuracy of the computational results. Therefore, it can be demonstrated that the proposed ADNOLACO is a promising and excellent algorithm based on the results. Graphical Abstract Open in new tabDownload slide ant colony optimization, continues optimization, opposition-based learning, all-dimension neighborhood mechanism, engineering design Highlights This paper proposed a modified continuous ant colony optimization called ADNOLACO. An opposition-based learning mechanism was introduced to improve the convergence speed. All-dimension neighborhood mechanism was introduced to step out of local optimum. A series of comparative experiments were carried out to analyse ADNOLACO’s performance. The ADNOLACO was applied to engineering problems and obtained some excellent results. 1. Introduction In the background of today’s highly advanced technology and industry, not only a variety of optimization problems (Liu et al., 2020b; Zhou et al., 2021) have emerged, but this has led to an increasingly wide range and scope of application of optimization algorithms (Zhao et al., 2021a, b). At the same time, due to the complexity and specificity of various optimization problems, the performance requirements of optimization algorithms have become more stringent. During recent years, many scholars have proposed different optimization algorithms to solve various optimization problems (Li et al., 2021), including not only some basic original algorithms, such as ant colony optimization for continuous domains (ACOR; Socha & Dorigo, 2008), differential evolution (DE; Storn & Price, 1997), firefly algorithm (FA; Yang, 2009), grey wolf optimization (GWO; Mirjalili et al., 2014), Harris hawks optimization (HHO; Heidari et al., 2019a), hunger games search (Yang et al., 2021), Runge Kutta optimizer (Ahmadianfar et al., 2021), moth-flame optimization (MFO; Mirjalili, 2015), particle swarm optimization (PSO; Kennedy & Eberhart, ), colony predation algorithm (CPA; Tu et al., 2021), slime mould algorithm (SMA; Li et al., 2020c), sine cosine algorithm (SCA; Mirjalili, 2016), weighted mean of vectors (Ahmadianfar et al., 2022), and whale optimizer (WOA; Mirjalili & Lewis, 2016), but also some variants with superior performance, such as bat algorithm based on collaborative and dynamic learning (CDLOBA; Yong et al., 2018), enhanced moth flame optimization (SMFO; Zhao et al., 2021a, b), hybridizing grey wolf optimization (HGWO; Zhu et al., 2015), boosted GWO (OBLGWO; Heidari et al., 2019b), enhanced comprehensive learning particle swarm optimization (GLOPSO; Liu et al., 2020b; Zhou et al., 2021), optimization (CGSCA; Kumar et al., 2017), adaptive chaotic sine cosine algorithm (ASCA; Ji et al., 2020), smile and Levy multi-strategy enhanced grey wolf optimization (SLEGWO; Li et al., 2021), modified SCA (m_SCA; Qu et al., 2018), improved fluid search optimization (Socha & Dorigo, 2008), the dynamic learning evolution algorithm (Li et al., 2021), learning-based elephant herding optimization algorithm (Li et al., 2020e), opposition-based krill herd algorithm with Cauchy mutation and position clamping (Wang et al., 2016), elephant herding optimization using dynamic topology and biogeography-based optimization based on learning (Li & Wang, 2021), an improved cuckoo search algorithm with self-adaptive knowledge learning (Li et al., 2020b), and double adaptive random spare reinforced whale optimization algorithm (RDWOA; Chen et al., 2019). These optimization algorithms have played an important role in various fields and effectively solved many problems in related fields such as image segmentation (Liu et al., 2021a; Zhao et al., 2021d, f; Chen et al., 2022; Yu et al., 2022b), plant disease recognition (Yu et al., 2022a), feature selection (Hu et al., 2021a, b, 2022b; Too et al., 2021), economic emission dispatch problem (Dong et al., 2021), engineering design (Abbasi et al., 2021; Nautiyal et al., 2021; Zhang et al., 2022), medical diagnosis (Hu et al., 2022a; Xia et al., 2022a, b), parameter tuning for machine learning models (Shi et al., 2021; Wu et al., 2021b; Zhang et al., 2021b), bankruptcy prediction (Cai et al., 2019; Xu et al., 2019), PID optimization control (Zeng et al., 2014, 2019), combination optimization problems (Zhao et al., 2021e), expensive optimization problems (Li et al., 2020a; Wu et al., 2021a), green supplier selection (Liu & Gao, 2020), multi-objective or many optimization problems (Liu et al., 2018; Hua et al., 2021; Zhang et al., 2021a; Deng et al., 2022), scheduling problems (Gao et al., 2020; Han et al., 2021), and big data optimization problems (Yi et al., 2018). Even though many optimization algorithms have been proposed, they still have some common problems for different practical problems, such as low convergence accuracy, slow convergence speed, and easy to fall into local optimum. The ant colony optimization algorithm (ACO) is one of the well-classic algorithms proposed by Dorigo et al. (2006), which is used to solve discrete-type optimization problems such as traveling salesman problem (Dorigo & Gambardella, 1997), assignment problems (Stützle & Hoos, 2000; Socha et al., 2003), and vehicle routing problems (Reimann et al., 2004). Although ACO shows excellent performance in discrete class problems, various continuous class optimization problems (Socha & Blum, 2007; Madadgar & Afshar, 2009; Hajizadeh et al., 2011; Xiao & Li, 2011; Chen & Wang, 2014; Fetanat & Khorasaninejad, 2015; Kunakote et al., 2021) cannot be solved using ACO in recent years. Therefore, aiming to make ACO also available for solving numerous continuous optimization problems, Socha and Dorigo (2008) proposed an optimization algorithm for solving continuous optimization problems (ACOR) based on the idea of ACO. Socha and Blum (2007) used the training of feed-forward neural networks for pattern classification as a test case for ACOR. It was applied to classification problems from the medical field. Chen and Wang (2014) applied a neural network method to model the RFID reflected signal strength distribution, in which ACOR was combined with a neural network to achieve a satisfactory solution. Kunakote et al. (2021) applied ACOR to solve four wind farm layout optimization problems. In contrast, the design problem is an attempt to simultaneously minimize wind farm cost and maximize wind farm totally produced power. Hajizadeh et al. (2011) applied ACOR to the problem of reservoir history matching and uncertainty quantification and employed it to generate multiple history matched models for two reservoir modes: a simple model of a real reservoir (Teal South), and a more complex synthetic model (PUNQ-S3) with more degrees of freedom and variables. Fetanat and Khorasaninejad (2015) employed ACOR for size optimization in a hybrid photovoltaic (PV)–wind energy system, of which the results are compared with other artificial intelligent approaches and a conventional optimization method, and outperforms them in terms of reaching an optimal solution and speed. In response to the needs of different practical problems and ACOR problems, many optimization schemes were proposed to alleviate them. Xiao and Li (2011) used ACOR for introducing a population-based functionality in continuous domains. A new variant of the ACO incorporating continuous population-based incremental learning and DE was proposed in their paper. The proposed method alleviates the more minor diversity problem in traditional population-based ACO methods. Madadgar and Afshar (2009) proposed an improved and adaptive ACO by integrating both adaptation operator and explorer ants into the structure of the original ACOR for the optimization of water resource problems in continuous domains. The proposed algorithm emphasizes the robustness in searching the continuous space more efficiently as locating the closest to the global optimal solution. The proposed algorithm was tested on some well-known benchmark problems; it had better performance than the original ACOR. Chen and Wang (2017) improved the continuous ACO with the crossover operator. Three crossover approaches were utilized to produce some new probability density function set of ACOR. The proposed algorithms were assessed using 21 benchmark functions with 30–1000 variables. The simulation results showed that the proposed ACOR with diverse crossover operators significantly boosted ACOR results for global optimization. Omran and Al-Sharhan (2019) proposed two new variants of ACOR, namely IACOR and LIACOR, with improved performance in solving real-world engineering optimization problems. The IACOR used a success-based random-walk selection that chooses between Brownian motion and Lévy flights. Thus, trying to balance exploitation and exploration, respectively. The LIACOR, on the other hand, was a memetic version of IACOR where a local search was used to enhance solutions in the colony. When their proposed variants and ACOR were tested on the 22 real-world engineering optimization problems of the IEEE CEC2011, the proposed algorithm outperformed the original ACOR on most problems. ACOR is widely used in some practical problems because it not only breaks the limitation that it can only be used for discrete problems but also has a good convergence speed and convergence accuracy. However, there is still some room to improve its convergence speed on many complex multimodal functions. The ability to avoid falling into local optimum also needs to be further improved. Therefore, this paper proposes an improved structure of the ACOR (ADNOLACO). First, an opposition-based learning (OBL) mechanism is introduced into ACOR, which effectively improves the convergence speed of ACOR. Based on this, an all-dimension neighborhood (ADN) mechanism is also introduced into ACOR to further enhance the ability of ACOR to avoid getting trapped in the local optimum. To demonstrate the performance of ADNOLACO, we first conducted variant comparison experiments. The impact of the two new mechanisms on ACOR was analysed in detail in terms of multiple perspectives, balance, and diversity. Then, the performance of ADNOLACO and ACOR was analysed in multiple dimensions to compare them more comprehensively. Finally, we compare ADNOLACO with some traditional basic algorithms and some improved ones. The Wilcoxon signed-rank test analysis (García et al., 2010), Friedman test analysis (Derracet al., 2011), and the results of the associated convergence curves are used to conduct the analysis of the experimental results. In addition, ADNOLACO is used to deal with four engineering problems. In conclusion, the proposed mechanism effectively alleviates the problem of LO and premature convergence of the original ACOR. The main work of this study can be divided into the following points: (1) The OBL and ADN mechanisms are introduced to address the shortcomings of the ACOR, which solve some problems such as quickly falling into local optimum, slow convergence speed, and low convergence accuracy. (2) A series of comparative experiments on IEEE CEC2017 were carried out to analyse ADNOLACO’s performance and prove its core advantages. (3) The proposed ADNOLACO is applied to engineering problems, and some excellent results are obtained. The rest of this paper is prearranged as follows. The details of the improved ADNOLACO are shown in Section 2. Section 3 presents the results and thoughts. Section 4 presents the application of ADNOLACO to four fundamental engineering problems. In Section 5, the main work of this paper is discussed. Section 6 summarizes the main findings of this paper and introduces the future work. 2. Enhanced ACOR-Based Method This subsection focuses on two mechanisms, namely OBL and AND, on which an enhanced version of ACOR, called ADNOLACO, is proposed. It converges faster than the original ACOR and improves the ability to avoid getting trapped in the local optimum. 2.1. Opposition-based learning mechanism The OBL mechanism was originally designed in 2005 (Tizhoosh, 2005). This special technique has been further presented (Ventresca & Tizhoosh, 2007a;b; Tizhoosh & Sahba, 2009) since it was proposed, which has also been proved to be an operative tactic for humanizing the searching trends of meta-heuristic optimizers. This technique is derived from concurrently estimating the matching opposite pairs of the base agents to increase the chance of meeting an agent with a better fitness value. The opposite of a real number |$x \in [ {{l_b},\ {l_u}} ]$| can be given by |$\bar{x}$| as follows: $$\begin{equation*} \bar{x} = {l_b} + {l_u} - x, \end{equation*} $$(1) where |${l_b}$| and |${l_u}$| are the lowest and upper bounds, respectively. In the multidimensional space, the description of x can be generated as shown in a previous study (Tizhoosh, 2005). It was assumed that |${\rm{\ }}{x_i} = \{ {{x_{i1}},\ {x_{i2}},\ {x_{i3}},\ \cdots ,\ {x_{ij}}} \}$| and |${x_{ij}} \in [ {{l_{bj}},\ {l_{uj}}} ]$|⁠, where|$j\ = \ 1,\ 2,\ \cdots ,\ n$|⁠, and the opposite point was as follows: $$\begin{equation*} {\bar{x}_i} = \left\{ {{x_{i1}},{x_{i2}}, \ldots ,\overline {{x_{ij}}} } \right\},\overline {{x_{ij}}} = {l_{bj}} + {l_{uj}} - {x_{ij}}. \end{equation*} $$(2) In the process of optimization, the opposite point |${\bar{x}_i}$| was replaced by the corresponding solution |${x_i}$| based on the fitness function. If |$f( {{x_i}} )$| was better than |$f( {{{\bar{x}}_i}} )$|⁠, then the |${x_i}$| was not changed; otherwise, |${x_i} = {\bar{x}_i}$|⁠. In other words, the position of the population was updated based on the better values of |${x_j}$| and |${\bar{x}_i}$|⁠. 2.2. All-dimension neighborhood mechanism To further improve the search capability of individual ants in the ACOR algorithm, we try to enhance this capability by using the ADN mechanism. Sun et al. (2017) originally proposed the ADN approach in 2017, intending to improve local search capabilities around the global optimal particle in PSO. Consequently, ACOR has adopted ADN as a tactic to drive ants to depart the local ideal site, which was inspired by this. ADN generates |$2*dim$| ADN ants to explore the search space for BestAnt’s neighbors. Cr symbolizes the center in three-dimensional (3D) space. |${x_1}$|⁠, |${x_2}$|⁠, and |${x_3}$| are the names of the three coordinate axes. The six ADN ants are designated by the letters |$N{b_1},\ N{b_2},\ N{b_3} \ldots N{b_6}$|⁠. L signifies the Euclidian distance between the core ant and any ADN ant, which is referred to as the neighborhood distance. Only one dimension distinguishes an ADN ant from the core ant: the size of its head. Equations (3) and (4) of the ADN ant distribution may be used to estimate the positions of the ADN ants. $$\begin{equation*} \left\{ \begin{array}{@{}*{1}{c}@{}} {Nb_{2k - 1}^d = C{r^d}k \le D,k \ne d}\\ {Nb_{2k - 1}^d = C{r^d} + L,k\ = \ d\ } \end{array} \right. \end{equation*} $$(3) $$\begin{equation*} \left\{ \begin{array}{@{}*{1}{c}@{}} {Nb_{2k}^d = C{r^d}k \le D,k \ne d}\\ {Nb_{2k}^d = C{r^d} - L,k\ = \ d\ } \end{array} .\right. \end{equation*} $$(4) The |$N{b_j} = ( {Nb_j^1,\ Nb_j^2,\ Nb_j^3 \ldots Nb_j^D} )$| denotes the location of the jth ADN ant in the ADN graph. In the core ant, the location of the ants is given by |$Cr = ( {C{r^1},\ C{r^2},\ C{r^3} \ldots C{r^D}} )$|⁠. Using three operators, namely shrink (⁠|$L = {L^*}\rho ,\ \rho \in ( {0,1} )$|⁠), retain (⁠|$L\ = \ L$|⁠), and expand (⁠|$L = {L_0}*{\rm{\ rand}}$|⁠), the neighborhood distance L may be changed to meet your needs. 2.3. The proposed ADNOLACO Aiming to improve the convergence rate of the original ACOR, the OBL strategy is applied to the process of foraging ants located in the archive when the update of the pheromone has been performed. Then, to obtain high-quality solutions and a stronger ability to jump out of local optima states, the AND mechanism is adopted to strengthen local search capability around the global optimal ant. According to the application way of OBL and ADN, its flowchart is displayed in Fig. 1. Figure 1: Open in new tabDownload slide The flowchart of ADNOLACO. The ADNOLACO algorithm’s computational cost is primarily determined by the maximum evaluation number (MaxFEs), archive size (k), population size (m), and dimension (dim). T denotes the number of iterations produced via the use of the MaxFEs. Suppose the number of evaluations in a single iteration is N. Then, T will be equal to MaxFEs/N. According to the investigation results, the computational complexity of the proposed ADNOLACO is primarily driven by the initialization of the archive the production of the new population using the Gaussian kernel function, the OBL, and the ADN. |$O\ ( {k \times dim} ) + O( {{k^2}} )$| is the complexity of the initialization of the archive in terms of computing time. The time complexity of the component of the creation of the new population that uses the Gaussian kernel function is |$O( {T \times \ ( {m \times dim \times k + m \times dim \times k + {m^2}} )} )$|⁠. Specifically, the computational complexity of OBL and ADN is |$O( {T \times \ ( {3\ \times k \times dim + k} )} )$|⁠. Therefore, |$O( {{\rm{ADNOLACO}}} )\ = \ O\ ( {k \times dim} ) + O( {{k^2}} ) + \ O( {T \times \ ( {m \times dim \times k + m \times dim \times k + {m^2}} )} )\ + \ O( {T \times \ ( {3\ \times k \times dim + k} )} )$|⁠. 3. Benchmark Function Validation In this section, to demonstrate the performance of the proposed ADNOLACO, a series of experiments were conducted on IEEE CEC2017, which included impacts of components, scalability test, qualitative analysis, comparison with conventional peers, and comparison with advanced peers. Furthermore, it has also been applied to deal with four engineering problems: tension/compression spring design (TCSD) problem, welded beam design (WBD) problem, pressure vessel design (PVD) problem, and hydrostatic thrust bearing design (HTBD) problem. 3.1. Experiment set During this experimental section, the effectiveness of the optimizers is tested using 30 benchmark functions from the well-known IEEE CEC2017. The relevant descriptions of the specific functions are shown in Table A1, where “Name of function” denotes the name of the benchmark function, and “Optimum” denotes the optimal value of the test function. These test functions can generally be divided into four categories. The first 10 functions, F1–F3, indicate unimodal functions, the remaining ones are multimodal functions, the middle 10 are hybrid functions, and the last 10 are composition functions. As is well known, unimodal functions are a well-proven ability to exploit methods since they have only one optimal solution. In contrast to unimodal functions, multimodal functions have a large number of locally optimal positions and increase with the number of dimensions, which allows them to test the ability of the algorithm to exploit and jump out of the local optimum. In computational sciences and example problems such as molecular signature identification (Li et al., 2017; Yang et al., 2020; Fu et al., 2022), pharmacoinformatic data mining (Zhu et al., 2012; Yin et al., 2020), drug discovery (Zhu et al., 2011, 2018; Li et al., 2020d), image super resolution (Zhuet al., 2021a, b), it is required to make sure that the settings of the validation process are independent and accurate. Hence, to ensure fairness and reliability of the experimental results, all the algorithms involved in the comparison are performed under the same conditions, where the population size is set to 30, and the maximum evaluation number is uniformly set to 300 000 times. In addition, all algorithms are independently tested 30 times to reduce the effect of random conditions. This consideration is to ensure the reliability of the obtained results, following idea of previous works in doing reliable experiments (Guo et al., 2020; Liu et al., 2021b). We have adopted the same values as in the original paper regarding the parameters that affect the algorithms involved in the comparison. Detailed statistics and analysis were performed for all experimental results obtained on the benchmark functions using the mean, variance, Wilcoxon signed-rank test, and Friedman test. 3.2. Impacts of parameter setting on ADNOLACO The experiments in this subsection focus on different values of the parameter q analysis, archive size analysis, and pheromone evaporation rate analysis on the 30 benchmark functions in Table A1 and the effects of different values of the parameters on the performance of the algorithm are analysed. 3.2.1 The parameter |${\boldsymbol{q}}$| analysis After 30 benchmark functions have been run using the parameter q, the values of the other parameters are maintained stable, and the values of the parameter q are set in the range of 0.01–1.0. This is shown in Table A4, which includes the relevant experimental data in terms of the average value (AVG) and standard deviation (STD) and how the ideal value of parameter q differs across the benchmark functions. The average value (Avg) and ranking (Rank) results generated by the Freidman test, on the other hand, reveal that when the parameter q is chosen as 0.3, the algorithm performs better than when the parameter q is taken as other values. As a result, the parameter q in ADNOLACO has been set to 0.3. 3.2.2. Archive size analysis In the experimental process of using 30 benchmark functions for the analysis of the archive size, the values of k were set to 2–12 and m,|$\ 2\ \times m$|⁠,|$\ m/2$|⁠, where m indicates the population size and the values of other parameters are kept consistent. The experimental results corresponding to parameter k are shown in Table A5. From AVG and STD, different benchmark functions have different optimal values of parameter k. However, from Avg and Rank of Freidman test results, when the value of k is 7, this algorithm performs better than other values. Therefore, the value of k is 7. 3.2.3. Pheromone evaporation rate analysis Pheromone evaporation rate (⁠|$\xi $|⁠) was evaluated on 30 benchmark functions with varying parameter values. The results in Table A6 showed that the values of |$\xi $| should be in the range 0.5–1.5, and that all of the other parameters should be constant. According to the Freidman test, the experimental findings for various values of |$\xi $| are shown in Table 4, which includes AVG, STD, Avg, and Rank, among others. The mean value obtained by the Freidman test analysis demonstrates that when |$\xi $| is accepted as 1, it performs better than when the other values are taken into consideration. As a result, the variable |$\xi $| takes on the value 1. 3.3. Impacts of components The composition methods of various ACOR versions are given in Table 1, where ADN denotes ADN mechanism, OL denotes position-based learning mechanism, “1” denotes that the operation is available in the corresponding ACOR version, and “0” denotes that the operation is not available in the corresponding ACOR version. Through the observation of Table 1, where ACOR is the original version, ADNACO is the version with an ADN mechanism, OLACO indicates the version with a position-based learning mechanism, and ADNOLACO is the version with both. Table 1: The composition methods of various ACOR versions. . ADN . OL . ACOR 0 0 ADNACO 1 0 OLACO 0 1 ADNOLACO 1 1 . ADN . OL . ACOR 0 0 ADNACO 1 0 OLACO 0 1 ADNOLACO 1 1 Open in new tab Table 1: The composition methods of various ACOR versions. . ADN . OL . ACOR 0 0 ADNACO 1 0 OLACO 0 1 ADNOLACO 1 1 . ADN . OL . ACOR 0 0 ADNACO 1 0 OLACO 0 1 ADNOLACO 1 1 Open in new tab In Table A2, the mean, variance obtained by four different versions of ACOR are presented after 30 random experiments on 30 test functions. In addition, the symbol “AVG” is involved in Table A2, indicating the mean value obtained on the benchmark functions, and the symbol “STD” indicates the variance obtained. In Table 2, the analysis results of the Wilcoxon signed-rank test are given, where the symbol “+” means the number of functions in which the combined performance of ADNOLACO is better than that of the other methods among the 30 tested functions, the symbol “−” means the number of functions in which the combined performance of ADNOLACO is worse than that of the other methods, the symbol “=” means that the performance of ADNOLACO and the other methods are equal, the symbol “Mean” means the overall ranking average obtained by each method. The symbol “Rank” indicates the final ranking result based on the performance of each algorithm. In terms of the overall ranking mean, ADNOLACO obtains the No. 1 result with 1.93 and can obtain better results than the other algorithm variants on most of the functions. In addition, the results of the Friedman analysis given in Fig. 2, where ADNOLACO outperforms ADNACO, OLACO, and ACOR, have been verified once again. Therefore, it is beyond doubt that ADNOLACO is a high-performance variant of ACOR. Figure 2: Open in new tabDownload slide The results of Friedman analysis of four different versions. Table 2: The analysis results of the Wilcoxon signed-rank test of four different versions. Item . ADNOLACO . ADNACO . OLACO . ACOR . +/−/= ∼ 13/5/12 13/9/8 23/0/7 Mean 1.93 2.37 2.23 3.47 Rank 1 3 2 4 Item . ADNOLACO . ADNACO . OLACO . ACOR . +/−/= ∼ 13/5/12 13/9/8 23/0/7 Mean 1.93 2.37 2.23 3.47 Rank 1 3 2 4 Open in new tab Table 2: The analysis results of the Wilcoxon signed-rank test of four different versions. Item . ADNOLACO . ADNACO . OLACO . ACOR . +/−/= ∼ 13/5/12 13/9/8 23/0/7 Mean 1.93 2.37 2.23 3.47 Rank 1 3 2 4 Item . ADNOLACO . ADNACO . OLACO . ACOR . +/−/= ∼ 13/5/12 13/9/8 23/0/7 Mean 1.93 2.37 2.23 3.47 Rank 1 3 2 4 Open in new tab 3.4. Scalability test To test the performance of both algorithms ADNOLACO and ACOR under different pressures, in this subsection, a comparative analysis of ADNOLACO and ACOR is performed based on IEEE CEC2017 with the dimensions of the problem being set to 30, 50, and 100, respectively. In Table A3, the corresponding mean, variance results are presented. In Table 3, the results of the Wilcoxon signed-rank test analyses are presented. As far as the mean is concerned, ADNOLACO obtained the minimum mean level on 25 functions when the problem dimension was set to 30. At problem dimension 50, ADNOLACO obtained the minimum mean level on 28 functions. When the problem dimension is 100, ADNOLACO obtains the minimum mean level on 27 functions. Regarding the variance, it is shown that ADNOLACO is more stable than ACOR on most of the functions, with the dimensionality being set to 30, 50, and 100, respectively. Furthermore, in the given Wilcoxon signed-rank test results, when the problem dimension is set to 30 and 50, ADNOLACO outperforms ACOR on 23 functions. at the problem dimension 100, ADNOLACO exceeds ACOR on 26 functions. Additionally, the convergence curves on functions F1, F4, F5, F8, F9, F12, F13, F19, F20, F25, F28, and F30 are given in Figs 3–5 when the problem dimensions are 30, 50, 100, respectively. The convergence speed and the convergence accuracy of ADNOLACO are superior to the original ACOR in different dimensions, as shown in the given convergence curves. Evidently, it is not only an indication of the strong performance of ADNOLACO in different complexity dimensions, but also this is a good proof of the speed-up of ADNOLACO in terms of convergence speed, as well as the significant enhancement of its ability to find the global optimum. Figure 3: Open in new tabDownload slide Some convergence curves of ADNOLACO and ACOR at dimension 30. Figure 4: Open in new tabDownload slide Some convergence curves of ADNOLACO and ACOR at dimension 50. Figure 5: Open in new tabDownload slide Some convergence curves of ADNOLACO and ACOR at dimension 100. Table 3: The results of the Wilcoxon signed-rank test analyses. Item . 30 . 50 . 100 . ADNOLACO . ACOR . ADNOLACO . ACOR . ADNOLACO . ACOR . +/−/= ∼ 23/0/7 ∼ 23/1/6 ∼ 26/2/2 Mean 1.17 1.83 1.07 1.93 1.10 1.90 Rank 1 2 1 2 1 2 Item . 30 . 50 . 100 . ADNOLACO . ACOR . ADNOLACO . ACOR . ADNOLACO . ACOR . +/−/= ∼ 23/0/7 ∼ 23/1/6 ∼ 26/2/2 Mean 1.17 1.83 1.07 1.93 1.10 1.90 Rank 1 2 1 2 1 2 Open in new tab Table 3: The results of the Wilcoxon signed-rank test analyses. Item . 30 . 50 . 100 . ADNOLACO . ACOR . ADNOLACO . ACOR . ADNOLACO . ACOR . +/−/= ∼ 23/0/7 ∼ 23/1/6 ∼ 26/2/2 Mean 1.17 1.83 1.07 1.93 1.10 1.90 Rank 1 2 1 2 1 2 Item . 30 . 50 . 100 . ADNOLACO . ACOR . ADNOLACO . ACOR . ADNOLACO . ACOR . +/−/= ∼ 23/0/7 ∼ 23/1/6 ∼ 26/2/2 Mean 1.17 1.83 1.07 1.93 1.10 1.90 Rank 1 2 1 2 1 2 Open in new tab Through the above analysis of the experimental results of ADNOLACO and AOCR on 30 function problems, it is clear that ADNOLACO can achieve better results and greater stability on problems of varying complexity. Also, it has a stronger ability to avoid getting trapped in the local optimum in solving problems, which helps to find a more optimal solution to the problem. Meanwhile, the convergence speed and the convergence accuracy of ADNOLACO have significantly been improved. In short, the proposed ADNOLACO has a stronger ability to solve problems and more significant advantages over AOCR. 3.5. The qualitative analysis of ADNOLACO Figure 6 gives the results of analyzing ADNOLACO from multiple perspectives. Figure 6a provides a 3D view of the benchmark function. Figure 6b shows the 2D distribution of the searched positions, in which the red dots represent the optimal position, and the black dots represent the searched positions. Figure 6c shows the variation of the individual position’s first dimension during the iteration. The variation of the average fitness of all individuals during the iteration is given in Fig. 6d. The convergence curves of ADNOLACO and ACOR are presented in Fig. 6e. Distributions in three and two dimensions reveal that ADNOLACO eventually traverses the optimal position and obtains the optimal solution on benchmark functions of different complexity. It can be seen from the variation of the first dimension of the individual positions that the oscillation amplitude is large at the beginning of the iteration. Then, the amplitude decreases and converges at the later stage, illustrating that the individuals can traverse the whole search space and improve the ability to avoid falling into the local optimum. ADNOLACO and AOCR convergence curves show that the final convergence accuracy of ADNOLACO is better than that of AOCR. The convergence curves on F7 and F8 also indicate that ADNOLACO converges faster than AOCR. The convergence curves on F1, F4, and F24 reflect that ADNOLACO has a stronger ability to escape from the local optimal solution and find the global optimal solution. Figure 6: Open in new tabDownload slide The results of analysing ADNOLACO from multiple perspectives. The analytical results for balance and diversity on the corresponding benchmark functions are given in Figs 7–9. The results of ADNOLACO’s analysis on balance are given in Fig. 7a. The result of the ACOR analysis on balance is given in Fig. 7b. The results of ADNACO’s analysis on balance are shown in Fig. 8a. The results of the OLACO’s analysis on balance are given in Fig. 8b. Figure 9 gives their analysis results of the diversity. It can be seen from the analysis of the balance results that the incorporation of ADN strategy and OBL strategy makes ADNOLACO reach a better balance point in exploration and exploitation so that the convergence speed and the final convergence accuracy of ADNOLACO can be better than ADNACO, OLACO, and AOCR. It can be seen that there is not much change on F1 and F4. The diversity curves of ADNOLACO converge slower than ADNACO, OLACO, and AOCR on F7, F8, and F24 in the early stage, with the distance between ADNOLACO search individuals being greater than that between ADNACO, OLACO, and AOCR search individuals in the late stage, which means that ADNOLACO can traverse the entire search space more fully throughout the search process, and this makes ADNOLACO have a stronger ability to escape from the local optimal solution and find the global optimal solution. Figure 7: Open in new tabDownload slide The balance analysis results of ADNOLACO and ACOR on benchmark functions. Figure 8: Open in new tabDownload slide The balance analysis results of ADNACO and OLACO on benchmark functions. Figure 9: Open in new tabDownload slide The analytical results for diversity on benchmark functions. 3.6. Comparison with conventional algorithms This subsection focuses on comparing ADNOLACO with some very classical basic algorithms to further demonstrate the core advantages of ADNOLACO. In this experiment, the basic algorithms involved in the comparison include ACOR, DE, FA, GWO, HHO, MFO, PSO, SCA, and WOA. The relevant parameters are taken using the parameter values set by the algorithms themselves. The results of the comparison between ADNOLACO and the nine basic algorithms, including the mean and variance analysis results, are given in Table A7. In terms of the optimal values of the functions obtained, ADNOLACO ranks first, i.e. receives the minimum mean value, for the greatest number of function problems, which indicates that ADNOLACO still has a greater advantage when comparing it with the basic algorithms. The analysis of the Wilcoxon signed-rank test in Table 4 shows that ADNOLACO obtained No. 1 with the ranked overall mean 2.23 and performed better on the 18 function problems than DE, which ranked No. 2. The results of the p-values obtained during the Wilcoxon signed-rank test are given in Table A8, and a value less than 0.05 indicates that the result is trustworthy. It can be seen that the p-values are basically less than 0.05, which also indicates that it is trustworthy to obtain better results than other methods when ADNOLACO is compared with the basic algorithms at that time. The analysis results using the Friedman test are given in Fig. 10 for ADNOLACO, and the other nine basic methods, where ADNOLACO is ranked No. 1 with the value 2.35 obtained and DE is ranked No. 2 with the value 3.48 obtained. This further shows that ADNOLACO still has a greater advantage compared to the basic algorithms. The convergence curves of ADNOLACO and the other nine basic methods on some benchmark functions are given in Fig. 11, where the given convergence curves show that the convergence accuracy of ADNOLACO is better than the other algorithms, F19 shows that ADNOLACO has been enhanced in terms of convergence speed, and F1, F5, F8, F12, F21, F23, F24, and F26 show that ADNOLACO is also better than the other algorithms in avoiding falling into local optimum. Therefore, its core advantages are also well demonstrated when ADNOLACO is compared with other basic algorithms. Figure 10: Open in new tabDownload slide The results of the analysis using the Friedman test. Figure 11: Open in new tabDownload slide The convergence curves of ADNOLACO and the other nine basic methods. Table 4: The analysis of the Wilcoxon signed-rank test. Method . Rank . Mean . +/−/= . ADNOLACO 1 2.23 ∼ ACOR 5 4.70 23/2/5 DE 2 3.33 18/8/4 FA 9 8.20 29/1/0 GWO 3 4.43 23/6/1 HHO 6 4.90 24/3/3 MFO 8 7.23 28/0/2 PSO 4 4.63 21/5/4 SCA 10 9.23 29/1/0 WOA 7 6.10 28/0/2 Method . Rank . Mean . +/−/= . ADNOLACO 1 2.23 ∼ ACOR 5 4.70 23/2/5 DE 2 3.33 18/8/4 FA 9 8.20 29/1/0 GWO 3 4.43 23/6/1 HHO 6 4.90 24/3/3 MFO 8 7.23 28/0/2 PSO 4 4.63 21/5/4 SCA 10 9.23 29/1/0 WOA 7 6.10 28/0/2 Open in new tab Table 4: The analysis of the Wilcoxon signed-rank test. Method . Rank . Mean . +/−/= . ADNOLACO 1 2.23 ∼ ACOR 5 4.70 23/2/5 DE 2 3.33 18/8/4 FA 9 8.20 29/1/0 GWO 3 4.43 23/6/1 HHO 6 4.90 24/3/3 MFO 8 7.23 28/0/2 PSO 4 4.63 21/5/4 SCA 10 9.23 29/1/0 WOA 7 6.10 28/0/2 Method . Rank . Mean . +/−/= . ADNOLACO 1 2.23 ∼ ACOR 5 4.70 23/2/5 DE 2 3.33 18/8/4 FA 9 8.20 29/1/0 GWO 3 4.43 23/6/1 HHO 6 4.90 24/3/3 MFO 8 7.23 28/0/2 PSO 4 4.63 21/5/4 SCA 10 9.23 29/1/0 WOA 7 6.10 28/0/2 Open in new tab 3.7. Comparison with advanced algorithms To enable further demonstration of the core advantages of ADNOLACO, this section compares ADNOLACO with some improved variants proposed in recent years, where the algorithms involved in the comparison include MOFOA, CDLOBA, HGWO, OBLGWO, CGSCA, DECLS, m_SCA, ASCA, and RDWOA. Table A9 gives the experimental results of each algorithm after 30 independent runs, including the mean, variance, and Table 5 gives the analytical results of the Wilcoxon signed-rank test. When it comes to obtaining optimal values for functional problems, ADNOLACO obtains optimal values for most functional problems. Therefore, ADNOLACO is the best performer among the obtained optimal values for function problems, having a better performance than other advanced counterparts. Moreover, in the results of the analysis of the Wilcoxon signed-rank test, it can be seen that ADNOLACO performs better than DECLS, which is ranked No. 2, on 21 function problems, which also further indicates that ADNOLACO performs better than other similar methods. The Friedman test given in Fig. 12 shows that ADNOLACO ranks first with 2.07 and DECLS ranks No. 2 with 3.40, which further shows that ADNOLACO performs better than other comparable methods. ADNOLACO has the highest convergence accuracy on some benchmark functions in the convergence curves given in Fig. 13. In terms of convergence speed, it has relatively good results on functions F19 and F30, while the ability to escape from local optimal solutions is well demonstrated on F1, F5, F8, F12, F15, F21, and F26. Consequently, it is also well demonstrated by the abovementioned correlation analysis that ADNOLACO has greater advantages when compared with other advanced variants of the algorithm. Figure 12: Open in new tabDownload slide The Friedman test of ADNOLACO and nine variants. Figure 13: Open in new tabDownload slide The convergence curves of ADNOLACO and the other nine advanced methods. Table 5: The analytical results of the Wilcoxon signed-rank test. Method . Rank . Mean . +/−/= . ADNOLACO 1 2.067 ∼ MOFOA 10 9.800 29/1/0 CDLOBA 6 4.933 22/4/4 HGWO 7 6.167 28/2/0 OBLGWO 3 3.733 24/3/3 CGSCA 8 7.967 29/1/0 DECLS 2 3.200 21/7/2 m_SCA 5 4.733 27/2/1 ASCA 9 8.267 29/1/0 RDWOA 4 4.133 24/5/1 Method . Rank . Mean . +/−/= . ADNOLACO 1 2.067 ∼ MOFOA 10 9.800 29/1/0 CDLOBA 6 4.933 22/4/4 HGWO 7 6.167 28/2/0 OBLGWO 3 3.733 24/3/3 CGSCA 8 7.967 29/1/0 DECLS 2 3.200 21/7/2 m_SCA 5 4.733 27/2/1 ASCA 9 8.267 29/1/0 RDWOA 4 4.133 24/5/1 Open in new tab Table 5: The analytical results of the Wilcoxon signed-rank test. Method . Rank . Mean . +/−/= . ADNOLACO 1 2.067 ∼ MOFOA 10 9.800 29/1/0 CDLOBA 6 4.933 22/4/4 HGWO 7 6.167 28/2/0 OBLGWO 3 3.733 24/3/3 CGSCA 8 7.967 29/1/0 DECLS 2 3.200 21/7/2 m_SCA 5 4.733 27/2/1 ASCA 9 8.267 29/1/0 RDWOA 4 4.133 24/5/1 Method . Rank . Mean . +/−/= . ADNOLACO 1 2.067 ∼ MOFOA 10 9.800 29/1/0 CDLOBA 6 4.933 22/4/4 HGWO 7 6.167 28/2/0 OBLGWO 3 3.733 24/3/3 CGSCA 8 7.967 29/1/0 DECLS 2 3.200 21/7/2 m_SCA 5 4.733 27/2/1 ASCA 9 8.267 29/1/0 RDWOA 4 4.133 24/5/1 Open in new tab 4. The ADNOLACO for the Engineering Applications In this section, to demonstrate the practicality of ADNOLACO, we apply ADNOLACO to solve several engineering cases. It is widely accepted that in complex feature spaces, the relation of variables can be more complicated than we efficiently utilize an exact algorithm (Zhang et al., 2021c). In addition, for many real-world applications such as information retrieval services (Wu et al., 2020a, b; 2021c), human motion capture (Qiu et al., 2021b), microgrid planning (Cao et al., 2020), kayak cycle phase segmentation (Qiu et al., 2021a), large-scale network analysis (Liu et al., 2021c), the solution space that we need to deal with, is also not unconstrained and several limits are there for decision makers. Hence, to benchmark the performance of the ACO-based optimizer, we tried to consider some constrained problems that have been accepted by the literature as good benchmark. These cases include TCSD, welded beam, pressure vessel, and HTBD problems. 4.1. Tension/compression spring design problem The mathematical model of TCSD is designed to minimize the weight of the spring; among them, three variables need to be optimized, including the wire diameter (d), mean coil diameter (D), and number of active coils (N). The mathematical model of this problem is as follows: Consider |$\vec{x} = [ {{x_1}\ {x_2}\ {x_3}} ] = [ {d\ D\ N} ]$| Objective function: $$\begin{equation*} f{\left( {\vec{x}} \right)_{\mathrm{ min}}} = x_1^2{x_2}{x_3} + 2x_1^2{x_2} \end{equation*} $$ Subject to $$\begin{eqnarray*} {h_1}\left( {\vec{x}} \right) &=& 1 - \frac{{x_2^3{x_3}}}{{71785x_1^4}} \le 0, \\ {h_2}\left( {\vec{x}} \right) &=& \frac{{4x_2^2 - {x_1}{x_2}}}{{12566\left( {{x_2}x_1^3 - x_1^4} \right)}} + \frac{1}{{5180x_1^2}} \le 0, \\ {h_3}\left( {\vec{x}} \right) &=& 1 - \frac{{140.45{x_1}}}{{x_2^3{x_3}}} \le 0,\\ {h_4}\left( {\vec{x}} \right) &=& \frac{{{x_1} + {x_2}}}{{1.5}} - 1 \le 0 \end{eqnarray*} $$ $$\begin{equation*} \end{equation*} $$ Variable ranges: $$\begin{eqnarray*} && 0.05 \le {x_1} \le 1.00, \\ && 0.25 \le {x_2} \le 1.30, \\ && 2.00 \le {x_3} \le 15.0. \end{eqnarray*} $$ The proposed ADNOLACO is used to realize the aspects of the TSCD problem to check its successes in this kind of engineering problem. Table 6 records the experimental results where ADNOLACO could catch the optimal cost, confirming the improved effectiveness of the proposed ADNOLACO in actual engineering applications compared with other deep-rooted approaches. Table 6: Comparison results of the TSCD problem. Method . Best variables . Best weight . . d . D . N . . ADNOLACO 0.051684 0.356589 11.29651 0.012665 WOA (Mirjalili & Lewis, 2016) 0.051207 0.345215 12.0043032 0.0126763 PSO (He & Wang, 2007) 0.015728 0.357644 11.244543 0.0126747 GA (Coello, 2000) 0.051480 0.351661 11.632201 0.0127048 RO (Kaveh & Khayatazad, 2012) 0.051370 0.349096 11.762790 0.0126788 IHS (Mahdavi et al., 2007) 0.051154 0.349871 12.076432 0.0126706 Constraint correction (Arora, 2004) 0.050000 0.315900 14.250000 0.0128334 Math. optimization (Belegundu & Arora, 1985) 0.053396 0.399180 901854000 0.0127303 ES (Mezura-Montes & Coello, 2008) 0.051989 0.363965 10.890522 0.0126810 GSA (Rashedi et al., 2009) 0.050276 0.323680 13.525410 0.0127022 DE (Huang et al., 2007) 0.051609 0.354714 11.41083 0.012670 HS (Mahdavi et al., 2007) 0.051154 0.349871 12.07643 0.012678 Method . Best variables . Best weight . . d . D . N . . ADNOLACO 0.051684 0.356589 11.29651 0.012665 WOA (Mirjalili & Lewis, 2016) 0.051207 0.345215 12.0043032 0.0126763 PSO (He & Wang, 2007) 0.015728 0.357644 11.244543 0.0126747 GA (Coello, 2000) 0.051480 0.351661 11.632201 0.0127048 RO (Kaveh & Khayatazad, 2012) 0.051370 0.349096 11.762790 0.0126788 IHS (Mahdavi et al., 2007) 0.051154 0.349871 12.076432 0.0126706 Constraint correction (Arora, 2004) 0.050000 0.315900 14.250000 0.0128334 Math. optimization (Belegundu & Arora, 1985) 0.053396 0.399180 901854000 0.0127303 ES (Mezura-Montes & Coello, 2008) 0.051989 0.363965 10.890522 0.0126810 GSA (Rashedi et al., 2009) 0.050276 0.323680 13.525410 0.0127022 DE (Huang et al., 2007) 0.051609 0.354714 11.41083 0.012670 HS (Mahdavi et al., 2007) 0.051154 0.349871 12.07643 0.012678 Open in new tab Table 6: Comparison results of the TSCD problem. Method . Best variables . Best weight . . d . D . N . . ADNOLACO 0.051684 0.356589 11.29651 0.012665 WOA (Mirjalili & Lewis, 2016) 0.051207 0.345215 12.0043032 0.0126763 PSO (He & Wang, 2007) 0.015728 0.357644 11.244543 0.0126747 GA (Coello, 2000) 0.051480 0.351661 11.632201 0.0127048 RO (Kaveh & Khayatazad, 2012) 0.051370 0.349096 11.762790 0.0126788 IHS (Mahdavi et al., 2007) 0.051154 0.349871 12.076432 0.0126706 Constraint correction (Arora, 2004) 0.050000 0.315900 14.250000 0.0128334 Math. optimization (Belegundu & Arora, 1985) 0.053396 0.399180 901854000 0.0127303 ES (Mezura-Montes & Coello, 2008) 0.051989 0.363965 10.890522 0.0126810 GSA (Rashedi et al., 2009) 0.050276 0.323680 13.525410 0.0127022 DE (Huang et al., 2007) 0.051609 0.354714 11.41083 0.012670 HS (Mahdavi et al., 2007) 0.051154 0.349871 12.07643 0.012678 Method . Best variables . Best weight . . d . D . N . . ADNOLACO 0.051684 0.356589 11.29651 0.012665 WOA (Mirjalili & Lewis, 2016) 0.051207 0.345215 12.0043032 0.0126763 PSO (He & Wang, 2007) 0.015728 0.357644 11.244543 0.0126747 GA (Coello, 2000) 0.051480 0.351661 11.632201 0.0127048 RO (Kaveh & Khayatazad, 2012) 0.051370 0.349096 11.762790 0.0126788 IHS (Mahdavi et al., 2007) 0.051154 0.349871 12.076432 0.0126706 Constraint correction (Arora, 2004) 0.050000 0.315900 14.250000 0.0128334 Math. optimization (Belegundu & Arora, 1985) 0.053396 0.399180 901854000 0.0127303 ES (Mezura-Montes & Coello, 2008) 0.051989 0.363965 10.890522 0.0126810 GSA (Rashedi et al., 2009) 0.050276 0.323680 13.525410 0.0127022 DE (Huang et al., 2007) 0.051609 0.354714 11.41083 0.012670 HS (Mahdavi et al., 2007) 0.051154 0.349871 12.07643 0.012678 Open in new tab 4.2. Welded beam design problem The WBD problem is to achieve the lowest cost of expenditure by optimizing the following parameters: shear stress (⁠|$\tau $|⁠), bending stress (⁠|$\theta $|⁠), buckling load (⁠|${P_c}$|⁠), and deflection (⁠|$\delta $|⁠). These four variables of this problem include the welding seam thickness (h), welding joint length|$,$| beam width |$( t )$|⁠, and beam thickness |$( b )$|⁠. The mathematical model is as follows: $$\begin{eqnarray*} && {\rm Consider} \quad \,\,\,\, {\vec{x}} = [ {{x_1},\ {x_2},\ {x_3},\ {x_4}} ] = [ {h\ l\ t\ b} ]\\ && {\rm Minimize} \quad \,\, f( {{\vec{x}}} ) = 1.10471x_1^2 + 0.04811{x_3}{x_4}( {14.0 + {x_4}} )\\ && {\rm Subject\, to} \quad \,\, {g_1}( {{\vec{x}}} ) = \tau ( {\vec{x}} ) - {\tau _{\mathrm{ max}}} \le 0, \\ && \qquad \qquad \qquad {g_2}\left( {\vec{x}} \right) = \sigma \left( {\vec{x}} \right) - {\sigma _{\mathrm{ max}}} \le 0, \\ && \qquad \qquad \qquad {g_3}\left( {\vec{x}} \right) = \delta \left( {\vec{x}} \right) - {\delta _{\mathrm{ max}}} \le 0, \\ && \qquad \qquad \qquad {g_4}\left( {\vec{x}} \right) = {x_1} - {x_4} \le 0, \\ && \qquad \qquad \qquad {g_5}\left( {\vec{x}} \right) = P - {P_C}\left( {\vec{x}} \right) \le 0, \\ \end{eqnarray*} $$ $$\begin{eqnarray*} && \qquad \qquad \qquad {g_6}\left( {\vec{x}} \right) = 0.125 - {x_1} \le 0, \\ && \qquad \qquad \qquad {g_7}\left( {\vec{x}} \right) = 1.10471x_1^2 + 0.04811{x_3}{x_4}\left( {14.0 + {x_2}} \right) \\ && \qquad \qquad \quad \,\,\,\,\qquad \qquad - \,5.0 \le 0 , \end{eqnarray*} $$ Variable ranges: |$0.1 \le {x_1} \le 2$|⁠, |$0.1 \le {x_2} \le 10$|⁠, |$0.1 \le {x_3} \le 10$|⁠, |$0.1 \le {x_4} \le 2$| where |$\tau ( {\vec{x}} ) = \sqrt {{{( {\tau ^{\prime}} )}^2} + 2\tau ^{\prime}\tau ^{\prime\prime}\frac{{{x_2}}}{{2R}} + {{( {\tau ^{\prime\prime}} )}^2}} $|⁠, |$\tau ^{\prime} = \frac{P}{{\sqrt 2 {x_1}{x_2}}},\ \tau ^{\prime\prime} = \frac{{MR}}{J},\ M\ = \ P( {L + \frac{{{x_2}}}{2}} )$| $$\begin{eqnarray*} && \sigma \left( {\vec{x}} \right) = \frac{{6PL}}{{{x_4}{x_3}^2}},\ \delta \left( {\vec{x}} \right) = \frac{{6P{L^3}}}{{Ex_3^2{x_4}}}, \\ && {P_C}\left( {\vec{x}} \right) = \frac{{4.013E\sqrt {\frac{{x_3^2x_4^6}}{{36}}} }}{{{L^2}}}\left( {1 - \frac{{{x_3}}}{{2L}}\sqrt {\frac{E}{{4G}}} } \right) \\ \end{eqnarray*} $$ $$\begin{eqnarray*} && P = 60001b,\ L = 14 \in ..{\delta _{\mathrm{ max}}} = 0.25 \in .. \\ && E = 30\ \times {1^6}psi,\ G = 12 \times {10^6}psi \\ && {\tau _{\mathrm{ max}}} = 13600psi,\ {\sigma _{\mathrm{ max}}} = 30000psi \end{eqnarray*} $$ The performance of ADNOLACO was compared with some peers. We can find from Table 7 that the ADNOLACO has the best performance, achieving the value 1.72002. Table 7: Comparison results of the WBD problem. Technique . Best variables . Best cost . . h . l . t . b . . ADNOLACO 0.1885 3.6205 9.02577 0.20623 1.72002 RO (Kaveh & Khayatazad, 2012) 0.203687 3.528467 9.004233 0.207241 1.735344 IHS (Mahdavi et al., 2007) 0.20573 3.47049 9.03662 0.20573 1.7248 SSA (Mirjalili et al., 2017) 0.205700 3.471400 9.036600 0.205700 1.724910 CDE (Huang et al., 2007) 0.203137 3.542998 9.033498 0.206179 1.733462 GWO (Mirjalili et al., 2014) 0.205700 3.478400 9.036800 0.205800 1.726240 GSA (Rashedi et al., 2009) 0.182129 3.856979 10.00000 0.202376 1.879950 NDE (Wagdy, 2017) 0.205729 3.470488 9.903662 0.205729 1.724852 GA3 (Coello Coello & Mezura Montes, 2002) 0.205986 3.471328 9.020224 0.206480 1.728226 HGA (Yuan & Qian, 2010) 0.205700 3.470500 9.036600 0.205700 1.724852 NM-PSO (Zahara & Kao, 2009) 0.205830 3.468338 9.036624 0.205730 1.724717 WCA (Eskandar et al., 2012) 0.205728 3.470522 9.036620 0.205729 1.724856 Coello (Coello Coello, 2002) 0.208800 3.420500 8.997500 0.2100 1.74831 Coello and Montes (Coello Coello & Mezura Montes, 2002) 0.205986 3.471328 9.020224 0.206480 1.72822 CAEP (Coello Coello & Becerra, 2004) 0.205700 3.470500 9.036600 0.205700 1.724852 CPSO (Krohling & Coelho, 2006) 0.202369 3.544214 9.048210 0.205723 1.728024 Technique . Best variables . Best cost . . h . l . t . b . . ADNOLACO 0.1885 3.6205 9.02577 0.20623 1.72002 RO (Kaveh & Khayatazad, 2012) 0.203687 3.528467 9.004233 0.207241 1.735344 IHS (Mahdavi et al., 2007) 0.20573 3.47049 9.03662 0.20573 1.7248 SSA (Mirjalili et al., 2017) 0.205700 3.471400 9.036600 0.205700 1.724910 CDE (Huang et al., 2007) 0.203137 3.542998 9.033498 0.206179 1.733462 GWO (Mirjalili et al., 2014) 0.205700 3.478400 9.036800 0.205800 1.726240 GSA (Rashedi et al., 2009) 0.182129 3.856979 10.00000 0.202376 1.879950 NDE (Wagdy, 2017) 0.205729 3.470488 9.903662 0.205729 1.724852 GA3 (Coello Coello & Mezura Montes, 2002) 0.205986 3.471328 9.020224 0.206480 1.728226 HGA (Yuan & Qian, 2010) 0.205700 3.470500 9.036600 0.205700 1.724852 NM-PSO (Zahara & Kao, 2009) 0.205830 3.468338 9.036624 0.205730 1.724717 WCA (Eskandar et al., 2012) 0.205728 3.470522 9.036620 0.205729 1.724856 Coello (Coello Coello, 2002) 0.208800 3.420500 8.997500 0.2100 1.74831 Coello and Montes (Coello Coello & Mezura Montes, 2002) 0.205986 3.471328 9.020224 0.206480 1.72822 CAEP (Coello Coello & Becerra, 2004) 0.205700 3.470500 9.036600 0.205700 1.724852 CPSO (Krohling & Coelho, 2006) 0.202369 3.544214 9.048210 0.205723 1.728024 Open in new tab Table 7: Comparison results of the WBD problem. Technique . Best variables . Best cost . . h . l . t . b . . ADNOLACO 0.1885 3.6205 9.02577 0.20623 1.72002 RO (Kaveh & Khayatazad, 2012) 0.203687 3.528467 9.004233 0.207241 1.735344 IHS (Mahdavi et al., 2007) 0.20573 3.47049 9.03662 0.20573 1.7248 SSA (Mirjalili et al., 2017) 0.205700 3.471400 9.036600 0.205700 1.724910 CDE (Huang et al., 2007) 0.203137 3.542998 9.033498 0.206179 1.733462 GWO (Mirjalili et al., 2014) 0.205700 3.478400 9.036800 0.205800 1.726240 GSA (Rashedi et al., 2009) 0.182129 3.856979 10.00000 0.202376 1.879950 NDE (Wagdy, 2017) 0.205729 3.470488 9.903662 0.205729 1.724852 GA3 (Coello Coello & Mezura Montes, 2002) 0.205986 3.471328 9.020224 0.206480 1.728226 HGA (Yuan & Qian, 2010) 0.205700 3.470500 9.036600 0.205700 1.724852 NM-PSO (Zahara & Kao, 2009) 0.205830 3.468338 9.036624 0.205730 1.724717 WCA (Eskandar et al., 2012) 0.205728 3.470522 9.036620 0.205729 1.724856 Coello (Coello Coello, 2002) 0.208800 3.420500 8.997500 0.2100 1.74831 Coello and Montes (Coello Coello & Mezura Montes, 2002) 0.205986 3.471328 9.020224 0.206480 1.72822 CAEP (Coello Coello & Becerra, 2004) 0.205700 3.470500 9.036600 0.205700 1.724852 CPSO (Krohling & Coelho, 2006) 0.202369 3.544214 9.048210 0.205723 1.728024 Technique . Best variables . Best cost . . h . l . t . b . . ADNOLACO 0.1885 3.6205 9.02577 0.20623 1.72002 RO (Kaveh & Khayatazad, 2012) 0.203687 3.528467 9.004233 0.207241 1.735344 IHS (Mahdavi et al., 2007) 0.20573 3.47049 9.03662 0.20573 1.7248 SSA (Mirjalili et al., 2017) 0.205700 3.471400 9.036600 0.205700 1.724910 CDE (Huang et al., 2007) 0.203137 3.542998 9.033498 0.206179 1.733462 GWO (Mirjalili et al., 2014) 0.205700 3.478400 9.036800 0.205800 1.726240 GSA (Rashedi et al., 2009) 0.182129 3.856979 10.00000 0.202376 1.879950 NDE (Wagdy, 2017) 0.205729 3.470488 9.903662 0.205729 1.724852 GA3 (Coello Coello & Mezura Montes, 2002) 0.205986 3.471328 9.020224 0.206480 1.728226 HGA (Yuan & Qian, 2010) 0.205700 3.470500 9.036600 0.205700 1.724852 NM-PSO (Zahara & Kao, 2009) 0.205830 3.468338 9.036624 0.205730 1.724717 WCA (Eskandar et al., 2012) 0.205728 3.470522 9.036620 0.205729 1.724856 Coello (Coello Coello, 2002) 0.208800 3.420500 8.997500 0.2100 1.74831 Coello and Montes (Coello Coello & Mezura Montes, 2002) 0.205986 3.471328 9.020224 0.206480 1.72822 CAEP (Coello Coello & Becerra, 2004) 0.205700 3.470500 9.036600 0.205700 1.724852 CPSO (Krohling & Coelho, 2006) 0.202369 3.544214 9.048210 0.205723 1.728024 Open in new tab 4.3. Pressure vessel design problem The PVD problem is considered a well-researched test case for structural optimization to control costs as much as possible. One end of the container is covered, and the other end is a hemisphere, for which the total manufacturing costs are determined by four variables – the thickness of the shell |$( {{T_s}} )$|⁠, the thickness of the head (⁠|${T_h}$|⁠), inner radius |$( R )$|⁠, and the span of the cylindrical part of the container |$( L )$| – to determine the total manufacturing cost. The relevant formulas are as follows: $$\begin{eqnarray*} && {\rm Consider} \quad \, \,\,\, \vec{x} = [ {{x_1},{\rm{\ }}{x_2},{\rm{\ }}{x_3},{\rm{\ }}{x_4}} ] = [ {{T_s}\ {T_h}\ R\ L} ] \\ && {\rm Minimize} \quad \,\, f{( {\vec{x}} )_{\mathrm{ min}}} = {\rm{0}}{\rm{.6224}}{x_1}{x_3}{x_4} + {\rm{1}}{\rm{.7781}}{x_3}x_1^2 \nonumber \\ && \qquad \qquad \qquad \qquad \qquad \quad + \,{\rm{3}}{\rm{.1661}}{x_4}x_1^2 + {\rm{19}}{\rm{.84}}{x_3}x_1^2 \\ && {\rm Subject\, to} \quad \, {g_1}( {\vec{x}} ) = - {x_1} + {\rm{0}}{\rm{.0193}}{x_3} \le 0, \\ && \qquad \qquad \qquad {g_2}\left( {\vec{x}} \right) = - {x_2} + {\rm{0}}{\rm{.0095}}{x_3} \le 0, \\ && \qquad \qquad \qquad {g_3}\left( {\vec{x}} \right) = - \pi {x_4}x_3^2 - \frac{4}{3}\pi x_3^3 + {\rm{1296000}} \le 0, \\ && \qquad \qquad \qquad {g_4}\left( {\vec{x}} \right) = {x_4} - {\rm{240}} \le 0 \end{eqnarray*} $$ Variable ranges: |$0 \le {x_1} \le {\rm{99}}$|⁠, |$0 \le {x_2} \le {\rm{99}}$|⁠, |$10 \le {x_3} \le {\rm{200}}$|⁠, |$10 \le {x_4} \le {\rm{200}}$|⁠. ADNOLACO has solved this problem, and its results are compared with those of CPSO (He & Wang, 2007), ACO (Kaveh & Talatahari, 2010), WOA (Mirjalili & Lewis, 2016), Branch-bound (Sandgren, 1988), GSA (Rashedi et al., 2009), CDE (Huang et al., 2007), GA3 (Coello Coello & Mezura Montes, 2002), G-QPSO (Coelho, 2010), and Lagrangian multiplier (Kannan & Kramer, 1994). The comparison results are shown in Table 8. The performance of ADNOLACO is better than other methods, which shows that our proposed ADNOLACO can also effectively solve this problem. Table 8: Comparison results of the PVD problem. Algorithm . Optimum variables . Optimum cost . . |${T_s}$| . |${T_h}$| . R . L . . ADNOLACO 0.8125 0.4375 42.09845 176.6366 6059.714 CPSO (He & Wang, 2007) 0.8125 0.4375 42.0912 176.7465 6061.0777 ACO (Kaveh & Talatahari, 2010) 0.8125 0.4375 42.1036 176.5727 6059.0888 WOA (Mirjalili & Lewis, 2016) 0.8125 0.4375 42.0983 176.6390 6059.7410 Branch-bound (Sandgren, 1988) 1.1250 0.6250 47.7000 117.7010 8129.1036 GSA (Rashedi et al., 2009) 1.1250 0.6250 55.988659 84.452025 8538.8359 CDE (Huang et al., 2007) 0.812500 0.437500 42.098400 176.637600 6059.7340 GA3 (Coello Coello & Mezura Montes, 2002) 0.812500 0.437500 42.097400 176.654000 6059.9463 G-QPSO (Coelho, 2010) 0.812500 0.437500 42.098400 176.637200 6059.7208 Lagrangian multiplier (Kannan & Kramer, 1994) 1.125000 0.625000 58.291000 43.690000 7198.0428 Algorithm . Optimum variables . Optimum cost . . |${T_s}$| . |${T_h}$| . R . L . . ADNOLACO 0.8125 0.4375 42.09845 176.6366 6059.714 CPSO (He & Wang, 2007) 0.8125 0.4375 42.0912 176.7465 6061.0777 ACO (Kaveh & Talatahari, 2010) 0.8125 0.4375 42.1036 176.5727 6059.0888 WOA (Mirjalili & Lewis, 2016) 0.8125 0.4375 42.0983 176.6390 6059.7410 Branch-bound (Sandgren, 1988) 1.1250 0.6250 47.7000 117.7010 8129.1036 GSA (Rashedi et al., 2009) 1.1250 0.6250 55.988659 84.452025 8538.8359 CDE (Huang et al., 2007) 0.812500 0.437500 42.098400 176.637600 6059.7340 GA3 (Coello Coello & Mezura Montes, 2002) 0.812500 0.437500 42.097400 176.654000 6059.9463 G-QPSO (Coelho, 2010) 0.812500 0.437500 42.098400 176.637200 6059.7208 Lagrangian multiplier (Kannan & Kramer, 1994) 1.125000 0.625000 58.291000 43.690000 7198.0428 Open in new tab Table 8: Comparison results of the PVD problem. Algorithm . Optimum variables . Optimum cost . . |${T_s}$| . |${T_h}$| . R . L . . ADNOLACO 0.8125 0.4375 42.09845 176.6366 6059.714 CPSO (He & Wang, 2007) 0.8125 0.4375 42.0912 176.7465 6061.0777 ACO (Kaveh & Talatahari, 2010) 0.8125 0.4375 42.1036 176.5727 6059.0888 WOA (Mirjalili & Lewis, 2016) 0.8125 0.4375 42.0983 176.6390 6059.7410 Branch-bound (Sandgren, 1988) 1.1250 0.6250 47.7000 117.7010 8129.1036 GSA (Rashedi et al., 2009) 1.1250 0.6250 55.988659 84.452025 8538.8359 CDE (Huang et al., 2007) 0.812500 0.437500 42.098400 176.637600 6059.7340 GA3 (Coello Coello & Mezura Montes, 2002) 0.812500 0.437500 42.097400 176.654000 6059.9463 G-QPSO (Coelho, 2010) 0.812500 0.437500 42.098400 176.637200 6059.7208 Lagrangian multiplier (Kannan & Kramer, 1994) 1.125000 0.625000 58.291000 43.690000 7198.0428 Algorithm . Optimum variables . Optimum cost . . |${T_s}$| . |${T_h}$| . R . L . . ADNOLACO 0.8125 0.4375 42.09845 176.6366 6059.714 CPSO (He & Wang, 2007) 0.8125 0.4375 42.0912 176.7465 6061.0777 ACO (Kaveh & Talatahari, 2010) 0.8125 0.4375 42.1036 176.5727 6059.0888 WOA (Mirjalili & Lewis, 2016) 0.8125 0.4375 42.0983 176.6390 6059.7410 Branch-bound (Sandgren, 1988) 1.1250 0.6250 47.7000 117.7010 8129.1036 GSA (Rashedi et al., 2009) 1.1250 0.6250 55.988659 84.452025 8538.8359 CDE (Huang et al., 2007) 0.812500 0.437500 42.098400 176.637600 6059.7340 GA3 (Coello Coello & Mezura Montes, 2002) 0.812500 0.437500 42.097400 176.654000 6059.9463 G-QPSO (Coelho, 2010) 0.812500 0.437500 42.098400 176.637200 6059.7208 Lagrangian multiplier (Kannan & Kramer, 1994) 1.125000 0.625000 58.291000 43.690000 7198.0428 Open in new tab 4.4. Hydrostatic thrust bearing design problem In this problem, it is desired to minimize the power loss during a hydrostatic thrust bearing that can withstand a specified load while providing axial support. There are four design variables: bearing step radius (R), recess radius (R0), oil viscosity (μ), and flow rate (Q). The mathematical model of this problem is as follows: $$\begin{eqnarray*} && {\rm Minimize:}\, {\rm{f}}\left( {\rm{x}} \right) = \frac{{{\rm{Q}}{{\rm{P}}_0}}}{{0.7}} + {{\rm{E}}_{\rm{f}}}, \\ && {\rm Subject\, to:} \, {{\rm{g}}_1}\left( {\rm{x}} \right) = \frac{{{\rm{\pi }}{{\rm{P}}_0}}}{2} \times \frac{{{{\rm{R}}^2} - {\rm{R}}_0^2}}{{{\rm{ln}}\left( {{\rm{R}}/{{\rm{R}}_0}} \right)}} - {{\rm{W}}_{\rm{s}}} \ge 0, \\ && {{\rm{g}}_2}\left( x \right) = {P_{\mathrm{ max}}} - {P_0} \ge 0, \\ && {{\rm{g}}_3}\left( x \right) = \Delta {T_{\mathrm{ max}}} - \Delta T \ge 0,\\ && {{\rm{g}}_4} = h - {h_{\mathrm{ min}}} \ge 0,\\ && {{\rm{g}}_5}\left( x \right) = R - {R_0} \ge 0,\\ \end{eqnarray*} $$ $$\begin{eqnarray*} && {{\rm{g}}_6}\left( x \right) = 0.001 - \gamma /g{P_0}\left( {Q/2\pi Rh} \right) \ge 0, \\ && {{\rm{g}}_7}\left( x \right) = 5000 - \frac{W}{{\pi \left( {{R^2} - R_0^2} \right)}} \ge 0, \end{eqnarray*} $$ where |${P_0} = \frac{{6\mu Q}}{{\pi {h^3}}}\ln (\frac{R}{{{R_0}}}),{E_f} = 9336Q\gamma C\Delta T,\,\Delta T = 2\left( {{{10}^{\rm{P}}} - 560} \right)\!,\,P = \frac{{\log \left( {\log \left( {8.122\ \times {{10}^6} + 0.8} \right)} \right) - {C_1}}}{n}$|⁠, |$h = {( {\frac{{2\pi N}}{{60}}} )^2}\frac{{2\pi \mu }}{{{E_f}}}( {\frac{{{R^4}}}{4} - \frac{{R_0^4}}{4}} )$|⁠, |${{\rm{C}}_1} = 10.04$|⁠, n = −3.55, Pmax = 1000, Ws = 101 000, |$\Delta {{\rm{T}}_{\mathrm{ max}}} = 50$|⁠, |${h_{\mathrm{ min}}} = 0.001$|⁠, g = 386.4, N = 750. $$\begin{equation*} 5 \le {D_e},{D_i} \le 15, 0.01 \le t \le 6, 0.05 \le h \le 0.5. \end{equation*} $$ Table 9 shows the results of the hydrostatic thrust bearing problem. From the values of optimum cast, we can see that the optimal solution of ADNOLACO is 19 504.3965. It performs better than PSO (Kennedy & Eberhart, 1995a), NDE (Wagdy, 2017), TLBO (Rao et al., 2011), SQP (Kentli & Sahbaz, 2014), and GASO (He et al., 2004) in this engineering problem. Compared with SQP and GASO, ADNOLACO has significantly improved on hydrostatic thrust bearing problems. We think that these tests are proper to show the key feature of the proposed ADNOLACO in terms of performance. However, it is better to apply ADNOLACO to more complex problems, such as bankruptcy prediction (Luo et al., 2018; Zhang et al., 2020) and image segmentation (Zhao et al., 2021c, d). Because ADNOLACO has strong search ability, it can be applied in many problems such as essay recommendation (Liang et al., 2021), drug discovery (Zhu et al., 2018; Li et al., 2020d), text clustering (Guan et al., 2020), image retrieval (Liu et al., 2020a), crowd sensing (Jiang et al., 2020b), and sentiment classification (Wang et al., 2018; Jiang et al., 2020a). Table 9: Comparison results of the HTBD problem. Algorithm . Optimum variables . Optimum cost . . R . R0 . μ . Q . . ADNOLACO 5.955822 5.389059 5.36E-06 2.269683 19504.3965 PSO (Kennedy & Eberhart, 1995a) 5.956868 5.389175 5.4021E-6 2.301546 19586.5788 NDE (Wagdy, 2017) 5.955781 5.389013 5.3586E-6 2.269656 19506.0090 TLBO (Rao et al., 2011) 5.955781 5.389013 5.3586E-6 2.269656 19505.3132 SQP (Kentli & Sahbaz, 2014) 5.955800 5.389040 8.6332E-6 8.000010 26114.5450 GASO (He et al., 2004) 6.271000 12.901000 5.6050E-6 2.938000 23403.4320 Algorithm . Optimum variables . Optimum cost . . R . R0 . μ . Q . . ADNOLACO 5.955822 5.389059 5.36E-06 2.269683 19504.3965 PSO (Kennedy & Eberhart, 1995a) 5.956868 5.389175 5.4021E-6 2.301546 19586.5788 NDE (Wagdy, 2017) 5.955781 5.389013 5.3586E-6 2.269656 19506.0090 TLBO (Rao et al., 2011) 5.955781 5.389013 5.3586E-6 2.269656 19505.3132 SQP (Kentli & Sahbaz, 2014) 5.955800 5.389040 8.6332E-6 8.000010 26114.5450 GASO (He et al., 2004) 6.271000 12.901000 5.6050E-6 2.938000 23403.4320 Open in new tab Table 9: Comparison results of the HTBD problem. Algorithm . Optimum variables . Optimum cost . . R . R0 . μ . Q . . ADNOLACO 5.955822 5.389059 5.36E-06 2.269683 19504.3965 PSO (Kennedy & Eberhart, 1995a) 5.956868 5.389175 5.4021E-6 2.301546 19586.5788 NDE (Wagdy, 2017) 5.955781 5.389013 5.3586E-6 2.269656 19506.0090 TLBO (Rao et al., 2011) 5.955781 5.389013 5.3586E-6 2.269656 19505.3132 SQP (Kentli & Sahbaz, 2014) 5.955800 5.389040 8.6332E-6 8.000010 26114.5450 GASO (He et al., 2004) 6.271000 12.901000 5.6050E-6 2.938000 23403.4320 Algorithm . Optimum variables . Optimum cost . . R . R0 . μ . Q . . ADNOLACO 5.955822 5.389059 5.36E-06 2.269683 19504.3965 PSO (Kennedy & Eberhart, 1995a) 5.956868 5.389175 5.4021E-6 2.301546 19586.5788 NDE (Wagdy, 2017) 5.955781 5.389013 5.3586E-6 2.269656 19506.0090 TLBO (Rao et al., 2011) 5.955781 5.389013 5.3586E-6 2.269656 19505.3132 SQP (Kentli & Sahbaz, 2014) 5.955800 5.389040 8.6332E-6 8.000010 26114.5450 GASO (He et al., 2004) 6.271000 12.901000 5.6050E-6 2.938000 23403.4320 Open in new tab 5. Discussion We first performed comparative experiments on the variants constructed by the ADN mechanism and the opposition-based learning mechanism based on the 30 test functions from IEEE CEC2017. Among them, ADNOLACO obtained the minimum mean on all-function problems the most times and outperformed the other three variations in the analysis results of the Wilcoxon signed-rank test and Friedman test. It further provides a detailed analysis of the impact of the two new mechanisms on ACOR from multiperspective, balance, and diversity, whose results also strongly suggest that the balance between exploration and exploitation of ADNOLACO is further optimized based on ACOR, enabling ADNOLACO to handle more complex problems. It is then analysed in several dimensions to compare the performance of ADNOLACO and ACOR more comprehensively, where the results fully demonstrate that ADNOLACO can find better results and have greater stability. It is also shown that ADNOLACO has a stronger ability to avoid falling into local optimum in the problem-solving process, which can help find a better solution to the problem. Last but not least, a comparison between ADNOLACO and some traditional basic algorithms and some improved variants of the algorithm is carried out. The results of Wilcoxon signed-rank test analysis, Friedman test analysis, and the related convergence curves all fully demonstrate that ADNOLACO obtains high-quality solutions and has a certain acceleration in convergence speed and a significant enhancement in the ability to jump out of local optimum. When solving the above engineering design problems, the simulation results also show that ADNOLACO can improve the accuracy of the calculation results and has some practical value in the practical application. Therefore, the proposed ADNOLACO is effective. 6. Conclusions and Future Works This paper presents an enhanced version of ACOR (ADNOLACO). In ADNOLACO, an opposition-based learning mechanism is introduced into ACOR, which effectively improves the convergence speed of ACOR. On this basis, the ADN mechanism was also introduced to further enhance the ability of ACOR to avoid getting trapped in local optimum. With these core advantages of ADNOLACO as a strong proof, we qualitatively analyse ADNOLACO and ACOR in detail based on 30 benchmark functions from IEEE CEC2017 and compare ADNOLACO with 9 traditional basic algorithms as well as 9 variants in experiments, respectively. It is well demonstrated that ADNOLACO accelerates the convergence speed and enhances its ability to escape from the local optimum. It is applied to deal with four engineering problems, where the simulation results also show that ADNOLACO can improve the accuracy of the calculation results. As a result, ADNOLACO can be considered as an excellent method in the problem-solving process, which not only has a stronger ability to avoid falling into local optimum but also has a more significant improvement in convergence speed as well as convergence accuracy, which helps to find a more optimal solution to the problem. However, since AND and OBL are used to improve the performance of ACOR, this undoubtedly leads to an increase in the time cost of ADNOLACO. For future work, we first use some high-performance computing or parallel computing to improve the efficiency of ADNOLACO when it is applied to solve real-world problems. Our next step is to successfully use the proposed ADNOLACO to deal with multi-objective and dynamic landscapes. ACKNOWLEDGEMENTS This work was supported in part by the Science and Technology Research Project of the Education Department of Jilin Province (JJKH20210886KJ), the Industrial Technology Research and Development Project of Jilin Development and Reform Commission (2021C045-4), college-enterprise cooperation project of the domestic visiting engineer of colleges (FG2020077), the National Natural Science Foundation of China (42164002, 62076185, andU1809209), and Guangxi Project of technology base and special talent (AD20325004). We acknowledge comments of the reviewers. 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Unimodal functions F1 Shifted and rotated Bent Cigar Function 100 F2 Shifted and rotated sum of different power function 200 F3 Shifted and rotated Zakharov function 300 Multimodal functions F4 Shifted and rotated Rosenbrocks function 400 F5 Shifted and rotated Rastrigins function 500 F6 Shifted and rotated expanded Scaffers F6 function 600 F7 Shifted and rotated Lunacek Bi_Rastrigin function 700 F8 Shifted and rotated non-continuous Rastrigins function 800 F9 Shifted and rotated Levy function 900 F10 Shifted and rotated Schwefels function 1000 Hybrid functions F11 Hybrid function 1 (N = 3) 1100 F12 Hybrid function 2 (N = 3) 1200 F13 Hybrid function 3 (N = 3) 1300 F14 Hybrid function 4 (N = 4) 1400 F15 Hybrid function 5 (N = 4) 1500 F16 Hybrid function 6 (N = 4) 1600 F17 Hybrid function 6 (N = 5) 1700 F18 Hybrid function 6 (N = 5) 1800 F19 Hybrid function 6 (N = 5) 1900 F20 Hybrid function 6 (N = 6) 2000 Composition functions F21 Composition function 1 (N = 3) 2100 F22 Composition function 2 (N = 3) 2200 F23 Composition function 3 (N = 4) 2300 F24 Composition function 4 (N = 4) 2400 F25 Composition function 5 (N = 5) 2500 F26 Composition function 6 (N = 5) 2600 F27 Composition function 7 (N = 6) 2700 F28 Composition function 8 (N = 6) 2800 F29 Composition function 9 (N = 3) 2900 F30 Composition function 10 (N = 3) 3000 Class . ID . Name of function . Optimum . Unimodal functions F1 Shifted and rotated Bent Cigar Function 100 F2 Shifted and rotated sum of different power function 200 F3 Shifted and rotated Zakharov function 300 Multimodal functions F4 Shifted and rotated Rosenbrocks function 400 F5 Shifted and rotated Rastrigins function 500 F6 Shifted and rotated expanded Scaffers F6 function 600 F7 Shifted and rotated Lunacek Bi_Rastrigin function 700 F8 Shifted and rotated non-continuous Rastrigins function 800 F9 Shifted and rotated Levy function 900 F10 Shifted and rotated Schwefels function 1000 Hybrid functions F11 Hybrid function 1 (N = 3) 1100 F12 Hybrid function 2 (N = 3) 1200 F13 Hybrid function 3 (N = 3) 1300 F14 Hybrid function 4 (N = 4) 1400 F15 Hybrid function 5 (N = 4) 1500 F16 Hybrid function 6 (N = 4) 1600 F17 Hybrid function 6 (N = 5) 1700 F18 Hybrid function 6 (N = 5) 1800 F19 Hybrid function 6 (N = 5) 1900 F20 Hybrid function 6 (N = 6) 2000 Composition functions F21 Composition function 1 (N = 3) 2100 F22 Composition function 2 (N = 3) 2200 F23 Composition function 3 (N = 4) 2300 F24 Composition function 4 (N = 4) 2400 F25 Composition function 5 (N = 5) 2500 F26 Composition function 6 (N = 5) 2600 F27 Composition function 7 (N = 6) 2700 F28 Composition function 8 (N = 6) 2800 F29 Composition function 9 (N = 3) 2900 F30 Composition function 10 (N = 3) 3000 Open in new tab Table A1: The description of 30 benchmark functions in IEEE CEC2017. Class . ID . Name of function . Optimum . Unimodal functions F1 Shifted and rotated Bent Cigar Function 100 F2 Shifted and rotated sum of different power function 200 F3 Shifted and rotated Zakharov function 300 Multimodal functions F4 Shifted and rotated Rosenbrocks function 400 F5 Shifted and rotated Rastrigins function 500 F6 Shifted and rotated expanded Scaffers F6 function 600 F7 Shifted and rotated Lunacek Bi_Rastrigin function 700 F8 Shifted and rotated non-continuous Rastrigins function 800 F9 Shifted and rotated Levy function 900 F10 Shifted and rotated Schwefels function 1000 Hybrid functions F11 Hybrid function 1 (N = 3) 1100 F12 Hybrid function 2 (N = 3) 1200 F13 Hybrid function 3 (N = 3) 1300 F14 Hybrid function 4 (N = 4) 1400 F15 Hybrid function 5 (N = 4) 1500 F16 Hybrid function 6 (N = 4) 1600 F17 Hybrid function 6 (N = 5) 1700 F18 Hybrid function 6 (N = 5) 1800 F19 Hybrid function 6 (N = 5) 1900 F20 Hybrid function 6 (N = 6) 2000 Composition functions F21 Composition function 1 (N = 3) 2100 F22 Composition function 2 (N = 3) 2200 F23 Composition function 3 (N = 4) 2300 F24 Composition function 4 (N = 4) 2400 F25 Composition function 5 (N = 5) 2500 F26 Composition function 6 (N = 5) 2600 F27 Composition function 7 (N = 6) 2700 F28 Composition function 8 (N = 6) 2800 F29 Composition function 9 (N = 3) 2900 F30 Composition function 10 (N = 3) 3000 Class . ID . Name of function . Optimum . Unimodal functions F1 Shifted and rotated Bent Cigar Function 100 F2 Shifted and rotated sum of different power function 200 F3 Shifted and rotated Zakharov function 300 Multimodal functions F4 Shifted and rotated Rosenbrocks function 400 F5 Shifted and rotated Rastrigins function 500 F6 Shifted and rotated expanded Scaffers F6 function 600 F7 Shifted and rotated Lunacek Bi_Rastrigin function 700 F8 Shifted and rotated non-continuous Rastrigins function 800 F9 Shifted and rotated Levy function 900 F10 Shifted and rotated Schwefels function 1000 Hybrid functions F11 Hybrid function 1 (N = 3) 1100 F12 Hybrid function 2 (N = 3) 1200 F13 Hybrid function 3 (N = 3) 1300 F14 Hybrid function 4 (N = 4) 1400 F15 Hybrid function 5 (N = 4) 1500 F16 Hybrid function 6 (N = 4) 1600 F17 Hybrid function 6 (N = 5) 1700 F18 Hybrid function 6 (N = 5) 1800 F19 Hybrid function 6 (N = 5) 1900 F20 Hybrid function 6 (N = 6) 2000 Composition functions F21 Composition function 1 (N = 3) 2100 F22 Composition function 2 (N = 3) 2200 F23 Composition function 3 (N = 4) 2300 F24 Composition function 4 (N = 4) 2400 F25 Composition function 5 (N = 5) 2500 F26 Composition function 6 (N = 5) 2600 F27 Composition function 7 (N = 6) 2700 F28 Composition function 8 (N = 6) 2800 F29 Composition function 9 (N = 3) 2900 F30 Composition function 10 (N = 3) 3000 Open in new tab Table A2: The mean, variance results of four different versions. Fun . Item . ADNOLACO . ADNACO . OLACO . ACOR . F1 AVG 5.8804E+03 3.2517E+04 9.0994E+03 3.6559E+10 STD 7.2135E+03 2.9885E+04 9.8480E+03 1.9418E+10 F2 AVG 1.0802E+116 1.7955E+109 1.6280E+93 1.3781E+135 STD 5.6463E+116 9.8345E+109 8.9170E+93 6.3144E+135 F3 AVG 4.7678E+05 7.0613E+05 3.8146E+05 5.8751E+05 STD 8.1277E+04 9.9654E+04 7.3297E+04 6.4950E+04 F4 AVG 6.8327E+02 7.0901E+02 6.4511E+02 3.3025E+03 STD 5.7147E+01 7.2739E+01 3.1376E+01 2.0537E+03 F5 AVG 1.0430E+03 1.1786E+03 1.5649E+03 1.7101E+03 STD 9.5454E+01 1.0805E+02 1.0042E+02 8.1522E+01 F6 AVG 6.2503E+02 6.4383E+02 6.0431E+02 6.2943E+02 STD 6.5266E+00 7.4399E+00 1.7931E+00 6.4825E+00 F7 AVG 1.8305E+03 2.9259E+03 2.0619E+03 3.3872E+03 STD 1.8614E+02 4.9442E+02 1.0584E+02 4.7214E+02 F8 AVG 1.3276E+03 1.5427E+03 1.8530E+03 1.9377E+03 STD 6.2002E+01 1.0489E+02 6.6736E+01 2.6581E+02 F9 AVG 2.2166E+04 3.3112E+04 2.4877E+04 6.3594E+04 STD 6.5266E+03 7.1783E+03 9.9400E+03 1.5493E+04 F10 AVG 1.7622E+04 1.6950E+04 3.1556E+04 3.1126E+04 STD 9.7627E+02 1.0932E+03 5.7915E+02 9.3182E+02 F11 AVG 1.1374E+04 5.4317E+03 3.3665E+03 3.1595E+04 STD 8.6937E+03 1.2160E+03 1.2500E+03 2.6310E+04 F12 AVG 1.0844E+07 6.2847E+07 6.4425E+06 3.2357E+09 STD 1.5154E+07 1.0392E+08 3.3050E+06 6.3494E+09 F13 AVG 2.1797E+04 8.7867E+04 3.0924E+04 9.8565E+07 STD 6.7811E+04 1.5309E+05 1.1381E+04 3.2475E+08 F14 AVG 1.2604E+06 6.2351E+05 3.9436E+05 8.5414E+05 STD 1.2809E+06 2.8617E+05 2.2704E+05 1.2096E+06 F15 AVG 2.4349E+04 4.9327E+04 1.5291E+04 5.2536E+06 STD 6.6491E+04 1.0829E+05 1.2305E+04 2.7008E+07 F16 AVG 6.7082E+03 6.5353E+03 8.5775E+03 6.7550E+03 STD 7.6173E+02 9.4581E+02 2.6496E+03 2.3778E+03 F17 AVG 5.8282E+03 5.7951E+03 6.9987E+03 5.5249E+03 STD 6.6815E+02 9.5864E+02 1.2329E+03 1.1137E+03 F18 AVG 6.1527E+06 3.4307E+06 5.1825E+06 4.6595E+06 STD 4.6870E+06 2.6473E+06 3.8428E+06 5.8861E+06 F19 AVG 9.0112E+03 2.1963E+04 8.4414E+03 2.6565E+05 STD 9.1626E+03 4.6682E+04 6.2517E+03 8.9798E+05 F20 AVG 5.8114E+03 5.6614E+03 7.1945E+03 6.4157E+03 STD 5.6755E+02 6.7680E+02 2.9625E+02 1.3631E+03 F21 AVG 2.8459E+03 3.0844E+03 3.3660E+03 3.5356E+03 STD 6.7707E+01 1.0948E+02 6.1961E+01 1.8651E+02 F22 AVG 1.9682E+04 1.9637E+04 3.3365E+04 3.3063E+04 STD 9.8425E+02 1.4300E+03 5.4351E+02 1.1540E+03 F23 AVG 3.3567E+03 3.3920E+03 3.3285E+03 3.4417E+03 STD 1.3248E+02 8.7774E+01 1.6372E+02 9.9906E+01 F24 AVG 3.8807E+03 3.9374E+03 4.1287E+03 3.9651E+03 STD 1.5648E+02 1.2192E+02 2.7605E+02 1.5153E+02 F25 AVG 3.3936E+03 3.4727E+03 3.2822E+03 6.4598E+03 STD 6.9075E+01 9.2034E+01 7.0805E+01 1.8884E+03 F26 AVG 1.1676E+04 1.3398E+04 1.5109E+04 1.4004E+04 STD 7.0195E+02 9.6018E+02 2.5944E+03 1.8773E+03 F27 AVG 3.4898E+03 3.5091E+03 3.5336E+03 3.5841E+03 STD 8.0246E+01 7.0181E+01 9.6086E+01 9.1512E+01 F28 AVG 7.4099E+03 1.2971E+04 6.7627E+03 1.5685E+04 STD 5.2517E+03 3.9349E+03 5.6697E+03 2.1550E+03 F29 AVG 7.2129E+03 7.0096E+03 5.8147E+03 6.8607E+03 STD 8.9349E+02 6.0912E+02 4.9444E+02 5.9056E+02 F30 AVG 1.4514E+04 1.5197E+04 3.2559E+05 2.5189E+07 STD 5.6140E+03 6.2925E+03 3.9977E+05 1.2869E+08 Fun . Item . ADNOLACO . ADNACO . OLACO . ACOR . F1 AVG 5.8804E+03 3.2517E+04 9.0994E+03 3.6559E+10 STD 7.2135E+03 2.9885E+04 9.8480E+03 1.9418E+10 F2 AVG 1.0802E+116 1.7955E+109 1.6280E+93 1.3781E+135 STD 5.6463E+116 9.8345E+109 8.9170E+93 6.3144E+135 F3 AVG 4.7678E+05 7.0613E+05 3.8146E+05 5.8751E+05 STD 8.1277E+04 9.9654E+04 7.3297E+04 6.4950E+04 F4 AVG 6.8327E+02 7.0901E+02 6.4511E+02 3.3025E+03 STD 5.7147E+01 7.2739E+01 3.1376E+01 2.0537E+03 F5 AVG 1.0430E+03 1.1786E+03 1.5649E+03 1.7101E+03 STD 9.5454E+01 1.0805E+02 1.0042E+02 8.1522E+01 F6 AVG 6.2503E+02 6.4383E+02 6.0431E+02 6.2943E+02 STD 6.5266E+00 7.4399E+00 1.7931E+00 6.4825E+00 F7 AVG 1.8305E+03 2.9259E+03 2.0619E+03 3.3872E+03 STD 1.8614E+02 4.9442E+02 1.0584E+02 4.7214E+02 F8 AVG 1.3276E+03 1.5427E+03 1.8530E+03 1.9377E+03 STD 6.2002E+01 1.0489E+02 6.6736E+01 2.6581E+02 F9 AVG 2.2166E+04 3.3112E+04 2.4877E+04 6.3594E+04 STD 6.5266E+03 7.1783E+03 9.9400E+03 1.5493E+04 F10 AVG 1.7622E+04 1.6950E+04 3.1556E+04 3.1126E+04 STD 9.7627E+02 1.0932E+03 5.7915E+02 9.3182E+02 F11 AVG 1.1374E+04 5.4317E+03 3.3665E+03 3.1595E+04 STD 8.6937E+03 1.2160E+03 1.2500E+03 2.6310E+04 F12 AVG 1.0844E+07 6.2847E+07 6.4425E+06 3.2357E+09 STD 1.5154E+07 1.0392E+08 3.3050E+06 6.3494E+09 F13 AVG 2.1797E+04 8.7867E+04 3.0924E+04 9.8565E+07 STD 6.7811E+04 1.5309E+05 1.1381E+04 3.2475E+08 F14 AVG 1.2604E+06 6.2351E+05 3.9436E+05 8.5414E+05 STD 1.2809E+06 2.8617E+05 2.2704E+05 1.2096E+06 F15 AVG 2.4349E+04 4.9327E+04 1.5291E+04 5.2536E+06 STD 6.6491E+04 1.0829E+05 1.2305E+04 2.7008E+07 F16 AVG 6.7082E+03 6.5353E+03 8.5775E+03 6.7550E+03 STD 7.6173E+02 9.4581E+02 2.6496E+03 2.3778E+03 F17 AVG 5.8282E+03 5.7951E+03 6.9987E+03 5.5249E+03 STD 6.6815E+02 9.5864E+02 1.2329E+03 1.1137E+03 F18 AVG 6.1527E+06 3.4307E+06 5.1825E+06 4.6595E+06 STD 4.6870E+06 2.6473E+06 3.8428E+06 5.8861E+06 F19 AVG 9.0112E+03 2.1963E+04 8.4414E+03 2.6565E+05 STD 9.1626E+03 4.6682E+04 6.2517E+03 8.9798E+05 F20 AVG 5.8114E+03 5.6614E+03 7.1945E+03 6.4157E+03 STD 5.6755E+02 6.7680E+02 2.9625E+02 1.3631E+03 F21 AVG 2.8459E+03 3.0844E+03 3.3660E+03 3.5356E+03 STD 6.7707E+01 1.0948E+02 6.1961E+01 1.8651E+02 F22 AVG 1.9682E+04 1.9637E+04 3.3365E+04 3.3063E+04 STD 9.8425E+02 1.4300E+03 5.4351E+02 1.1540E+03 F23 AVG 3.3567E+03 3.3920E+03 3.3285E+03 3.4417E+03 STD 1.3248E+02 8.7774E+01 1.6372E+02 9.9906E+01 F24 AVG 3.8807E+03 3.9374E+03 4.1287E+03 3.9651E+03 STD 1.5648E+02 1.2192E+02 2.7605E+02 1.5153E+02 F25 AVG 3.3936E+03 3.4727E+03 3.2822E+03 6.4598E+03 STD 6.9075E+01 9.2034E+01 7.0805E+01 1.8884E+03 F26 AVG 1.1676E+04 1.3398E+04 1.5109E+04 1.4004E+04 STD 7.0195E+02 9.6018E+02 2.5944E+03 1.8773E+03 F27 AVG 3.4898E+03 3.5091E+03 3.5336E+03 3.5841E+03 STD 8.0246E+01 7.0181E+01 9.6086E+01 9.1512E+01 F28 AVG 7.4099E+03 1.2971E+04 6.7627E+03 1.5685E+04 STD 5.2517E+03 3.9349E+03 5.6697E+03 2.1550E+03 F29 AVG 7.2129E+03 7.0096E+03 5.8147E+03 6.8607E+03 STD 8.9349E+02 6.0912E+02 4.9444E+02 5.9056E+02 F30 AVG 1.4514E+04 1.5197E+04 3.2559E+05 2.5189E+07 STD 5.6140E+03 6.2925E+03 3.9977E+05 1.2869E+08 Open in new tab Table A2: The mean, variance results of four different versions. Fun . Item . ADNOLACO . ADNACO . OLACO . ACOR . F1 AVG 5.8804E+03 3.2517E+04 9.0994E+03 3.6559E+10 STD 7.2135E+03 2.9885E+04 9.8480E+03 1.9418E+10 F2 AVG 1.0802E+116 1.7955E+109 1.6280E+93 1.3781E+135 STD 5.6463E+116 9.8345E+109 8.9170E+93 6.3144E+135 F3 AVG 4.7678E+05 7.0613E+05 3.8146E+05 5.8751E+05 STD 8.1277E+04 9.9654E+04 7.3297E+04 6.4950E+04 F4 AVG 6.8327E+02 7.0901E+02 6.4511E+02 3.3025E+03 STD 5.7147E+01 7.2739E+01 3.1376E+01 2.0537E+03 F5 AVG 1.0430E+03 1.1786E+03 1.5649E+03 1.7101E+03 STD 9.5454E+01 1.0805E+02 1.0042E+02 8.1522E+01 F6 AVG 6.2503E+02 6.4383E+02 6.0431E+02 6.2943E+02 STD 6.5266E+00 7.4399E+00 1.7931E+00 6.4825E+00 F7 AVG 1.8305E+03 2.9259E+03 2.0619E+03 3.3872E+03 STD 1.8614E+02 4.9442E+02 1.0584E+02 4.7214E+02 F8 AVG 1.3276E+03 1.5427E+03 1.8530E+03 1.9377E+03 STD 6.2002E+01 1.0489E+02 6.6736E+01 2.6581E+02 F9 AVG 2.2166E+04 3.3112E+04 2.4877E+04 6.3594E+04 STD 6.5266E+03 7.1783E+03 9.9400E+03 1.5493E+04 F10 AVG 1.7622E+04 1.6950E+04 3.1556E+04 3.1126E+04 STD 9.7627E+02 1.0932E+03 5.7915E+02 9.3182E+02 F11 AVG 1.1374E+04 5.4317E+03 3.3665E+03 3.1595E+04 STD 8.6937E+03 1.2160E+03 1.2500E+03 2.6310E+04 F12 AVG 1.0844E+07 6.2847E+07 6.4425E+06 3.2357E+09 STD 1.5154E+07 1.0392E+08 3.3050E+06 6.3494E+09 F13 AVG 2.1797E+04 8.7867E+04 3.0924E+04 9.8565E+07 STD 6.7811E+04 1.5309E+05 1.1381E+04 3.2475E+08 F14 AVG 1.2604E+06 6.2351E+05 3.9436E+05 8.5414E+05 STD 1.2809E+06 2.8617E+05 2.2704E+05 1.2096E+06 F15 AVG 2.4349E+04 4.9327E+04 1.5291E+04 5.2536E+06 STD 6.6491E+04 1.0829E+05 1.2305E+04 2.7008E+07 F16 AVG 6.7082E+03 6.5353E+03 8.5775E+03 6.7550E+03 STD 7.6173E+02 9.4581E+02 2.6496E+03 2.3778E+03 F17 AVG 5.8282E+03 5.7951E+03 6.9987E+03 5.5249E+03 STD 6.6815E+02 9.5864E+02 1.2329E+03 1.1137E+03 F18 AVG 6.1527E+06 3.4307E+06 5.1825E+06 4.6595E+06 STD 4.6870E+06 2.6473E+06 3.8428E+06 5.8861E+06 F19 AVG 9.0112E+03 2.1963E+04 8.4414E+03 2.6565E+05 STD 9.1626E+03 4.6682E+04 6.2517E+03 8.9798E+05 F20 AVG 5.8114E+03 5.6614E+03 7.1945E+03 6.4157E+03 STD 5.6755E+02 6.7680E+02 2.9625E+02 1.3631E+03 F21 AVG 2.8459E+03 3.0844E+03 3.3660E+03 3.5356E+03 STD 6.7707E+01 1.0948E+02 6.1961E+01 1.8651E+02 F22 AVG 1.9682E+04 1.9637E+04 3.3365E+04 3.3063E+04 STD 9.8425E+02 1.4300E+03 5.4351E+02 1.1540E+03 F23 AVG 3.3567E+03 3.3920E+03 3.3285E+03 3.4417E+03 STD 1.3248E+02 8.7774E+01 1.6372E+02 9.9906E+01 F24 AVG 3.8807E+03 3.9374E+03 4.1287E+03 3.9651E+03 STD 1.5648E+02 1.2192E+02 2.7605E+02 1.5153E+02 F25 AVG 3.3936E+03 3.4727E+03 3.2822E+03 6.4598E+03 STD 6.9075E+01 9.2034E+01 7.0805E+01 1.8884E+03 F26 AVG 1.1676E+04 1.3398E+04 1.5109E+04 1.4004E+04 STD 7.0195E+02 9.6018E+02 2.5944E+03 1.8773E+03 F27 AVG 3.4898E+03 3.5091E+03 3.5336E+03 3.5841E+03 STD 8.0246E+01 7.0181E+01 9.6086E+01 9.1512E+01 F28 AVG 7.4099E+03 1.2971E+04 6.7627E+03 1.5685E+04 STD 5.2517E+03 3.9349E+03 5.6697E+03 2.1550E+03 F29 AVG 7.2129E+03 7.0096E+03 5.8147E+03 6.8607E+03 STD 8.9349E+02 6.0912E+02 4.9444E+02 5.9056E+02 F30 AVG 1.4514E+04 1.5197E+04 3.2559E+05 2.5189E+07 STD 5.6140E+03 6.2925E+03 3.9977E+05 1.2869E+08 Fun . Item . ADNOLACO . ADNACO . OLACO . ACOR . F1 AVG 5.8804E+03 3.2517E+04 9.0994E+03 3.6559E+10 STD 7.2135E+03 2.9885E+04 9.8480E+03 1.9418E+10 F2 AVG 1.0802E+116 1.7955E+109 1.6280E+93 1.3781E+135 STD 5.6463E+116 9.8345E+109 8.9170E+93 6.3144E+135 F3 AVG 4.7678E+05 7.0613E+05 3.8146E+05 5.8751E+05 STD 8.1277E+04 9.9654E+04 7.3297E+04 6.4950E+04 F4 AVG 6.8327E+02 7.0901E+02 6.4511E+02 3.3025E+03 STD 5.7147E+01 7.2739E+01 3.1376E+01 2.0537E+03 F5 AVG 1.0430E+03 1.1786E+03 1.5649E+03 1.7101E+03 STD 9.5454E+01 1.0805E+02 1.0042E+02 8.1522E+01 F6 AVG 6.2503E+02 6.4383E+02 6.0431E+02 6.2943E+02 STD 6.5266E+00 7.4399E+00 1.7931E+00 6.4825E+00 F7 AVG 1.8305E+03 2.9259E+03 2.0619E+03 3.3872E+03 STD 1.8614E+02 4.9442E+02 1.0584E+02 4.7214E+02 F8 AVG 1.3276E+03 1.5427E+03 1.8530E+03 1.9377E+03 STD 6.2002E+01 1.0489E+02 6.6736E+01 2.6581E+02 F9 AVG 2.2166E+04 3.3112E+04 2.4877E+04 6.3594E+04 STD 6.5266E+03 7.1783E+03 9.9400E+03 1.5493E+04 F10 AVG 1.7622E+04 1.6950E+04 3.1556E+04 3.1126E+04 STD 9.7627E+02 1.0932E+03 5.7915E+02 9.3182E+02 F11 AVG 1.1374E+04 5.4317E+03 3.3665E+03 3.1595E+04 STD 8.6937E+03 1.2160E+03 1.2500E+03 2.6310E+04 F12 AVG 1.0844E+07 6.2847E+07 6.4425E+06 3.2357E+09 STD 1.5154E+07 1.0392E+08 3.3050E+06 6.3494E+09 F13 AVG 2.1797E+04 8.7867E+04 3.0924E+04 9.8565E+07 STD 6.7811E+04 1.5309E+05 1.1381E+04 3.2475E+08 F14 AVG 1.2604E+06 6.2351E+05 3.9436E+05 8.5414E+05 STD 1.2809E+06 2.8617E+05 2.2704E+05 1.2096E+06 F15 AVG 2.4349E+04 4.9327E+04 1.5291E+04 5.2536E+06 STD 6.6491E+04 1.0829E+05 1.2305E+04 2.7008E+07 F16 AVG 6.7082E+03 6.5353E+03 8.5775E+03 6.7550E+03 STD 7.6173E+02 9.4581E+02 2.6496E+03 2.3778E+03 F17 AVG 5.8282E+03 5.7951E+03 6.9987E+03 5.5249E+03 STD 6.6815E+02 9.5864E+02 1.2329E+03 1.1137E+03 F18 AVG 6.1527E+06 3.4307E+06 5.1825E+06 4.6595E+06 STD 4.6870E+06 2.6473E+06 3.8428E+06 5.8861E+06 F19 AVG 9.0112E+03 2.1963E+04 8.4414E+03 2.6565E+05 STD 9.1626E+03 4.6682E+04 6.2517E+03 8.9798E+05 F20 AVG 5.8114E+03 5.6614E+03 7.1945E+03 6.4157E+03 STD 5.6755E+02 6.7680E+02 2.9625E+02 1.3631E+03 F21 AVG 2.8459E+03 3.0844E+03 3.3660E+03 3.5356E+03 STD 6.7707E+01 1.0948E+02 6.1961E+01 1.8651E+02 F22 AVG 1.9682E+04 1.9637E+04 3.3365E+04 3.3063E+04 STD 9.8425E+02 1.4300E+03 5.4351E+02 1.1540E+03 F23 AVG 3.3567E+03 3.3920E+03 3.3285E+03 3.4417E+03 STD 1.3248E+02 8.7774E+01 1.6372E+02 9.9906E+01 F24 AVG 3.8807E+03 3.9374E+03 4.1287E+03 3.9651E+03 STD 1.5648E+02 1.2192E+02 2.7605E+02 1.5153E+02 F25 AVG 3.3936E+03 3.4727E+03 3.2822E+03 6.4598E+03 STD 6.9075E+01 9.2034E+01 7.0805E+01 1.8884E+03 F26 AVG 1.1676E+04 1.3398E+04 1.5109E+04 1.4004E+04 STD 7.0195E+02 9.6018E+02 2.5944E+03 1.8773E+03 F27 AVG 3.4898E+03 3.5091E+03 3.5336E+03 3.5841E+03 STD 8.0246E+01 7.0181E+01 9.6086E+01 9.1512E+01 F28 AVG 7.4099E+03 1.2971E+04 6.7627E+03 1.5685E+04 STD 5.2517E+03 3.9349E+03 5.6697E+03 2.1550E+03 F29 AVG 7.2129E+03 7.0096E+03 5.8147E+03 6.8607E+03 STD 8.9349E+02 6.0912E+02 4.9444E+02 5.9056E+02 F30 AVG 1.4514E+04 1.5197E+04 3.2559E+05 2.5189E+07 STD 5.6140E+03 6.2925E+03 3.9977E+05 1.2869E+08 Open in new tab Table A3: The results of the corresponding mean, variance at different dimensions. . . 30 . 50 . 100 . Fun . Item . ADNOLACO . ACOR . ADNOLACO . ACOR . ADNOLACO . ACOR . F1 AVG 5.3769E+03 3.1512E+10 5.4398E+03 3.3528E+10 4.8859E+03 3.6756E+10 STD 6.8228E+03 1.5493E+10 6.9137E+03 1.6611E+10 6.5077E+03 1.7364E+10 F2 AVG 3.0260E+125 2.0172E+132 6.4262E+102 2.5287E+125 1.8456E+92 1.8554E+130 STD 1.6574E+126 1.0584E+133 3.5197E+103 1.3081E+126 9.7349E+92 7.9161E+130 F3 AVG 5.1010E+05 6.1926E+05 3.5156E+05 4.8201E+05 2.5957E+05 3.7165E+05 STD 1.0809E+05 8.7011E+04 7.8100E+04 6.9145E+04 5.8467E+04 7.2293E+04 F4 AVG 7.0876E+02 4.2138E+03 6.7278E+02 3.8467E+03 6.3768E+02 2.6961E+03 STD 5.0661E+01 3.5173E+03 6.2406E+01 2.3446E+03 5.1908E+01 1.8198E+03 F5 AVG 1.0513E+03 1.6009E+03 9.8216E+02 1.5904E+03 1.0019E+03 1.3741E+03 STD 7.6050E+01 2.3847E+02 7.0859E+01 2.5200E+02 8.3166E+01 3.1987E+02 F6 AVG 6.2533E+02 6.2846E+02 6.2717E+02 6.2691E+02 6.1577E+02 6.3026E+02 STD 6.3922E+00 5.6208E+00 7.1990E+00 5.6938E+00 6.6007E+00 5.5057E+00 F7 AVG 1.8366E+03 3.4527E+03 1.8742E+03 3.2140E+03 1.7876E+03 3.2280E+03 STD 1.8976E+02 5.2435E+02 2.0622E+02 4.3118E+02 1.6199E+02 5.1687E+02 F8 AVG 1.3608E+03 1.9655E+03 1.2909E+03 1.8178E+03 1.2435E+03 1.7525E+03 STD 8.3111E+01 2.3081E+02 5.7730E+01 3.0217E+02 6.9860E+01 3.2510E+02 F9 AVG 2.0845E+04 7.2321E+04 2.1396E+04 6.5506E+04 2.3060E+04 5.7308E+04 STD 5.4813E+03 1.8804E+04 7.0624E+03 1.3421E+04 6.0311E+03 1.7249E+04 F10 AVG 1.7467E+04 3.0255E+04 1.7207E+04 3.0446E+04 1.7419E+04 2.9410E+04 STD 1.5611E+03 4.0803E+03 1.4985E+03 3.8166E+03 1.3249E+03 4.3484E+03 F11 AVG 1.0933E+04 3.3929E+04 3.7730E+03 2.3301E+04 2.2248E+03 2.2783E+04 STD 5.8127E+03 3.4091E+04 1.6572E+03 1.5948E+04 2.7826E+02 1.5694E+04 F12 AVG 1.0594E+07 3.1872E+09 7.3848E+06 2.3337E+09 2.2982E+06 2.5920E+09 STD 1.8568E+07 6.6198E+09 9.2579E+06 3.4348E+09 1.4950E+06 2.8680E+09 F13 AVG 8.5805E+03 1.5665E+08 8.3469E+03 9.4123E+07 3.8380E+04 1.4334E+07 STD 8.4003E+03 4.6667E+08 7.9527E+03 3.6857E+08 9.4271E+04 5.2363E+07 F14 AVG 1.3498E+06 1.2407E+06 4.9768E+05 6.6531E+05 2.9483E+05 6.4348E+05 STD 1.9222E+06 1.4870E+06 5.8327E+05 8.7877E+05 3.3045E+05 6.2793E+05 F15 AVG 1.9014E+04 3.0051E+04 1.6192E+04 2.1751E+04 6.0500E+03 1.4081E+07 STD 6.0635E+04 2.1252E+04 5.1332E+04 1.6548E+04 4.6198E+03 7.5293E+07 F16 AVG 6.7034E+03 6.6281E+03 6.4800E+03 5.8567E+03 5.8343E+03 5.5429E+03 STD 6.0943E+02 2.1839E+03 8.4500E+02 1.4591E+03 7.9033E+02 1.3581E+03 F17 AVG 6.0181E+03 5.9799E+03 5.8787E+03 5.9098E+03 5.8617E+03 5.6103E+03 STD 7.2415E+02 1.4703E+03 6.0876E+02 1.3204E+03 6.8055E+02 1.4254E+03 F18 AVG 3.8191E+06 3.6316E+06 2.8595E+06 3.1456E+06 2.4034E+06 1.5561E+06 STD 2.9075E+06 2.2517E+06 1.5036E+06 4.1573E+06 1.2085E+06 1.6286E+06 F19 AVG 1.1979E+04 1.7927E+07 7.8780E+03 3.0047E+06 8.9584E+03 1.0777E+08 STD 2.8525E+04 9.4121E+07 6.9557E+03 1.4505E+07 8.7315E+03 5.8933E+08 F20 AVG 5.8266E+03 6.8325E+03 5.8701E+03 6.2133E+03 5.7647E+03 6.2865E+03 STD 6.3104E+02 1.2465E+03 5.4657E+02 1.4264E+03 6.7887E+02 1.3749E+03 F21 AVG 2.8462E+03 3.4812E+03 2.7755E+03 3.3808E+03 2.7796E+03 3.2107E+03 STD 7.4006E+01 2.3994E+02 7.1333E+01 2.7671E+02 6.9342E+01 2.8003E+02 F22 AVG 1.9525E+04 3.2308E+04 1.9356E+04 3.2553E+04 1.9152E+04 3.1679E+04 STD 1.2408E+03 3.3278E+03 1.3965E+03 1.4109E+03 1.3829E+03 2.9706E+03 F23 AVG 3.3840E+03 3.4406E+03 3.3531E+03 3.4256E+03 3.3292E+03 3.4515E+03 STD 1.1361E+02 1.1926E+02 1.0078E+02 9.2607E+01 7.8729E+01 7.8265E+01 F24 AVG 3.8528E+03 4.0098E+03 3.8268E+03 3.9217E+03 3.8373E+03 3.9658E+03 STD 1.0762E+02 1.3887E+02 1.2450E+02 1.1043E+02 1.4395E+02 2.0020E+02 F25 AVG 3.3924E+03 5.8749E+03 3.3462E+03 5.8191E+03 3.2732E+03 6.0467E+03 STD 8.6318E+01 1.6087E+03 6.8295E+01 1.5182E+03 5.9055E+01 1.9756E+03 F26 AVG 1.1587E+04 1.3924E+04 1.1066E+04 1.3782E+04 1.0858E+04 1.3483E+04 STD 9.2620E+02 1.9010E+03 9.9484E+02 1.6482E+03 9.9262E+02 1.1809E+03 F27 AVG 3.4982E+03 3.5886E+03 3.4975E+03 3.5854E+03 3.4961E+03 3.5702E+03 STD 7.1953E+01 8.2701E+01 8.7250E+01 8.1505E+01 4.8120E+01 7.4364E+01 F28 AVG 4.9069E+03 1.5405E+04 6.0291E+03 1.6216E+04 4.5738E+03 1.5069E+04 STD 3.7078E+03 1.6134E+03 4.3829E+03 9.1317E+02 2.7421E+03 2.4387E+03 F29 AVG 7.1249E+03 7.0248E+03 6.7150E+03 6.8557E+03 6.6273E+03 7.2768E+03 STD 1.0102E+03 7.0583E+02 9.2889E+02 7.1487E+02 6.1201E+02 7.6661E+02 F30 AVG 1.3616E+04 2.3084E+06 1.2601E+04 1.2863E+08 1.1419E+04 7.8237E+06 STD 5.3080E+03 2.6870E+06 4.9197E+03 3.4049E+08 6.2313E+03 2.7716E+07 . . 30 . 50 . 100 . Fun . Item . ADNOLACO . ACOR . ADNOLACO . ACOR . ADNOLACO . ACOR . F1 AVG 5.3769E+03 3.1512E+10 5.4398E+03 3.3528E+10 4.8859E+03 3.6756E+10 STD 6.8228E+03 1.5493E+10 6.9137E+03 1.6611E+10 6.5077E+03 1.7364E+10 F2 AVG 3.0260E+125 2.0172E+132 6.4262E+102 2.5287E+125 1.8456E+92 1.8554E+130 STD 1.6574E+126 1.0584E+133 3.5197E+103 1.3081E+126 9.7349E+92 7.9161E+130 F3 AVG 5.1010E+05 6.1926E+05 3.5156E+05 4.8201E+05 2.5957E+05 3.7165E+05 STD 1.0809E+05 8.7011E+04 7.8100E+04 6.9145E+04 5.8467E+04 7.2293E+04 F4 AVG 7.0876E+02 4.2138E+03 6.7278E+02 3.8467E+03 6.3768E+02 2.6961E+03 STD 5.0661E+01 3.5173E+03 6.2406E+01 2.3446E+03 5.1908E+01 1.8198E+03 F5 AVG 1.0513E+03 1.6009E+03 9.8216E+02 1.5904E+03 1.0019E+03 1.3741E+03 STD 7.6050E+01 2.3847E+02 7.0859E+01 2.5200E+02 8.3166E+01 3.1987E+02 F6 AVG 6.2533E+02 6.2846E+02 6.2717E+02 6.2691E+02 6.1577E+02 6.3026E+02 STD 6.3922E+00 5.6208E+00 7.1990E+00 5.6938E+00 6.6007E+00 5.5057E+00 F7 AVG 1.8366E+03 3.4527E+03 1.8742E+03 3.2140E+03 1.7876E+03 3.2280E+03 STD 1.8976E+02 5.2435E+02 2.0622E+02 4.3118E+02 1.6199E+02 5.1687E+02 F8 AVG 1.3608E+03 1.9655E+03 1.2909E+03 1.8178E+03 1.2435E+03 1.7525E+03 STD 8.3111E+01 2.3081E+02 5.7730E+01 3.0217E+02 6.9860E+01 3.2510E+02 F9 AVG 2.0845E+04 7.2321E+04 2.1396E+04 6.5506E+04 2.3060E+04 5.7308E+04 STD 5.4813E+03 1.8804E+04 7.0624E+03 1.3421E+04 6.0311E+03 1.7249E+04 F10 AVG 1.7467E+04 3.0255E+04 1.7207E+04 3.0446E+04 1.7419E+04 2.9410E+04 STD 1.5611E+03 4.0803E+03 1.4985E+03 3.8166E+03 1.3249E+03 4.3484E+03 F11 AVG 1.0933E+04 3.3929E+04 3.7730E+03 2.3301E+04 2.2248E+03 2.2783E+04 STD 5.8127E+03 3.4091E+04 1.6572E+03 1.5948E+04 2.7826E+02 1.5694E+04 F12 AVG 1.0594E+07 3.1872E+09 7.3848E+06 2.3337E+09 2.2982E+06 2.5920E+09 STD 1.8568E+07 6.6198E+09 9.2579E+06 3.4348E+09 1.4950E+06 2.8680E+09 F13 AVG 8.5805E+03 1.5665E+08 8.3469E+03 9.4123E+07 3.8380E+04 1.4334E+07 STD 8.4003E+03 4.6667E+08 7.9527E+03 3.6857E+08 9.4271E+04 5.2363E+07 F14 AVG 1.3498E+06 1.2407E+06 4.9768E+05 6.6531E+05 2.9483E+05 6.4348E+05 STD 1.9222E+06 1.4870E+06 5.8327E+05 8.7877E+05 3.3045E+05 6.2793E+05 F15 AVG 1.9014E+04 3.0051E+04 1.6192E+04 2.1751E+04 6.0500E+03 1.4081E+07 STD 6.0635E+04 2.1252E+04 5.1332E+04 1.6548E+04 4.6198E+03 7.5293E+07 F16 AVG 6.7034E+03 6.6281E+03 6.4800E+03 5.8567E+03 5.8343E+03 5.5429E+03 STD 6.0943E+02 2.1839E+03 8.4500E+02 1.4591E+03 7.9033E+02 1.3581E+03 F17 AVG 6.0181E+03 5.9799E+03 5.8787E+03 5.9098E+03 5.8617E+03 5.6103E+03 STD 7.2415E+02 1.4703E+03 6.0876E+02 1.3204E+03 6.8055E+02 1.4254E+03 F18 AVG 3.8191E+06 3.6316E+06 2.8595E+06 3.1456E+06 2.4034E+06 1.5561E+06 STD 2.9075E+06 2.2517E+06 1.5036E+06 4.1573E+06 1.2085E+06 1.6286E+06 F19 AVG 1.1979E+04 1.7927E+07 7.8780E+03 3.0047E+06 8.9584E+03 1.0777E+08 STD 2.8525E+04 9.4121E+07 6.9557E+03 1.4505E+07 8.7315E+03 5.8933E+08 F20 AVG 5.8266E+03 6.8325E+03 5.8701E+03 6.2133E+03 5.7647E+03 6.2865E+03 STD 6.3104E+02 1.2465E+03 5.4657E+02 1.4264E+03 6.7887E+02 1.3749E+03 F21 AVG 2.8462E+03 3.4812E+03 2.7755E+03 3.3808E+03 2.7796E+03 3.2107E+03 STD 7.4006E+01 2.3994E+02 7.1333E+01 2.7671E+02 6.9342E+01 2.8003E+02 F22 AVG 1.9525E+04 3.2308E+04 1.9356E+04 3.2553E+04 1.9152E+04 3.1679E+04 STD 1.2408E+03 3.3278E+03 1.3965E+03 1.4109E+03 1.3829E+03 2.9706E+03 F23 AVG 3.3840E+03 3.4406E+03 3.3531E+03 3.4256E+03 3.3292E+03 3.4515E+03 STD 1.1361E+02 1.1926E+02 1.0078E+02 9.2607E+01 7.8729E+01 7.8265E+01 F24 AVG 3.8528E+03 4.0098E+03 3.8268E+03 3.9217E+03 3.8373E+03 3.9658E+03 STD 1.0762E+02 1.3887E+02 1.2450E+02 1.1043E+02 1.4395E+02 2.0020E+02 F25 AVG 3.3924E+03 5.8749E+03 3.3462E+03 5.8191E+03 3.2732E+03 6.0467E+03 STD 8.6318E+01 1.6087E+03 6.8295E+01 1.5182E+03 5.9055E+01 1.9756E+03 F26 AVG 1.1587E+04 1.3924E+04 1.1066E+04 1.3782E+04 1.0858E+04 1.3483E+04 STD 9.2620E+02 1.9010E+03 9.9484E+02 1.6482E+03 9.9262E+02 1.1809E+03 F27 AVG 3.4982E+03 3.5886E+03 3.4975E+03 3.5854E+03 3.4961E+03 3.5702E+03 STD 7.1953E+01 8.2701E+01 8.7250E+01 8.1505E+01 4.8120E+01 7.4364E+01 F28 AVG 4.9069E+03 1.5405E+04 6.0291E+03 1.6216E+04 4.5738E+03 1.5069E+04 STD 3.7078E+03 1.6134E+03 4.3829E+03 9.1317E+02 2.7421E+03 2.4387E+03 F29 AVG 7.1249E+03 7.0248E+03 6.7150E+03 6.8557E+03 6.6273E+03 7.2768E+03 STD 1.0102E+03 7.0583E+02 9.2889E+02 7.1487E+02 6.1201E+02 7.6661E+02 F30 AVG 1.3616E+04 2.3084E+06 1.2601E+04 1.2863E+08 1.1419E+04 7.8237E+06 STD 5.3080E+03 2.6870E+06 4.9197E+03 3.4049E+08 6.2313E+03 2.7716E+07 Open in new tab Table A3: The results of the corresponding mean, variance at different dimensions. . . 30 . 50 . 100 . Fun . Item . ADNOLACO . ACOR . ADNOLACO . ACOR . ADNOLACO . ACOR . F1 AVG 5.3769E+03 3.1512E+10 5.4398E+03 3.3528E+10 4.8859E+03 3.6756E+10 STD 6.8228E+03 1.5493E+10 6.9137E+03 1.6611E+10 6.5077E+03 1.7364E+10 F2 AVG 3.0260E+125 2.0172E+132 6.4262E+102 2.5287E+125 1.8456E+92 1.8554E+130 STD 1.6574E+126 1.0584E+133 3.5197E+103 1.3081E+126 9.7349E+92 7.9161E+130 F3 AVG 5.1010E+05 6.1926E+05 3.5156E+05 4.8201E+05 2.5957E+05 3.7165E+05 STD 1.0809E+05 8.7011E+04 7.8100E+04 6.9145E+04 5.8467E+04 7.2293E+04 F4 AVG 7.0876E+02 4.2138E+03 6.7278E+02 3.8467E+03 6.3768E+02 2.6961E+03 STD 5.0661E+01 3.5173E+03 6.2406E+01 2.3446E+03 5.1908E+01 1.8198E+03 F5 AVG 1.0513E+03 1.6009E+03 9.8216E+02 1.5904E+03 1.0019E+03 1.3741E+03 STD 7.6050E+01 2.3847E+02 7.0859E+01 2.5200E+02 8.3166E+01 3.1987E+02 F6 AVG 6.2533E+02 6.2846E+02 6.2717E+02 6.2691E+02 6.1577E+02 6.3026E+02 STD 6.3922E+00 5.6208E+00 7.1990E+00 5.6938E+00 6.6007E+00 5.5057E+00 F7 AVG 1.8366E+03 3.4527E+03 1.8742E+03 3.2140E+03 1.7876E+03 3.2280E+03 STD 1.8976E+02 5.2435E+02 2.0622E+02 4.3118E+02 1.6199E+02 5.1687E+02 F8 AVG 1.3608E+03 1.9655E+03 1.2909E+03 1.8178E+03 1.2435E+03 1.7525E+03 STD 8.3111E+01 2.3081E+02 5.7730E+01 3.0217E+02 6.9860E+01 3.2510E+02 F9 AVG 2.0845E+04 7.2321E+04 2.1396E+04 6.5506E+04 2.3060E+04 5.7308E+04 STD 5.4813E+03 1.8804E+04 7.0624E+03 1.3421E+04 6.0311E+03 1.7249E+04 F10 AVG 1.7467E+04 3.0255E+04 1.7207E+04 3.0446E+04 1.7419E+04 2.9410E+04 STD 1.5611E+03 4.0803E+03 1.4985E+03 3.8166E+03 1.3249E+03 4.3484E+03 F11 AVG 1.0933E+04 3.3929E+04 3.7730E+03 2.3301E+04 2.2248E+03 2.2783E+04 STD 5.8127E+03 3.4091E+04 1.6572E+03 1.5948E+04 2.7826E+02 1.5694E+04 F12 AVG 1.0594E+07 3.1872E+09 7.3848E+06 2.3337E+09 2.2982E+06 2.5920E+09 STD 1.8568E+07 6.6198E+09 9.2579E+06 3.4348E+09 1.4950E+06 2.8680E+09 F13 AVG 8.5805E+03 1.5665E+08 8.3469E+03 9.4123E+07 3.8380E+04 1.4334E+07 STD 8.4003E+03 4.6667E+08 7.9527E+03 3.6857E+08 9.4271E+04 5.2363E+07 F14 AVG 1.3498E+06 1.2407E+06 4.9768E+05 6.6531E+05 2.9483E+05 6.4348E+05 STD 1.9222E+06 1.4870E+06 5.8327E+05 8.7877E+05 3.3045E+05 6.2793E+05 F15 AVG 1.9014E+04 3.0051E+04 1.6192E+04 2.1751E+04 6.0500E+03 1.4081E+07 STD 6.0635E+04 2.1252E+04 5.1332E+04 1.6548E+04 4.6198E+03 7.5293E+07 F16 AVG 6.7034E+03 6.6281E+03 6.4800E+03 5.8567E+03 5.8343E+03 5.5429E+03 STD 6.0943E+02 2.1839E+03 8.4500E+02 1.4591E+03 7.9033E+02 1.3581E+03 F17 AVG 6.0181E+03 5.9799E+03 5.8787E+03 5.9098E+03 5.8617E+03 5.6103E+03 STD 7.2415E+02 1.4703E+03 6.0876E+02 1.3204E+03 6.8055E+02 1.4254E+03 F18 AVG 3.8191E+06 3.6316E+06 2.8595E+06 3.1456E+06 2.4034E+06 1.5561E+06 STD 2.9075E+06 2.2517E+06 1.5036E+06 4.1573E+06 1.2085E+06 1.6286E+06 F19 AVG 1.1979E+04 1.7927E+07 7.8780E+03 3.0047E+06 8.9584E+03 1.0777E+08 STD 2.8525E+04 9.4121E+07 6.9557E+03 1.4505E+07 8.7315E+03 5.8933E+08 F20 AVG 5.8266E+03 6.8325E+03 5.8701E+03 6.2133E+03 5.7647E+03 6.2865E+03 STD 6.3104E+02 1.2465E+03 5.4657E+02 1.4264E+03 6.7887E+02 1.3749E+03 F21 AVG 2.8462E+03 3.4812E+03 2.7755E+03 3.3808E+03 2.7796E+03 3.2107E+03 STD 7.4006E+01 2.3994E+02 7.1333E+01 2.7671E+02 6.9342E+01 2.8003E+02 F22 AVG 1.9525E+04 3.2308E+04 1.9356E+04 3.2553E+04 1.9152E+04 3.1679E+04 STD 1.2408E+03 3.3278E+03 1.3965E+03 1.4109E+03 1.3829E+03 2.9706E+03 F23 AVG 3.3840E+03 3.4406E+03 3.3531E+03 3.4256E+03 3.3292E+03 3.4515E+03 STD 1.1361E+02 1.1926E+02 1.0078E+02 9.2607E+01 7.8729E+01 7.8265E+01 F24 AVG 3.8528E+03 4.0098E+03 3.8268E+03 3.9217E+03 3.8373E+03 3.9658E+03 STD 1.0762E+02 1.3887E+02 1.2450E+02 1.1043E+02 1.4395E+02 2.0020E+02 F25 AVG 3.3924E+03 5.8749E+03 3.3462E+03 5.8191E+03 3.2732E+03 6.0467E+03 STD 8.6318E+01 1.6087E+03 6.8295E+01 1.5182E+03 5.9055E+01 1.9756E+03 F26 AVG 1.1587E+04 1.3924E+04 1.1066E+04 1.3782E+04 1.0858E+04 1.3483E+04 STD 9.2620E+02 1.9010E+03 9.9484E+02 1.6482E+03 9.9262E+02 1.1809E+03 F27 AVG 3.4982E+03 3.5886E+03 3.4975E+03 3.5854E+03 3.4961E+03 3.5702E+03 STD 7.1953E+01 8.2701E+01 8.7250E+01 8.1505E+01 4.8120E+01 7.4364E+01 F28 AVG 4.9069E+03 1.5405E+04 6.0291E+03 1.6216E+04 4.5738E+03 1.5069E+04 STD 3.7078E+03 1.6134E+03 4.3829E+03 9.1317E+02 2.7421E+03 2.4387E+03 F29 AVG 7.1249E+03 7.0248E+03 6.7150E+03 6.8557E+03 6.6273E+03 7.2768E+03 STD 1.0102E+03 7.0583E+02 9.2889E+02 7.1487E+02 6.1201E+02 7.6661E+02 F30 AVG 1.3616E+04 2.3084E+06 1.2601E+04 1.2863E+08 1.1419E+04 7.8237E+06 STD 5.3080E+03 2.6870E+06 4.9197E+03 3.4049E+08 6.2313E+03 2.7716E+07 . . 30 . 50 . 100 . Fun . Item . ADNOLACO . ACOR . ADNOLACO . ACOR . ADNOLACO . ACOR . F1 AVG 5.3769E+03 3.1512E+10 5.4398E+03 3.3528E+10 4.8859E+03 3.6756E+10 STD 6.8228E+03 1.5493E+10 6.9137E+03 1.6611E+10 6.5077E+03 1.7364E+10 F2 AVG 3.0260E+125 2.0172E+132 6.4262E+102 2.5287E+125 1.8456E+92 1.8554E+130 STD 1.6574E+126 1.0584E+133 3.5197E+103 1.3081E+126 9.7349E+92 7.9161E+130 F3 AVG 5.1010E+05 6.1926E+05 3.5156E+05 4.8201E+05 2.5957E+05 3.7165E+05 STD 1.0809E+05 8.7011E+04 7.8100E+04 6.9145E+04 5.8467E+04 7.2293E+04 F4 AVG 7.0876E+02 4.2138E+03 6.7278E+02 3.8467E+03 6.3768E+02 2.6961E+03 STD 5.0661E+01 3.5173E+03 6.2406E+01 2.3446E+03 5.1908E+01 1.8198E+03 F5 AVG 1.0513E+03 1.6009E+03 9.8216E+02 1.5904E+03 1.0019E+03 1.3741E+03 STD 7.6050E+01 2.3847E+02 7.0859E+01 2.5200E+02 8.3166E+01 3.1987E+02 F6 AVG 6.2533E+02 6.2846E+02 6.2717E+02 6.2691E+02 6.1577E+02 6.3026E+02 STD 6.3922E+00 5.6208E+00 7.1990E+00 5.6938E+00 6.6007E+00 5.5057E+00 F7 AVG 1.8366E+03 3.4527E+03 1.8742E+03 3.2140E+03 1.7876E+03 3.2280E+03 STD 1.8976E+02 5.2435E+02 2.0622E+02 4.3118E+02 1.6199E+02 5.1687E+02 F8 AVG 1.3608E+03 1.9655E+03 1.2909E+03 1.8178E+03 1.2435E+03 1.7525E+03 STD 8.3111E+01 2.3081E+02 5.7730E+01 3.0217E+02 6.9860E+01 3.2510E+02 F9 AVG 2.0845E+04 7.2321E+04 2.1396E+04 6.5506E+04 2.3060E+04 5.7308E+04 STD 5.4813E+03 1.8804E+04 7.0624E+03 1.3421E+04 6.0311E+03 1.7249E+04 F10 AVG 1.7467E+04 3.0255E+04 1.7207E+04 3.0446E+04 1.7419E+04 2.9410E+04 STD 1.5611E+03 4.0803E+03 1.4985E+03 3.8166E+03 1.3249E+03 4.3484E+03 F11 AVG 1.0933E+04 3.3929E+04 3.7730E+03 2.3301E+04 2.2248E+03 2.2783E+04 STD 5.8127E+03 3.4091E+04 1.6572E+03 1.5948E+04 2.7826E+02 1.5694E+04 F12 AVG 1.0594E+07 3.1872E+09 7.3848E+06 2.3337E+09 2.2982E+06 2.5920E+09 STD 1.8568E+07 6.6198E+09 9.2579E+06 3.4348E+09 1.4950E+06 2.8680E+09 F13 AVG 8.5805E+03 1.5665E+08 8.3469E+03 9.4123E+07 3.8380E+04 1.4334E+07 STD 8.4003E+03 4.6667E+08 7.9527E+03 3.6857E+08 9.4271E+04 5.2363E+07 F14 AVG 1.3498E+06 1.2407E+06 4.9768E+05 6.6531E+05 2.9483E+05 6.4348E+05 STD 1.9222E+06 1.4870E+06 5.8327E+05 8.7877E+05 3.3045E+05 6.2793E+05 F15 AVG 1.9014E+04 3.0051E+04 1.6192E+04 2.1751E+04 6.0500E+03 1.4081E+07 STD 6.0635E+04 2.1252E+04 5.1332E+04 1.6548E+04 4.6198E+03 7.5293E+07 F16 AVG 6.7034E+03 6.6281E+03 6.4800E+03 5.8567E+03 5.8343E+03 5.5429E+03 STD 6.0943E+02 2.1839E+03 8.4500E+02 1.4591E+03 7.9033E+02 1.3581E+03 F17 AVG 6.0181E+03 5.9799E+03 5.8787E+03 5.9098E+03 5.8617E+03 5.6103E+03 STD 7.2415E+02 1.4703E+03 6.0876E+02 1.3204E+03 6.8055E+02 1.4254E+03 F18 AVG 3.8191E+06 3.6316E+06 2.8595E+06 3.1456E+06 2.4034E+06 1.5561E+06 STD 2.9075E+06 2.2517E+06 1.5036E+06 4.1573E+06 1.2085E+06 1.6286E+06 F19 AVG 1.1979E+04 1.7927E+07 7.8780E+03 3.0047E+06 8.9584E+03 1.0777E+08 STD 2.8525E+04 9.4121E+07 6.9557E+03 1.4505E+07 8.7315E+03 5.8933E+08 F20 AVG 5.8266E+03 6.8325E+03 5.8701E+03 6.2133E+03 5.7647E+03 6.2865E+03 STD 6.3104E+02 1.2465E+03 5.4657E+02 1.4264E+03 6.7887E+02 1.3749E+03 F21 AVG 2.8462E+03 3.4812E+03 2.7755E+03 3.3808E+03 2.7796E+03 3.2107E+03 STD 7.4006E+01 2.3994E+02 7.1333E+01 2.7671E+02 6.9342E+01 2.8003E+02 F22 AVG 1.9525E+04 3.2308E+04 1.9356E+04 3.2553E+04 1.9152E+04 3.1679E+04 STD 1.2408E+03 3.3278E+03 1.3965E+03 1.4109E+03 1.3829E+03 2.9706E+03 F23 AVG 3.3840E+03 3.4406E+03 3.3531E+03 3.4256E+03 3.3292E+03 3.4515E+03 STD 1.1361E+02 1.1926E+02 1.0078E+02 9.2607E+01 7.8729E+01 7.8265E+01 F24 AVG 3.8528E+03 4.0098E+03 3.8268E+03 3.9217E+03 3.8373E+03 3.9658E+03 STD 1.0762E+02 1.3887E+02 1.2450E+02 1.1043E+02 1.4395E+02 2.0020E+02 F25 AVG 3.3924E+03 5.8749E+03 3.3462E+03 5.8191E+03 3.2732E+03 6.0467E+03 STD 8.6318E+01 1.6087E+03 6.8295E+01 1.5182E+03 5.9055E+01 1.9756E+03 F26 AVG 1.1587E+04 1.3924E+04 1.1066E+04 1.3782E+04 1.0858E+04 1.3483E+04 STD 9.2620E+02 1.9010E+03 9.9484E+02 1.6482E+03 9.9262E+02 1.1809E+03 F27 AVG 3.4982E+03 3.5886E+03 3.4975E+03 3.5854E+03 3.4961E+03 3.5702E+03 STD 7.1953E+01 8.2701E+01 8.7250E+01 8.1505E+01 4.8120E+01 7.4364E+01 F28 AVG 4.9069E+03 1.5405E+04 6.0291E+03 1.6216E+04 4.5738E+03 1.5069E+04 STD 3.7078E+03 1.6134E+03 4.3829E+03 9.1317E+02 2.7421E+03 2.4387E+03 F29 AVG 7.1249E+03 7.0248E+03 6.7150E+03 6.8557E+03 6.6273E+03 7.2768E+03 STD 1.0102E+03 7.0583E+02 9.2889E+02 7.1487E+02 6.1201E+02 7.6661E+02 F30 AVG 1.3616E+04 2.3084E+06 1.2601E+04 1.2863E+08 1.1419E+04 7.8237E+06 STD 5.3080E+03 2.6870E+06 4.9197E+03 3.4049E+08 6.2313E+03 2.7716E+07 Open in new tab Table A4: The relevant experimental results of the parameter q. Fun . Item . 0.1 . 0.2 . 0.3 . 0.4 . 0.5 . 0.6 . 0.7 . 0.8 . 0.9 . 1 . F1 AVG 6.5678E+03 6.8625E+03 6.1167E+03 9.3720E+03 6.9967E+03 4.1536E+03 7.4378E+03 5.0378E+03 6.7730E+03 7.6799E+03 STD 8.2021E+03 8.4706E+03 6.9894E+03 1.1057E+04 6.9010E+03 4.3847E+03 6.7041E+03 8.2853E+03 8.0858E+03 7.5867E+03 F2 AVG 1.1438E+63 1.5595E+92 2.3026E+113 5.9673E+121 1.0136E+110 1.1121E+112 5.6366E+118 1.6013E+117 4.3998E+118 3.5869E+127 STD 6.1003E+63 8.5417E+92 1.2612E+114 3.2682E+122 3.2050E+110 6.0914E+112 3.0825E+119 6.8836E+117 2.2719E+119 1.9646E+128 F3 AVG 3.4469E+05 4.3270E+05 4.4861E+05 4.7737E+05 4.9535E+05 5.0088E+05 5.0959E+05 5.0138E+05 5.0772E+05 5.0315E+05 STD 6.9251E+04 6.7985E+04 8.3864E+04 9.2438E+04 6.7698E+04 8.2213E+04 7.9418E+04 8.4233E+04 8.7172E+04 8.7118E+04 F4 AVG 6.9799E+02 7.0503E+02 6.8172E+02 7.2623E+02 7.0697E+02 6.9778E+02 7.2539E+02 7.2192E+02 7.3184E+02 7.1329E+02 STD 7.6926E+01 7.2838E+01 6.0623E+01 6.3688E+01 5.4650E+01 5.2304E+01 8.0301E+01 5.4309E+01 5.6784E+01 4.1086E+01 F5 AVG 1.0565E+03 1.0316E+03 1.0399E+03 1.0546E+03 1.0501E+03 1.0662E+03 1.0430E+03 1.0493E+03 1.0624E+03 1.0657E+03 STD 9.3388E+01 7.8835E+01 9.5189E+01 6.9011E+01 4.8211E+01 6.5838E+01 8.9899E+01 7.5206E+01 7.4861E+01 7.1286E+01 F6 AVG 6.3221E+02 6.3025E+02 6.2594E+02 6.2684E+02 6.2672E+02 6.2662E+02 6.2713E+02 6.2578E+02 6.2693E+02 6.2651E+02 STD 9.2044E+00 7.3376E+00 5.6316E+00 7.1253E+00 7.1998E+00 5.7329E+00 6.5618E+00 6.4953E+00 6.4007E+00 7.6934E+00 F7 AVG 2.0341E+03 1.8640E+03 1.9179E+03 1.8731E+03 1.8263E+03 1.9036E+03 1.8299E+03 1.8265E+03 1.8081E+03 1.8022E+03 STD 1.8890E+02 1.7093E+02 1.7772E+02 2.1811E+02 1.6464E+02 1.8945E+02 1.9722E+02 1.7579E+02 1.7865E+02 1.8568E+02 F8 AVG 1.3493E+03 1.3541E+03 1.3390E+03 1.3221E+03 1.3371E+03 1.3344E+03 1.3114E+03 1.3155E+03 1.3427E+03 1.3149E+03 STD 9.3232E+01 9.0337E+01 8.5518E+01 7.0439E+01 8.4618E+01 7.3790E+01 6.7596E+01 6.3629E+01 7.3616E+01 6.9223E+01 F9 AVG 2.3355E+04 2.3255E+04 2.3276E+04 2.2298E+04 2.2078E+04 2.1955E+04 2.2944E+04 2.2029E+04 2.4225E+04 2.1512E+04 STD 4.9870E+03 5.5244E+03 5.7880E+03 5.6531E+03 6.5192E+03 6.5953E+03 8.3271E+03 6.3560E+03 4.4684E+03 5.1996E+03 F10 AVG 1.7563E+04 1.7587E+04 1.7489E+04 1.7470E+04 1.7499E+04 1.7565E+04 1.7699E+04 1.7344E+04 1.7332E+04 1.7650E+04 STD 1.2993E+03 1.0930E+03 1.1644E+03 1.3116E+03 1.2551E+03 1.0060E+03 1.1170E+03 9.4689E+02 1.2942E+03 9.3811E+02 F11 AVG 3.1015E+03 2.7797E+03 3.3285E+03 7.1500E+03 1.0524E+04 1.2914E+04 1.4608E+04 1.8379E+04 1.7439E+04 1.6696E+04 STD 4.1772E+02 3.6048E+02 7.4831E+02 3.4018E+03 5.0358E+03 9.8060E+03 8.9784E+03 9.0064E+03 9.5436E+03 7.8208E+03 F12 AVG 3.0392E+06 3.5343E+06 7.7886E+06 1.2902E+07 1.0568E+07 1.1755E+07 1.3762E+07 1.2837E+07 1.8425E+07 1.9415E+07 STD 2.7736E+06 1.5396E+06 1.0041E+07 2.4047E+07 1.0212E+07 1.5811E+07 1.5010E+07 7.8933E+06 2.6386E+07 3.1848E+07 F13 AVG 1.1429E+04 2.0039E+04 2.2405E+04 2.1040E+04 8.8846E+03 7.5299E+03 7.5430E+03 3.4291E+04 3.5167E+04 1.0307E+04 STD 6.6504E+03 5.5334E+04 7.4811E+04 6.9606E+04 7.7558E+03 4.9626E+03 6.8174E+03 8.6540E+04 1.1057E+05 8.9218E+03 F14 AVG 3.7009E+05 4.5872E+05 5.4713E+05 9.5130E+05 1.1194E+06 1.2031E+06 1.4135E+06 1.7473E+06 1.5874E+06 1.6356E+06 STD 1.8996E+05 3.2004E+05 3.5099E+05 8.5673E+05 2.0043E+06 1.1431E+06 8.1714E+05 1.3958E+06 1.4322E+06 1.4362E+06 F15 AVG 1.1357E+04 1.7487E+04 1.9298E+04 3.0388E+04 2.5430E+04 2.1861E+04 1.2926E+04 7.3377E+03 1.9600E+04 1.3484E+04 STD 2.4883E+04 5.3990E+04 4.9242E+04 8.8647E+04 7.3981E+04 5.6724E+04 4.1984E+04 5.1992E+03 6.7550E+04 4.2563E+04 F16 AVG 5.8838E+03 6.3132E+03 6.4346E+03 6.6993E+03 6.7399E+03 6.6638E+03 6.7826E+03 6.6998E+03 6.8991E+03 6.7041E+03 STD 6.7570E+02 8.8355E+02 1.1585E+03 1.0566E+03 7.8529E+02 6.0425E+02 9.2828E+02 6.6941E+02 8.7126E+02 6.6058E+02 F17 AVG 5.4470E+03 5.9292E+03 5.8696E+03 6.0257E+03 5.9559E+03 5.9322E+03 5.9456E+03 5.9164E+03 5.6954E+03 5.7931E+03 STD 7.3288E+02 6.5981E+02 6.4787E+02 5.7279E+02 7.0255E+02 5.4236E+02 7.2223E+02 5.1422E+02 5.9739E+02 5.8934E+02 F18 AVG 1.1552E+06 2.2813E+06 2.7169E+06 3.5409E+06 4.4954E+06 3.9682E+06 6.6234E+06 6.2897E+06 5.0526E+06 6.4303E+06 STD 6.6917E+05 2.0946E+06 2.4195E+06 2.5261E+06 4.0698E+06 2.6624E+06 4.2223E+06 5.2913E+06 3.6509E+06 4.7915E+06 F19 AVG 8.1991E+03 8.3134E+03 7.7305E+03 8.5784E+03 7.0682E+03 6.5331E+03 6.8235E+03 9.9550E+03 8.9564E+03 7.7808E+03 STD 6.7237E+03 6.8684E+03 6.0332E+03 6.8845E+03 4.7466E+03 4.5654E+03 7.0013E+03 9.7331E+03 8.5027E+03 7.3342E+03 F20 AVG 5.7142E+03 5.8217E+03 5.9156E+03 5.7342E+03 5.8127E+03 5.8962E+03 5.7449E+03 5.7768E+03 5.8604E+03 5.8903E+03 STD 7.1365E+02 5.4117E+02 4.7893E+02 6.2403E+02 5.9272E+02 6.9267E+02 4.9619E+02 6.2496E+02 6.0946E+02 5.7183E+02 F21 AVG 2.8591E+03 2.8848E+03 2.8402E+03 2.8527E+03 2.8395E+03 2.8159E+03 2.8506E+03 2.8605E+03 2.8491E+03 2.8439E+03 STD 8.3374E+01 8.6637E+01 9.0731E+01 6.6941E+01 6.3448E+01 7.0710E+01 6.8368E+01 7.0339E+01 8.4844E+01 6.7750E+01 F22 AVG 1.9561E+04 1.9816E+04 1.9006E+04 1.9581E+04 1.9942E+04 1.9496E+04 1.9008E+04 1.9575E+04 1.9592E+04 1.9641E+04 STD 1.5544E+03 1.3078E+03 1.1168E+03 1.3356E+03 1.0210E+03 1.2549E+03 1.3953E+03 1.2213E+03 1.2045E+03 1.2566E+03 F23 AVG 3.5603E+03 3.4257E+03 3.3548E+03 3.3552E+03 3.3650E+03 3.3974E+03 3.3721E+03 3.4187E+03 3.4060E+03 3.3860E+03 STD 1.5644E+02 1.2296E+02 1.0754E+02 1.1808E+02 1.2562E+02 9.9671E+01 9.6089E+01 8.3865E+01 1.0289E+02 9.1434E+01 F24 AVG 4.2245E+03 3.9469E+03 3.9186E+03 3.8312E+03 3.8717E+03 3.8963E+03 3.8794E+03 3.8598E+03 3.8820E+03 3.9165E+03 STD 2.6532E+02 1.5255E+02 1.1589E+02 1.2104E+02 9.8206E+01 9.1552E+01 8.5171E+01 9.6725E+01 1.0909E+02 1.3854E+02 F25 AVG 3.4122E+03 3.3829E+03 3.3928E+03 3.3841E+03 3.4058E+03 3.3778E+03 3.3949E+03 3.4523E+03 3.4345E+03 3.4292E+03 STD 8.2159E+01 9.0518E+01 8.4311E+01 7.5241E+01 7.0072E+01 7.0959E+01 8.6147E+01 7.0201E+01 6.4704E+01 9.7063E+01 F26 AVG 1.2409E+04 1.1709E+04 1.1838E+04 1.1318E+04 1.1759E+04 1.1602E+04 1.1638E+04 1.1524E+04 1.1627E+04 1.1601E+04 STD 1.5653E+03 1.3959E+03 1.1176E+03 8.0358E+02 7.9216E+02 8.5178E+02 8.2102E+02 9.2957E+02 7.6956E+02 7.3029E+02 F27 AVG 3.6624E+03 3.5683E+03 3.5146E+03 3.5022E+03 3.5039E+03 3.5095E+03 3.4707E+03 3.5006E+03 3.4691E+03 3.4735E+03 STD 1.3941E+02 9.1965E+01 6.6825E+01 7.3245E+01 6.6392E+01 8.2823E+01 5.8819E+01 8.0520E+01 7.5749E+01 5.2387E+01 F28 AVG 3.8356E+03 3.8346E+03 3.8423E+03 4.9581E+03 4.5641E+03 6.3805E+03 7.0352E+03 6.9987E+03 6.3417E+03 7.3898E+03 STD 1.9822E+03 1.9816E+03 2.0423E+03 3.8340E+03 3.3078E+03 4.8790E+03 5.1051E+03 5.0252E+03 4.7956E+03 5.2092E+03 F29 AVG 6.7984E+03 6.7590E+03 6.6082E+03 7.0184E+03 7.1578E+03 7.3394E+03 7.6571E+03 7.3985E+03 7.5505E+03 7.1240E+03 STD 7.8595E+02 6.6109E+02 9.8104E+02 9.1907E+02 1.0391E+03 9.4327E+02 8.2898E+02 6.6601E+02 9.8834E+02 9.6735E+02 F30 AVG 1.5572E+04 2.3471E+04 1.4151E+04 1.9994E+04 1.3069E+04 1.2905E+04 2.3037E+04 1.3387E+04 1.2225E+04 1.1408E+04 STD 1.8653E+04 5.1730E+04 6.0027E+03 4.3680E+04 4.8897E+03 5.1675E+03 5.1325E+04 5.3044E+03 4.5179E+03 2.8090E+03 Avg 5.101 5.144 5.014 5.274 5.529 5.617 5.698 5.898 5.952 5.772 Rank 2 3 1 4 5 6 7 9 10 8 Fun . Item . 0.1 . 0.2 . 0.3 . 0.4 . 0.5 . 0.6 . 0.7 . 0.8 . 0.9 . 1 . F1 AVG 6.5678E+03 6.8625E+03 6.1167E+03 9.3720E+03 6.9967E+03 4.1536E+03 7.4378E+03 5.0378E+03 6.7730E+03 7.6799E+03 STD 8.2021E+03 8.4706E+03 6.9894E+03 1.1057E+04 6.9010E+03 4.3847E+03 6.7041E+03 8.2853E+03 8.0858E+03 7.5867E+03 F2 AVG 1.1438E+63 1.5595E+92 2.3026E+113 5.9673E+121 1.0136E+110 1.1121E+112 5.6366E+118 1.6013E+117 4.3998E+118 3.5869E+127 STD 6.1003E+63 8.5417E+92 1.2612E+114 3.2682E+122 3.2050E+110 6.0914E+112 3.0825E+119 6.8836E+117 2.2719E+119 1.9646E+128 F3 AVG 3.4469E+05 4.3270E+05 4.4861E+05 4.7737E+05 4.9535E+05 5.0088E+05 5.0959E+05 5.0138E+05 5.0772E+05 5.0315E+05 STD 6.9251E+04 6.7985E+04 8.3864E+04 9.2438E+04 6.7698E+04 8.2213E+04 7.9418E+04 8.4233E+04 8.7172E+04 8.7118E+04 F4 AVG 6.9799E+02 7.0503E+02 6.8172E+02 7.2623E+02 7.0697E+02 6.9778E+02 7.2539E+02 7.2192E+02 7.3184E+02 7.1329E+02 STD 7.6926E+01 7.2838E+01 6.0623E+01 6.3688E+01 5.4650E+01 5.2304E+01 8.0301E+01 5.4309E+01 5.6784E+01 4.1086E+01 F5 AVG 1.0565E+03 1.0316E+03 1.0399E+03 1.0546E+03 1.0501E+03 1.0662E+03 1.0430E+03 1.0493E+03 1.0624E+03 1.0657E+03 STD 9.3388E+01 7.8835E+01 9.5189E+01 6.9011E+01 4.8211E+01 6.5838E+01 8.9899E+01 7.5206E+01 7.4861E+01 7.1286E+01 F6 AVG 6.3221E+02 6.3025E+02 6.2594E+02 6.2684E+02 6.2672E+02 6.2662E+02 6.2713E+02 6.2578E+02 6.2693E+02 6.2651E+02 STD 9.2044E+00 7.3376E+00 5.6316E+00 7.1253E+00 7.1998E+00 5.7329E+00 6.5618E+00 6.4953E+00 6.4007E+00 7.6934E+00 F7 AVG 2.0341E+03 1.8640E+03 1.9179E+03 1.8731E+03 1.8263E+03 1.9036E+03 1.8299E+03 1.8265E+03 1.8081E+03 1.8022E+03 STD 1.8890E+02 1.7093E+02 1.7772E+02 2.1811E+02 1.6464E+02 1.8945E+02 1.9722E+02 1.7579E+02 1.7865E+02 1.8568E+02 F8 AVG 1.3493E+03 1.3541E+03 1.3390E+03 1.3221E+03 1.3371E+03 1.3344E+03 1.3114E+03 1.3155E+03 1.3427E+03 1.3149E+03 STD 9.3232E+01 9.0337E+01 8.5518E+01 7.0439E+01 8.4618E+01 7.3790E+01 6.7596E+01 6.3629E+01 7.3616E+01 6.9223E+01 F9 AVG 2.3355E+04 2.3255E+04 2.3276E+04 2.2298E+04 2.2078E+04 2.1955E+04 2.2944E+04 2.2029E+04 2.4225E+04 2.1512E+04 STD 4.9870E+03 5.5244E+03 5.7880E+03 5.6531E+03 6.5192E+03 6.5953E+03 8.3271E+03 6.3560E+03 4.4684E+03 5.1996E+03 F10 AVG 1.7563E+04 1.7587E+04 1.7489E+04 1.7470E+04 1.7499E+04 1.7565E+04 1.7699E+04 1.7344E+04 1.7332E+04 1.7650E+04 STD 1.2993E+03 1.0930E+03 1.1644E+03 1.3116E+03 1.2551E+03 1.0060E+03 1.1170E+03 9.4689E+02 1.2942E+03 9.3811E+02 F11 AVG 3.1015E+03 2.7797E+03 3.3285E+03 7.1500E+03 1.0524E+04 1.2914E+04 1.4608E+04 1.8379E+04 1.7439E+04 1.6696E+04 STD 4.1772E+02 3.6048E+02 7.4831E+02 3.4018E+03 5.0358E+03 9.8060E+03 8.9784E+03 9.0064E+03 9.5436E+03 7.8208E+03 F12 AVG 3.0392E+06 3.5343E+06 7.7886E+06 1.2902E+07 1.0568E+07 1.1755E+07 1.3762E+07 1.2837E+07 1.8425E+07 1.9415E+07 STD 2.7736E+06 1.5396E+06 1.0041E+07 2.4047E+07 1.0212E+07 1.5811E+07 1.5010E+07 7.8933E+06 2.6386E+07 3.1848E+07 F13 AVG 1.1429E+04 2.0039E+04 2.2405E+04 2.1040E+04 8.8846E+03 7.5299E+03 7.5430E+03 3.4291E+04 3.5167E+04 1.0307E+04 STD 6.6504E+03 5.5334E+04 7.4811E+04 6.9606E+04 7.7558E+03 4.9626E+03 6.8174E+03 8.6540E+04 1.1057E+05 8.9218E+03 F14 AVG 3.7009E+05 4.5872E+05 5.4713E+05 9.5130E+05 1.1194E+06 1.2031E+06 1.4135E+06 1.7473E+06 1.5874E+06 1.6356E+06 STD 1.8996E+05 3.2004E+05 3.5099E+05 8.5673E+05 2.0043E+06 1.1431E+06 8.1714E+05 1.3958E+06 1.4322E+06 1.4362E+06 F15 AVG 1.1357E+04 1.7487E+04 1.9298E+04 3.0388E+04 2.5430E+04 2.1861E+04 1.2926E+04 7.3377E+03 1.9600E+04 1.3484E+04 STD 2.4883E+04 5.3990E+04 4.9242E+04 8.8647E+04 7.3981E+04 5.6724E+04 4.1984E+04 5.1992E+03 6.7550E+04 4.2563E+04 F16 AVG 5.8838E+03 6.3132E+03 6.4346E+03 6.6993E+03 6.7399E+03 6.6638E+03 6.7826E+03 6.6998E+03 6.8991E+03 6.7041E+03 STD 6.7570E+02 8.8355E+02 1.1585E+03 1.0566E+03 7.8529E+02 6.0425E+02 9.2828E+02 6.6941E+02 8.7126E+02 6.6058E+02 F17 AVG 5.4470E+03 5.9292E+03 5.8696E+03 6.0257E+03 5.9559E+03 5.9322E+03 5.9456E+03 5.9164E+03 5.6954E+03 5.7931E+03 STD 7.3288E+02 6.5981E+02 6.4787E+02 5.7279E+02 7.0255E+02 5.4236E+02 7.2223E+02 5.1422E+02 5.9739E+02 5.8934E+02 F18 AVG 1.1552E+06 2.2813E+06 2.7169E+06 3.5409E+06 4.4954E+06 3.9682E+06 6.6234E+06 6.2897E+06 5.0526E+06 6.4303E+06 STD 6.6917E+05 2.0946E+06 2.4195E+06 2.5261E+06 4.0698E+06 2.6624E+06 4.2223E+06 5.2913E+06 3.6509E+06 4.7915E+06 F19 AVG 8.1991E+03 8.3134E+03 7.7305E+03 8.5784E+03 7.0682E+03 6.5331E+03 6.8235E+03 9.9550E+03 8.9564E+03 7.7808E+03 STD 6.7237E+03 6.8684E+03 6.0332E+03 6.8845E+03 4.7466E+03 4.5654E+03 7.0013E+03 9.7331E+03 8.5027E+03 7.3342E+03 F20 AVG 5.7142E+03 5.8217E+03 5.9156E+03 5.7342E+03 5.8127E+03 5.8962E+03 5.7449E+03 5.7768E+03 5.8604E+03 5.8903E+03 STD 7.1365E+02 5.4117E+02 4.7893E+02 6.2403E+02 5.9272E+02 6.9267E+02 4.9619E+02 6.2496E+02 6.0946E+02 5.7183E+02 F21 AVG 2.8591E+03 2.8848E+03 2.8402E+03 2.8527E+03 2.8395E+03 2.8159E+03 2.8506E+03 2.8605E+03 2.8491E+03 2.8439E+03 STD 8.3374E+01 8.6637E+01 9.0731E+01 6.6941E+01 6.3448E+01 7.0710E+01 6.8368E+01 7.0339E+01 8.4844E+01 6.7750E+01 F22 AVG 1.9561E+04 1.9816E+04 1.9006E+04 1.9581E+04 1.9942E+04 1.9496E+04 1.9008E+04 1.9575E+04 1.9592E+04 1.9641E+04 STD 1.5544E+03 1.3078E+03 1.1168E+03 1.3356E+03 1.0210E+03 1.2549E+03 1.3953E+03 1.2213E+03 1.2045E+03 1.2566E+03 F23 AVG 3.5603E+03 3.4257E+03 3.3548E+03 3.3552E+03 3.3650E+03 3.3974E+03 3.3721E+03 3.4187E+03 3.4060E+03 3.3860E+03 STD 1.5644E+02 1.2296E+02 1.0754E+02 1.1808E+02 1.2562E+02 9.9671E+01 9.6089E+01 8.3865E+01 1.0289E+02 9.1434E+01 F24 AVG 4.2245E+03 3.9469E+03 3.9186E+03 3.8312E+03 3.8717E+03 3.8963E+03 3.8794E+03 3.8598E+03 3.8820E+03 3.9165E+03 STD 2.6532E+02 1.5255E+02 1.1589E+02 1.2104E+02 9.8206E+01 9.1552E+01 8.5171E+01 9.6725E+01 1.0909E+02 1.3854E+02 F25 AVG 3.4122E+03 3.3829E+03 3.3928E+03 3.3841E+03 3.4058E+03 3.3778E+03 3.3949E+03 3.4523E+03 3.4345E+03 3.4292E+03 STD 8.2159E+01 9.0518E+01 8.4311E+01 7.5241E+01 7.0072E+01 7.0959E+01 8.6147E+01 7.0201E+01 6.4704E+01 9.7063E+01 F26 AVG 1.2409E+04 1.1709E+04 1.1838E+04 1.1318E+04 1.1759E+04 1.1602E+04 1.1638E+04 1.1524E+04 1.1627E+04 1.1601E+04 STD 1.5653E+03 1.3959E+03 1.1176E+03 8.0358E+02 7.9216E+02 8.5178E+02 8.2102E+02 9.2957E+02 7.6956E+02 7.3029E+02 F27 AVG 3.6624E+03 3.5683E+03 3.5146E+03 3.5022E+03 3.5039E+03 3.5095E+03 3.4707E+03 3.5006E+03 3.4691E+03 3.4735E+03 STD 1.3941E+02 9.1965E+01 6.6825E+01 7.3245E+01 6.6392E+01 8.2823E+01 5.8819E+01 8.0520E+01 7.5749E+01 5.2387E+01 F28 AVG 3.8356E+03 3.8346E+03 3.8423E+03 4.9581E+03 4.5641E+03 6.3805E+03 7.0352E+03 6.9987E+03 6.3417E+03 7.3898E+03 STD 1.9822E+03 1.9816E+03 2.0423E+03 3.8340E+03 3.3078E+03 4.8790E+03 5.1051E+03 5.0252E+03 4.7956E+03 5.2092E+03 F29 AVG 6.7984E+03 6.7590E+03 6.6082E+03 7.0184E+03 7.1578E+03 7.3394E+03 7.6571E+03 7.3985E+03 7.5505E+03 7.1240E+03 STD 7.8595E+02 6.6109E+02 9.8104E+02 9.1907E+02 1.0391E+03 9.4327E+02 8.2898E+02 6.6601E+02 9.8834E+02 9.6735E+02 F30 AVG 1.5572E+04 2.3471E+04 1.4151E+04 1.9994E+04 1.3069E+04 1.2905E+04 2.3037E+04 1.3387E+04 1.2225E+04 1.1408E+04 STD 1.8653E+04 5.1730E+04 6.0027E+03 4.3680E+04 4.8897E+03 5.1675E+03 5.1325E+04 5.3044E+03 4.5179E+03 2.8090E+03 Avg 5.101 5.144 5.014 5.274 5.529 5.617 5.698 5.898 5.952 5.772 Rank 2 3 1 4 5 6 7 9 10 8 Open in new tab Table A4: The relevant experimental results of the parameter q. Fun . Item . 0.1 . 0.2 . 0.3 . 0.4 . 0.5 . 0.6 . 0.7 . 0.8 . 0.9 . 1 . F1 AVG 6.5678E+03 6.8625E+03 6.1167E+03 9.3720E+03 6.9967E+03 4.1536E+03 7.4378E+03 5.0378E+03 6.7730E+03 7.6799E+03 STD 8.2021E+03 8.4706E+03 6.9894E+03 1.1057E+04 6.9010E+03 4.3847E+03 6.7041E+03 8.2853E+03 8.0858E+03 7.5867E+03 F2 AVG 1.1438E+63 1.5595E+92 2.3026E+113 5.9673E+121 1.0136E+110 1.1121E+112 5.6366E+118 1.6013E+117 4.3998E+118 3.5869E+127 STD 6.1003E+63 8.5417E+92 1.2612E+114 3.2682E+122 3.2050E+110 6.0914E+112 3.0825E+119 6.8836E+117 2.2719E+119 1.9646E+128 F3 AVG 3.4469E+05 4.3270E+05 4.4861E+05 4.7737E+05 4.9535E+05 5.0088E+05 5.0959E+05 5.0138E+05 5.0772E+05 5.0315E+05 STD 6.9251E+04 6.7985E+04 8.3864E+04 9.2438E+04 6.7698E+04 8.2213E+04 7.9418E+04 8.4233E+04 8.7172E+04 8.7118E+04 F4 AVG 6.9799E+02 7.0503E+02 6.8172E+02 7.2623E+02 7.0697E+02 6.9778E+02 7.2539E+02 7.2192E+02 7.3184E+02 7.1329E+02 STD 7.6926E+01 7.2838E+01 6.0623E+01 6.3688E+01 5.4650E+01 5.2304E+01 8.0301E+01 5.4309E+01 5.6784E+01 4.1086E+01 F5 AVG 1.0565E+03 1.0316E+03 1.0399E+03 1.0546E+03 1.0501E+03 1.0662E+03 1.0430E+03 1.0493E+03 1.0624E+03 1.0657E+03 STD 9.3388E+01 7.8835E+01 9.5189E+01 6.9011E+01 4.8211E+01 6.5838E+01 8.9899E+01 7.5206E+01 7.4861E+01 7.1286E+01 F6 AVG 6.3221E+02 6.3025E+02 6.2594E+02 6.2684E+02 6.2672E+02 6.2662E+02 6.2713E+02 6.2578E+02 6.2693E+02 6.2651E+02 STD 9.2044E+00 7.3376E+00 5.6316E+00 7.1253E+00 7.1998E+00 5.7329E+00 6.5618E+00 6.4953E+00 6.4007E+00 7.6934E+00 F7 AVG 2.0341E+03 1.8640E+03 1.9179E+03 1.8731E+03 1.8263E+03 1.9036E+03 1.8299E+03 1.8265E+03 1.8081E+03 1.8022E+03 STD 1.8890E+02 1.7093E+02 1.7772E+02 2.1811E+02 1.6464E+02 1.8945E+02 1.9722E+02 1.7579E+02 1.7865E+02 1.8568E+02 F8 AVG 1.3493E+03 1.3541E+03 1.3390E+03 1.3221E+03 1.3371E+03 1.3344E+03 1.3114E+03 1.3155E+03 1.3427E+03 1.3149E+03 STD 9.3232E+01 9.0337E+01 8.5518E+01 7.0439E+01 8.4618E+01 7.3790E+01 6.7596E+01 6.3629E+01 7.3616E+01 6.9223E+01 F9 AVG 2.3355E+04 2.3255E+04 2.3276E+04 2.2298E+04 2.2078E+04 2.1955E+04 2.2944E+04 2.2029E+04 2.4225E+04 2.1512E+04 STD 4.9870E+03 5.5244E+03 5.7880E+03 5.6531E+03 6.5192E+03 6.5953E+03 8.3271E+03 6.3560E+03 4.4684E+03 5.1996E+03 F10 AVG 1.7563E+04 1.7587E+04 1.7489E+04 1.7470E+04 1.7499E+04 1.7565E+04 1.7699E+04 1.7344E+04 1.7332E+04 1.7650E+04 STD 1.2993E+03 1.0930E+03 1.1644E+03 1.3116E+03 1.2551E+03 1.0060E+03 1.1170E+03 9.4689E+02 1.2942E+03 9.3811E+02 F11 AVG 3.1015E+03 2.7797E+03 3.3285E+03 7.1500E+03 1.0524E+04 1.2914E+04 1.4608E+04 1.8379E+04 1.7439E+04 1.6696E+04 STD 4.1772E+02 3.6048E+02 7.4831E+02 3.4018E+03 5.0358E+03 9.8060E+03 8.9784E+03 9.0064E+03 9.5436E+03 7.8208E+03 F12 AVG 3.0392E+06 3.5343E+06 7.7886E+06 1.2902E+07 1.0568E+07 1.1755E+07 1.3762E+07 1.2837E+07 1.8425E+07 1.9415E+07 STD 2.7736E+06 1.5396E+06 1.0041E+07 2.4047E+07 1.0212E+07 1.5811E+07 1.5010E+07 7.8933E+06 2.6386E+07 3.1848E+07 F13 AVG 1.1429E+04 2.0039E+04 2.2405E+04 2.1040E+04 8.8846E+03 7.5299E+03 7.5430E+03 3.4291E+04 3.5167E+04 1.0307E+04 STD 6.6504E+03 5.5334E+04 7.4811E+04 6.9606E+04 7.7558E+03 4.9626E+03 6.8174E+03 8.6540E+04 1.1057E+05 8.9218E+03 F14 AVG 3.7009E+05 4.5872E+05 5.4713E+05 9.5130E+05 1.1194E+06 1.2031E+06 1.4135E+06 1.7473E+06 1.5874E+06 1.6356E+06 STD 1.8996E+05 3.2004E+05 3.5099E+05 8.5673E+05 2.0043E+06 1.1431E+06 8.1714E+05 1.3958E+06 1.4322E+06 1.4362E+06 F15 AVG 1.1357E+04 1.7487E+04 1.9298E+04 3.0388E+04 2.5430E+04 2.1861E+04 1.2926E+04 7.3377E+03 1.9600E+04 1.3484E+04 STD 2.4883E+04 5.3990E+04 4.9242E+04 8.8647E+04 7.3981E+04 5.6724E+04 4.1984E+04 5.1992E+03 6.7550E+04 4.2563E+04 F16 AVG 5.8838E+03 6.3132E+03 6.4346E+03 6.6993E+03 6.7399E+03 6.6638E+03 6.7826E+03 6.6998E+03 6.8991E+03 6.7041E+03 STD 6.7570E+02 8.8355E+02 1.1585E+03 1.0566E+03 7.8529E+02 6.0425E+02 9.2828E+02 6.6941E+02 8.7126E+02 6.6058E+02 F17 AVG 5.4470E+03 5.9292E+03 5.8696E+03 6.0257E+03 5.9559E+03 5.9322E+03 5.9456E+03 5.9164E+03 5.6954E+03 5.7931E+03 STD 7.3288E+02 6.5981E+02 6.4787E+02 5.7279E+02 7.0255E+02 5.4236E+02 7.2223E+02 5.1422E+02 5.9739E+02 5.8934E+02 F18 AVG 1.1552E+06 2.2813E+06 2.7169E+06 3.5409E+06 4.4954E+06 3.9682E+06 6.6234E+06 6.2897E+06 5.0526E+06 6.4303E+06 STD 6.6917E+05 2.0946E+06 2.4195E+06 2.5261E+06 4.0698E+06 2.6624E+06 4.2223E+06 5.2913E+06 3.6509E+06 4.7915E+06 F19 AVG 8.1991E+03 8.3134E+03 7.7305E+03 8.5784E+03 7.0682E+03 6.5331E+03 6.8235E+03 9.9550E+03 8.9564E+03 7.7808E+03 STD 6.7237E+03 6.8684E+03 6.0332E+03 6.8845E+03 4.7466E+03 4.5654E+03 7.0013E+03 9.7331E+03 8.5027E+03 7.3342E+03 F20 AVG 5.7142E+03 5.8217E+03 5.9156E+03 5.7342E+03 5.8127E+03 5.8962E+03 5.7449E+03 5.7768E+03 5.8604E+03 5.8903E+03 STD 7.1365E+02 5.4117E+02 4.7893E+02 6.2403E+02 5.9272E+02 6.9267E+02 4.9619E+02 6.2496E+02 6.0946E+02 5.7183E+02 F21 AVG 2.8591E+03 2.8848E+03 2.8402E+03 2.8527E+03 2.8395E+03 2.8159E+03 2.8506E+03 2.8605E+03 2.8491E+03 2.8439E+03 STD 8.3374E+01 8.6637E+01 9.0731E+01 6.6941E+01 6.3448E+01 7.0710E+01 6.8368E+01 7.0339E+01 8.4844E+01 6.7750E+01 F22 AVG 1.9561E+04 1.9816E+04 1.9006E+04 1.9581E+04 1.9942E+04 1.9496E+04 1.9008E+04 1.9575E+04 1.9592E+04 1.9641E+04 STD 1.5544E+03 1.3078E+03 1.1168E+03 1.3356E+03 1.0210E+03 1.2549E+03 1.3953E+03 1.2213E+03 1.2045E+03 1.2566E+03 F23 AVG 3.5603E+03 3.4257E+03 3.3548E+03 3.3552E+03 3.3650E+03 3.3974E+03 3.3721E+03 3.4187E+03 3.4060E+03 3.3860E+03 STD 1.5644E+02 1.2296E+02 1.0754E+02 1.1808E+02 1.2562E+02 9.9671E+01 9.6089E+01 8.3865E+01 1.0289E+02 9.1434E+01 F24 AVG 4.2245E+03 3.9469E+03 3.9186E+03 3.8312E+03 3.8717E+03 3.8963E+03 3.8794E+03 3.8598E+03 3.8820E+03 3.9165E+03 STD 2.6532E+02 1.5255E+02 1.1589E+02 1.2104E+02 9.8206E+01 9.1552E+01 8.5171E+01 9.6725E+01 1.0909E+02 1.3854E+02 F25 AVG 3.4122E+03 3.3829E+03 3.3928E+03 3.3841E+03 3.4058E+03 3.3778E+03 3.3949E+03 3.4523E+03 3.4345E+03 3.4292E+03 STD 8.2159E+01 9.0518E+01 8.4311E+01 7.5241E+01 7.0072E+01 7.0959E+01 8.6147E+01 7.0201E+01 6.4704E+01 9.7063E+01 F26 AVG 1.2409E+04 1.1709E+04 1.1838E+04 1.1318E+04 1.1759E+04 1.1602E+04 1.1638E+04 1.1524E+04 1.1627E+04 1.1601E+04 STD 1.5653E+03 1.3959E+03 1.1176E+03 8.0358E+02 7.9216E+02 8.5178E+02 8.2102E+02 9.2957E+02 7.6956E+02 7.3029E+02 F27 AVG 3.6624E+03 3.5683E+03 3.5146E+03 3.5022E+03 3.5039E+03 3.5095E+03 3.4707E+03 3.5006E+03 3.4691E+03 3.4735E+03 STD 1.3941E+02 9.1965E+01 6.6825E+01 7.3245E+01 6.6392E+01 8.2823E+01 5.8819E+01 8.0520E+01 7.5749E+01 5.2387E+01 F28 AVG 3.8356E+03 3.8346E+03 3.8423E+03 4.9581E+03 4.5641E+03 6.3805E+03 7.0352E+03 6.9987E+03 6.3417E+03 7.3898E+03 STD 1.9822E+03 1.9816E+03 2.0423E+03 3.8340E+03 3.3078E+03 4.8790E+03 5.1051E+03 5.0252E+03 4.7956E+03 5.2092E+03 F29 AVG 6.7984E+03 6.7590E+03 6.6082E+03 7.0184E+03 7.1578E+03 7.3394E+03 7.6571E+03 7.3985E+03 7.5505E+03 7.1240E+03 STD 7.8595E+02 6.6109E+02 9.8104E+02 9.1907E+02 1.0391E+03 9.4327E+02 8.2898E+02 6.6601E+02 9.8834E+02 9.6735E+02 F30 AVG 1.5572E+04 2.3471E+04 1.4151E+04 1.9994E+04 1.3069E+04 1.2905E+04 2.3037E+04 1.3387E+04 1.2225E+04 1.1408E+04 STD 1.8653E+04 5.1730E+04 6.0027E+03 4.3680E+04 4.8897E+03 5.1675E+03 5.1325E+04 5.3044E+03 4.5179E+03 2.8090E+03 Avg 5.101 5.144 5.014 5.274 5.529 5.617 5.698 5.898 5.952 5.772 Rank 2 3 1 4 5 6 7 9 10 8 Fun . Item . 0.1 . 0.2 . 0.3 . 0.4 . 0.5 . 0.6 . 0.7 . 0.8 . 0.9 . 1 . F1 AVG 6.5678E+03 6.8625E+03 6.1167E+03 9.3720E+03 6.9967E+03 4.1536E+03 7.4378E+03 5.0378E+03 6.7730E+03 7.6799E+03 STD 8.2021E+03 8.4706E+03 6.9894E+03 1.1057E+04 6.9010E+03 4.3847E+03 6.7041E+03 8.2853E+03 8.0858E+03 7.5867E+03 F2 AVG 1.1438E+63 1.5595E+92 2.3026E+113 5.9673E+121 1.0136E+110 1.1121E+112 5.6366E+118 1.6013E+117 4.3998E+118 3.5869E+127 STD 6.1003E+63 8.5417E+92 1.2612E+114 3.2682E+122 3.2050E+110 6.0914E+112 3.0825E+119 6.8836E+117 2.2719E+119 1.9646E+128 F3 AVG 3.4469E+05 4.3270E+05 4.4861E+05 4.7737E+05 4.9535E+05 5.0088E+05 5.0959E+05 5.0138E+05 5.0772E+05 5.0315E+05 STD 6.9251E+04 6.7985E+04 8.3864E+04 9.2438E+04 6.7698E+04 8.2213E+04 7.9418E+04 8.4233E+04 8.7172E+04 8.7118E+04 F4 AVG 6.9799E+02 7.0503E+02 6.8172E+02 7.2623E+02 7.0697E+02 6.9778E+02 7.2539E+02 7.2192E+02 7.3184E+02 7.1329E+02 STD 7.6926E+01 7.2838E+01 6.0623E+01 6.3688E+01 5.4650E+01 5.2304E+01 8.0301E+01 5.4309E+01 5.6784E+01 4.1086E+01 F5 AVG 1.0565E+03 1.0316E+03 1.0399E+03 1.0546E+03 1.0501E+03 1.0662E+03 1.0430E+03 1.0493E+03 1.0624E+03 1.0657E+03 STD 9.3388E+01 7.8835E+01 9.5189E+01 6.9011E+01 4.8211E+01 6.5838E+01 8.9899E+01 7.5206E+01 7.4861E+01 7.1286E+01 F6 AVG 6.3221E+02 6.3025E+02 6.2594E+02 6.2684E+02 6.2672E+02 6.2662E+02 6.2713E+02 6.2578E+02 6.2693E+02 6.2651E+02 STD 9.2044E+00 7.3376E+00 5.6316E+00 7.1253E+00 7.1998E+00 5.7329E+00 6.5618E+00 6.4953E+00 6.4007E+00 7.6934E+00 F7 AVG 2.0341E+03 1.8640E+03 1.9179E+03 1.8731E+03 1.8263E+03 1.9036E+03 1.8299E+03 1.8265E+03 1.8081E+03 1.8022E+03 STD 1.8890E+02 1.7093E+02 1.7772E+02 2.1811E+02 1.6464E+02 1.8945E+02 1.9722E+02 1.7579E+02 1.7865E+02 1.8568E+02 F8 AVG 1.3493E+03 1.3541E+03 1.3390E+03 1.3221E+03 1.3371E+03 1.3344E+03 1.3114E+03 1.3155E+03 1.3427E+03 1.3149E+03 STD 9.3232E+01 9.0337E+01 8.5518E+01 7.0439E+01 8.4618E+01 7.3790E+01 6.7596E+01 6.3629E+01 7.3616E+01 6.9223E+01 F9 AVG 2.3355E+04 2.3255E+04 2.3276E+04 2.2298E+04 2.2078E+04 2.1955E+04 2.2944E+04 2.2029E+04 2.4225E+04 2.1512E+04 STD 4.9870E+03 5.5244E+03 5.7880E+03 5.6531E+03 6.5192E+03 6.5953E+03 8.3271E+03 6.3560E+03 4.4684E+03 5.1996E+03 F10 AVG 1.7563E+04 1.7587E+04 1.7489E+04 1.7470E+04 1.7499E+04 1.7565E+04 1.7699E+04 1.7344E+04 1.7332E+04 1.7650E+04 STD 1.2993E+03 1.0930E+03 1.1644E+03 1.3116E+03 1.2551E+03 1.0060E+03 1.1170E+03 9.4689E+02 1.2942E+03 9.3811E+02 F11 AVG 3.1015E+03 2.7797E+03 3.3285E+03 7.1500E+03 1.0524E+04 1.2914E+04 1.4608E+04 1.8379E+04 1.7439E+04 1.6696E+04 STD 4.1772E+02 3.6048E+02 7.4831E+02 3.4018E+03 5.0358E+03 9.8060E+03 8.9784E+03 9.0064E+03 9.5436E+03 7.8208E+03 F12 AVG 3.0392E+06 3.5343E+06 7.7886E+06 1.2902E+07 1.0568E+07 1.1755E+07 1.3762E+07 1.2837E+07 1.8425E+07 1.9415E+07 STD 2.7736E+06 1.5396E+06 1.0041E+07 2.4047E+07 1.0212E+07 1.5811E+07 1.5010E+07 7.8933E+06 2.6386E+07 3.1848E+07 F13 AVG 1.1429E+04 2.0039E+04 2.2405E+04 2.1040E+04 8.8846E+03 7.5299E+03 7.5430E+03 3.4291E+04 3.5167E+04 1.0307E+04 STD 6.6504E+03 5.5334E+04 7.4811E+04 6.9606E+04 7.7558E+03 4.9626E+03 6.8174E+03 8.6540E+04 1.1057E+05 8.9218E+03 F14 AVG 3.7009E+05 4.5872E+05 5.4713E+05 9.5130E+05 1.1194E+06 1.2031E+06 1.4135E+06 1.7473E+06 1.5874E+06 1.6356E+06 STD 1.8996E+05 3.2004E+05 3.5099E+05 8.5673E+05 2.0043E+06 1.1431E+06 8.1714E+05 1.3958E+06 1.4322E+06 1.4362E+06 F15 AVG 1.1357E+04 1.7487E+04 1.9298E+04 3.0388E+04 2.5430E+04 2.1861E+04 1.2926E+04 7.3377E+03 1.9600E+04 1.3484E+04 STD 2.4883E+04 5.3990E+04 4.9242E+04 8.8647E+04 7.3981E+04 5.6724E+04 4.1984E+04 5.1992E+03 6.7550E+04 4.2563E+04 F16 AVG 5.8838E+03 6.3132E+03 6.4346E+03 6.6993E+03 6.7399E+03 6.6638E+03 6.7826E+03 6.6998E+03 6.8991E+03 6.7041E+03 STD 6.7570E+02 8.8355E+02 1.1585E+03 1.0566E+03 7.8529E+02 6.0425E+02 9.2828E+02 6.6941E+02 8.7126E+02 6.6058E+02 F17 AVG 5.4470E+03 5.9292E+03 5.8696E+03 6.0257E+03 5.9559E+03 5.9322E+03 5.9456E+03 5.9164E+03 5.6954E+03 5.7931E+03 STD 7.3288E+02 6.5981E+02 6.4787E+02 5.7279E+02 7.0255E+02 5.4236E+02 7.2223E+02 5.1422E+02 5.9739E+02 5.8934E+02 F18 AVG 1.1552E+06 2.2813E+06 2.7169E+06 3.5409E+06 4.4954E+06 3.9682E+06 6.6234E+06 6.2897E+06 5.0526E+06 6.4303E+06 STD 6.6917E+05 2.0946E+06 2.4195E+06 2.5261E+06 4.0698E+06 2.6624E+06 4.2223E+06 5.2913E+06 3.6509E+06 4.7915E+06 F19 AVG 8.1991E+03 8.3134E+03 7.7305E+03 8.5784E+03 7.0682E+03 6.5331E+03 6.8235E+03 9.9550E+03 8.9564E+03 7.7808E+03 STD 6.7237E+03 6.8684E+03 6.0332E+03 6.8845E+03 4.7466E+03 4.5654E+03 7.0013E+03 9.7331E+03 8.5027E+03 7.3342E+03 F20 AVG 5.7142E+03 5.8217E+03 5.9156E+03 5.7342E+03 5.8127E+03 5.8962E+03 5.7449E+03 5.7768E+03 5.8604E+03 5.8903E+03 STD 7.1365E+02 5.4117E+02 4.7893E+02 6.2403E+02 5.9272E+02 6.9267E+02 4.9619E+02 6.2496E+02 6.0946E+02 5.7183E+02 F21 AVG 2.8591E+03 2.8848E+03 2.8402E+03 2.8527E+03 2.8395E+03 2.8159E+03 2.8506E+03 2.8605E+03 2.8491E+03 2.8439E+03 STD 8.3374E+01 8.6637E+01 9.0731E+01 6.6941E+01 6.3448E+01 7.0710E+01 6.8368E+01 7.0339E+01 8.4844E+01 6.7750E+01 F22 AVG 1.9561E+04 1.9816E+04 1.9006E+04 1.9581E+04 1.9942E+04 1.9496E+04 1.9008E+04 1.9575E+04 1.9592E+04 1.9641E+04 STD 1.5544E+03 1.3078E+03 1.1168E+03 1.3356E+03 1.0210E+03 1.2549E+03 1.3953E+03 1.2213E+03 1.2045E+03 1.2566E+03 F23 AVG 3.5603E+03 3.4257E+03 3.3548E+03 3.3552E+03 3.3650E+03 3.3974E+03 3.3721E+03 3.4187E+03 3.4060E+03 3.3860E+03 STD 1.5644E+02 1.2296E+02 1.0754E+02 1.1808E+02 1.2562E+02 9.9671E+01 9.6089E+01 8.3865E+01 1.0289E+02 9.1434E+01 F24 AVG 4.2245E+03 3.9469E+03 3.9186E+03 3.8312E+03 3.8717E+03 3.8963E+03 3.8794E+03 3.8598E+03 3.8820E+03 3.9165E+03 STD 2.6532E+02 1.5255E+02 1.1589E+02 1.2104E+02 9.8206E+01 9.1552E+01 8.5171E+01 9.6725E+01 1.0909E+02 1.3854E+02 F25 AVG 3.4122E+03 3.3829E+03 3.3928E+03 3.3841E+03 3.4058E+03 3.3778E+03 3.3949E+03 3.4523E+03 3.4345E+03 3.4292E+03 STD 8.2159E+01 9.0518E+01 8.4311E+01 7.5241E+01 7.0072E+01 7.0959E+01 8.6147E+01 7.0201E+01 6.4704E+01 9.7063E+01 F26 AVG 1.2409E+04 1.1709E+04 1.1838E+04 1.1318E+04 1.1759E+04 1.1602E+04 1.1638E+04 1.1524E+04 1.1627E+04 1.1601E+04 STD 1.5653E+03 1.3959E+03 1.1176E+03 8.0358E+02 7.9216E+02 8.5178E+02 8.2102E+02 9.2957E+02 7.6956E+02 7.3029E+02 F27 AVG 3.6624E+03 3.5683E+03 3.5146E+03 3.5022E+03 3.5039E+03 3.5095E+03 3.4707E+03 3.5006E+03 3.4691E+03 3.4735E+03 STD 1.3941E+02 9.1965E+01 6.6825E+01 7.3245E+01 6.6392E+01 8.2823E+01 5.8819E+01 8.0520E+01 7.5749E+01 5.2387E+01 F28 AVG 3.8356E+03 3.8346E+03 3.8423E+03 4.9581E+03 4.5641E+03 6.3805E+03 7.0352E+03 6.9987E+03 6.3417E+03 7.3898E+03 STD 1.9822E+03 1.9816E+03 2.0423E+03 3.8340E+03 3.3078E+03 4.8790E+03 5.1051E+03 5.0252E+03 4.7956E+03 5.2092E+03 F29 AVG 6.7984E+03 6.7590E+03 6.6082E+03 7.0184E+03 7.1578E+03 7.3394E+03 7.6571E+03 7.3985E+03 7.5505E+03 7.1240E+03 STD 7.8595E+02 6.6109E+02 9.8104E+02 9.1907E+02 1.0391E+03 9.4327E+02 8.2898E+02 6.6601E+02 9.8834E+02 9.6735E+02 F30 AVG 1.5572E+04 2.3471E+04 1.4151E+04 1.9994E+04 1.3069E+04 1.2905E+04 2.3037E+04 1.3387E+04 1.2225E+04 1.1408E+04 STD 1.8653E+04 5.1730E+04 6.0027E+03 4.3680E+04 4.8897E+03 5.1675E+03 5.1325E+04 5.3044E+03 4.5179E+03 2.8090E+03 Avg 5.101 5.144 5.014 5.274 5.529 5.617 5.698 5.898 5.952 5.772 Rank 2 3 1 4 5 6 7 9 10 8 Open in new tab Table A5: The relevant experimental results of the size of the archive. Fun . Item . 2 . 3 . 4 . 5 . 6 . 7 . 8 . F1 AVG 7.1804E+09 1.0104E+04 6.5408E+03 8.2055E+03 1.0053E+04 6.2719E+03 7.1812E+03 STD 5.4088E+09 1.3565E+04 7.3344E+03 1.2296E+04 1.4234E+04 5.6768E+03 9.3133E+03 F2 AVG 1.6879E+117 4.1155E+102 2.9505E+84 2.0344E+71 3.9933E+68 6.0119E+62 1.9875E+108 STD 9.1480E+117 2.2540E+103 1.6161E+85 1.1142E+72 2.1872E+69 2.8414E+63 1.0886E+109 F3 AVG 8.0614E+05 3.2088E+05 1.7117E+05 2.4094E+05 3.0007E+05 3.4393E+05 4.2434E+05 STD 1.3236E+05 1.6731E+05 5.2316E+04 6.5200E+04 6.8758E+04 9.4540E+04 8.1802E+04 F4 AVG 1.6091E+03 8.7567E+02 7.8847E+02 7.4569E+02 7.4751E+02 6.9740E+02 6.9020E+02 STD 3.6239E+02 1.5055E+02 9.3875E+01 8.9137E+01 7.9240E+01 6.8406E+01 6.1617E+01 F5 AVG 1.3360E+03 1.2051E+03 1.1313E+03 1.0797E+03 1.1001E+03 1.0685E+03 1.0845E+03 STD 9.0122E+01 7.5637E+01 7.8424E+01 6.6965E+01 9.2841E+01 7.5740E+01 1.0163E+02 F6 AVG 6.5957E+02 6.5151E+02 6.4563E+02 6.3645E+02 6.3036E+02 6.2871E+02 6.2948E+02 STD 3.5052E+00 4.1109E+00 4.4569E+00 6.8871E+00 6.7447E+00 7.2641E+00 8.0682E+00 F7 AVG 3.0663E+03 2.6014E+03 2.3913E+03 2.1716E+03 2.0881E+03 2.0554E+03 2.0082E+03 STD 2.0101E+02 1.6121E+02 1.9519E+02 1.9221E+02 2.5886E+02 1.8246E+02 1.8334E+02 F8 AVG 1.7448E+03 1.5844E+03 1.4598E+03 1.3876E+03 1.3995E+03 1.3716E+03 1.3755E+03 STD 1.0279E+02 1.0661E+02 8.2951E+01 9.3012E+01 1.3786E+02 8.2917E+01 7.9233E+01 F9 AVG 2.4590E+04 2.3007E+04 2.3722E+04 2.2598E+04 2.3260E+04 2.2611E+04 2.2596E+04 STD 3.0034E+03 3.3783E+03 4.5861E+03 2.7892E+03 4.3199E+03 4.0715E+03 4.4909E+03 F10 AVG 1.6598E+04 1.5804E+04 1.6329E+04 1.7291E+04 1.6833E+04 1.7532E+04 1.7258E+04 STD 1.7383E+03 1.5440E+03 1.7496E+03 1.4613E+03 1.0571E+03 1.3410E+03 1.3224E+03 F11 AVG 9.3035E+04 2.7613E+04 1.5496E+04 7.1644E+03 4.4574E+03 3.5331E+03 3.0142E+03 STD 3.4925E+04 1.2544E+04 9.2731E+03 6.4614E+03 2.2261E+03 8.0321E+02 5.3579E+02 F12 AVG 2.7758E+08 1.9218E+07 1.1814E+07 9.2409E+06 5.3477E+06 7.5569E+06 6.4178E+06 STD 4.3611E+08 2.4459E+07 1.6710E+07 1.3488E+07 4.8010E+06 1.4285E+07 7.3343E+06 F13 AVG 1.1184E+05 4.3365E+04 2.8164E+04 1.3749E+04 1.5457E+04 2.3299E+04 9.4844E+03 STD 3.6282E+04 1.9678E+04 6.0474E+04 6.8155E+03 8.3252E+03 6.5433E+04 6.9073E+03 F14 AVG 1.7751E+06 1.4709E+06 1.0776E+06 6.7843E+05 4.3442E+05 3.8413E+05 5.5463E+05 STD 1.2208E+06 7.7293E+05 8.1086E+05 5.3584E+05 2.0929E+05 1.9925E+05 5.6678E+05 F15 AVG 7.4718E+04 4.2772E+04 2.3866E+04 2.0771E+04 2.9160E+04 1.2730E+04 7.1162E+03 STD 5.5953E+04 8.0024E+04 7.0886E+04 4.8992E+04 8.5171E+04 4.0644E+04 5.5599E+03 F16 AVG 6.4497E+03 6.1165E+03 5.7215E+03 5.6920E+03 5.8327E+03 6.1294E+03 6.4905E+03 STD 8.9718E+02 8.0772E+02 7.4823E+02 8.6622E+02 9.5451E+02 9.9792E+02 1.1286E+03 F17 AVG 6.4634E+03 6.2552E+03 5.6976E+03 5.2670E+03 5.4252E+03 5.4645E+03 5.5989E+03 STD 7.9534E+02 8.1125E+02 7.8391E+02 6.3973E+02 5.9873E+02 7.9492E+02 7.4707E+02 F18 AVG 1.8836E+06 1.6637E+06 1.1950E+06 1.4119E+06 1.3872E+06 1.7249E+06 1.6466E+06 STD 9.9606E+05 9.2139E+05 5.6851E+05 5.8794E+05 7.9922E+05 1.4242E+06 7.9161E+05 F19 AVG 1.7701E+04 3.0590E+04 1.1784E+04 1.5925E+04 8.6091E+03 6.3173E+03 5.9897E+03 STD 2.1471E+04 1.3584E+05 3.0732E+04 4.4640E+04 6.5532E+03 5.8492E+03 5.0915E+03 F20 AVG 5.7008E+03 5.9165E+03 5.4408E+03 5.8210E+03 5.6719E+03 5.6949E+03 5.9163E+03 STD 6.7873E+02 6.3756E+02 6.3485E+02 5.3380E+02 5.4259E+02 5.9978E+02 5.5936E+02 F21 AVG 3.6475E+03 3.1866E+03 3.0035E+03 2.9271E+03 2.8429E+03 2.8806E+03 2.8411E+03 STD 3.4330E+02 1.5336E+02 9.4240E+01 9.3150E+01 8.9407E+01 8.1129E+01 8.5704E+01 F22 AVG 1.9082E+04 1.8131E+04 1.9082E+04 1.9121E+04 1.9529E+04 1.9292E+04 1.9414E+04 STD 1.5800E+03 1.7786E+03 1.5116E+03 1.7940E+03 1.3685E+03 1.4222E+03 1.2100E+03 F23 AVG 4.5578E+03 4.0427E+03 3.8404E+03 3.6848E+03 3.6228E+03 3.5075E+03 3.4353E+03 STD 2.5970E+02 1.9348E+02 1.8389E+02 1.9275E+02 1.6264E+02 1.4044E+02 1.3760E+02 F24 AVG 6.2129E+03 5.1950E+03 4.6864E+03 4.4478E+03 4.1874E+03 4.0361E+03 3.9765E+03 STD 5.3096E+02 4.6604E+02 2.9826E+02 3.0567E+02 2.1216E+02 1.7093E+02 1.5981E+02 F25 AVG 4.5951E+03 3.7186E+03 3.5412E+03 3.4841E+03 3.4402E+03 3.4081E+03 3.3902E+03 STD 4.0886E+02 1.4575E+02 1.4991E+02 8.0945E+01 8.7436E+01 8.6940E+01 9.0235E+01 F26 AVG 2.7687E+04 2.0863E+04 1.6056E+04 1.4387E+04 1.3073E+04 1.1802E+04 1.1667E+04 STD 3.2515E+03 3.5464E+03 2.4413E+03 1.9014E+03 1.5027E+03 1.3063E+03 1.5034E+03 F27 AVG 5.1033E+03 4.0649E+03 3.8027E+03 3.7210E+03 3.6330E+03 3.5986E+03 3.5919E+03 STD 9.5742E+02 2.2184E+02 1.7896E+02 1.4162E+02 1.1269E+02 1.2315E+02 1.2182E+02 F28 AVG 5.7850E+03 3.7325E+03 3.5575E+03 3.5249E+03 3.4870E+03 3.4948E+03 3.8440E+03 STD 8.5128E+02 1.7265E+02 6.4074E+01 5.1161E+01 4.8977E+01 4.6886E+01 2.0245E+03 F29 AVG 8.6416E+03 7.7365E+03 7.6587E+03 7.1360E+03 6.9983E+03 6.7558E+03 6.7501E+03 STD 7.0136E+02 7.4767E+02 6.9488E+02 5.3438E+02 7.1650E+02 5.1479E+02 7.4395E+02 F30 AVG 1.8430E+06 1.4989E+05 1.1158E+05 1.7986E+04 4.8317E+04 1.4804E+04 1.2655E+04 STD 1.4094E+06 1.7872E+05 1.8724E+05 6.8275E+03 1.0530E+05 5.9214E+03 5.4702E+03 Avg 11.573 9.394 7.680 6.818 6.250 5.747 5.757 Rank 14 12 10 8 6 1 3 Fun Item 9 10 11 12 13 m 2*m F1 AVG 9.0369E+03 6.9012E+03 6.1618E+03 6.0730E+03 8.1622E+03 7.3594E+08 1.0836E+10 STD 1.0548E+04 9.7268E+03 7.0016E+03 6.9873E+03 1.2778E+04 7.2589E+08 2.0999E+10 F2 AVG 2.2865E+99 1.3053E+101 4.9971E+110 2.5328E+127 3.2047E+120 4.4023E+136 6.9465E+146 STD 1.2524E+100 7.1268E+101 2.4864E+111 1.3873E+128 1.7530E+121 2.4108E+137 3.8029E+147 F3 AVG 4.3394E+05 4.3811E+05 5.0447E+05 5.1956E+05 5.4894E+05 6.9552E+05 8.2104E+05 STD 9.4997E+04 9.8550E+04 7.7476E+04 1.0707E+05 8.7441E+04 7.4016E+04 1.1296E+05 F4 AVG 6.9430E+02 7.1122E+02 6.9581E+02 7.1864E+02 7.4141E+02 1.2427E+03 2.7616E+03 STD 4.9275E+01 5.8479E+01 5.3181E+01 5.9310E+01 6.3111E+01 2.8544E+02 9.6750E+02 F5 AVG 1.0490E+03 1.0279E+03 1.0651E+03 1.0593E+03 1.0710E+03 1.1301E+03 1.3305E+03 STD 6.0311E+01 7.9387E+01 8.8449E+01 6.0890E+01 7.9501E+01 8.1460E+01 1.1592E+02 F6 AVG 6.2513E+02 6.2632E+02 6.2345E+02 6.2421E+02 6.2343E+02 6.3338E+02 6.4977E+02 STD 1.0386E+01 7.3776E+00 5.0661E+00 6.3056E+00 6.0107E+00 7.7141E+00 6.9125E+00 F7 AVG 1.9345E+03 1.9153E+03 1.8145E+03 1.8949E+03 1.8031E+03 1.6713E+03 1.5460E+03 STD 1.7240E+02 1.6694E+02 1.7511E+02 1.3402E+02 2.0136E+02 1.6895E+02 1.5674E+02 F8 AVG 1.3852E+03 1.3383E+03 1.3331E+03 1.3165E+03 1.3348E+03 1.4242E+03 1.6381E+03 STD 9.8592E+01 8.7670E+01 5.9035E+01 1.0280E+02 6.1706E+01 7.8331E+01 9.3751E+01 F9 AVG 2.3696E+04 2.3422E+04 2.2924E+04 2.3198E+04 2.3096E+04 2.7227E+04 3.4603E+04 STD 6.2334E+03 5.4137E+03 9.2735E+03 7.2277E+03 7.7298E+03 9.1945E+03 8.2326E+03 F10 AVG 1.7045E+04 1.7248E+04 1.7642E+04 1.7251E+04 1.7854E+04 1.8543E+04 1.9698E+04 STD 1.3249E+03 1.4194E+03 9.6921E+02 1.3424E+03 1.1929E+03 1.0228E+03 1.0305E+03 F11 AVG 3.1737E+03 4.6846E+03 8.3573E+03 1.2829E+04 2.3009E+04 7.6195E+04 1.3919E+05 STD 8.3708E+02 3.7793E+03 6.0282E+03 8.5488E+03 8.7973E+03 2.1956E+04 3.1991E+04 F12 AVG 1.0143E+07 5.8599E+06 5.8153E+06 1.5087E+07 1.5085E+07 2.4365E+08 4.1569E+09 STD 1.8458E+07 8.0539E+06 6.3937E+06 2.2991E+07 1.0279E+07 2.5523E+08 1.9486E+09 F13 AVG 2.2684E+04 2.4871E+04 8.4200E+03 2.1854E+04 1.1785E+04 4.2100E+04 4.2468E+04 STD 6.5593E+04 7.4253E+04 7.5411E+03 7.3280E+04 1.0431E+04 1.2002E+05 2.4654E+04 F14 AVG 7.6569E+05 5.1922E+05 7.4413E+05 1.2964E+06 1.8241E+06 6.6127E+06 1.1347E+07 STD 1.0378E+06 5.9510E+05 5.4741E+05 1.1490E+06 1.2247E+06 4.0234E+06 7.3522E+06 F15 AVG 1.6046E+04 2.1950E+04 1.6727E+04 1.6701E+04 1.4987E+04 1.7684E+04 1.0649E+04 STD 4.7291E+04 6.6229E+04 5.1893E+04 4.7647E+04 5.3897E+04 5.4946E+04 1.0282E+04 F16 AVG 6.2705E+03 6.4812E+03 6.6390E+03 6.5394E+03 6.6394E+03 7.2110E+03 7.4178E+03 STD 1.0306E+03 7.8505E+02 9.7237E+02 7.3847E+02 6.1689E+02 7.2422E+02 6.2755E+02 F17 AVG 5.7245E+03 5.8350E+03 5.8167E+03 5.8920E+03 5.6917E+03 5.9155E+03 6.1354E+03 STD 8.0389E+02 6.9572E+02 5.7676E+02 6.5784E+02 5.9097E+02 5.6716E+02 6.8967E+02 F18 AVG 1.9576E+06 2.7016E+06 3.5492E+06 4.4467E+06 6.4497E+06 1.2330E+07 1.6580E+07 STD 1.0148E+06 1.4311E+06 1.9187E+06 3.0298E+06 5.5555E+06 9.2955E+06 1.0307E+07 F19 AVG 8.6680E+03 7.1669E+03 8.1501E+03 1.4831E+04 9.2364E+03 1.4771E+04 4.5532E+05 STD 6.3252E+03 8.6001E+03 4.9781E+03 3.6482E+04 8.9352E+03 1.3781E+04 2.3511E+06 F20 AVG 5.6925E+03 5.9227E+03 5.9940E+03 5.7750E+03 5.9300E+03 5.9179E+03 6.0097E+03 STD 5.2418E+02 5.6020E+02 5.5003E+02 5.2303E+02 5.2844E+02 6.5216E+02 5.3580E+02 F21 AVG 2.8490E+03 2.8571E+03 2.8407E+03 2.8638E+03 2.8844E+03 2.9974E+03 3.2289E+03 STD 8.8457E+01 5.9545E+01 7.2296E+01 6.5192E+01 7.9936E+01 8.0000E+01 7.0348E+01 F22 AVG 1.9806E+04 1.9561E+04 1.9374E+04 1.9775E+04 1.9444E+04 2.0563E+04 2.2546E+04 STD 1.1720E+03 9.8467E+02 1.3263E+03 1.2058E+03 1.0574E+03 9.7573E+02 1.1730E+03 F23 AVG 3.3586E+03 3.3678E+03 3.3792E+03 3.3900E+03 3.4362E+03 3.5215E+03 3.6047E+03 STD 1.1409E+02 1.0621E+02 1.2973E+02 1.1469E+02 9.2403E+01 6.1049E+01 5.2735E+01 F24 AVG 3.9112E+03 3.9717E+03 3.9025E+03 3.8697E+03 3.8859E+03 3.9046E+03 4.0170E+03 STD 1.8323E+02 1.7559E+02 1.2429E+02 8.7540E+01 1.0458E+02 6.1411E+01 5.0683E+01 F25 AVG 3.3737E+03 3.3870E+03 3.3758E+03 3.3933E+03 3.4355E+03 3.8943E+03 4.9258E+03 STD 7.4242E+01 7.0720E+01 8.5621E+01 7.8764E+01 7.2810E+01 2.6210E+02 6.8592E+02 F26 AVG 1.2001E+04 1.1607E+04 1.1624E+04 1.1721E+04 1.2146E+04 1.2858E+04 1.3813E+04 STD 1.4118E+03 9.1440E+02 6.3715E+02 9.0176E+02 6.6466E+02 8.1247E+02 5.5354E+02 F27 AVG 3.5402E+03 3.5656E+03 3.4943E+03 3.5355E+03 3.4929E+03 3.4235E+03 3.4845E+03 STD 1.0721E+02 8.3709E+01 6.3851E+01 7.1976E+01 6.5933E+01 3.8909E+01 5.6213E+01 F28 AVG 4.6494E+03 4.8960E+03 4.5710E+03 5.3127E+03 7.1886E+03 1.3257E+04 1.5074E+04 STD 3.5966E+03 3.6935E+03 3.3636E+03 4.1910E+03 5.2921E+03 3.3913E+03 9.4930E+02 F29 AVG 6.5446E+03 6.5298E+03 6.8516E+03 7.0426E+03 7.3777E+03 7.8648E+03 8.2344E+03 STD 9.5339E+02 9.1810E+02 1.1785E+03 8.7025E+02 9.4837E+02 6.9074E+02 6.4989E+02 F30 AVG 1.8891E+04 1.4259E+04 1.3664E+04 1.4264E+04 1.1200E+04 3.2763E+04 3.4358E+05 STD 2.1036E+04 5.5468E+03 6.0615E+03 6.4128E+03 4.5468E+03 1.3235E+04 1.6077E+05 Avg 5.753 5.833 6.083 6.464 6.894 9.372 11.380 Rank 2 4 5 7 9 11 13 Fun . Item . 2 . 3 . 4 . 5 . 6 . 7 . 8 . F1 AVG 7.1804E+09 1.0104E+04 6.5408E+03 8.2055E+03 1.0053E+04 6.2719E+03 7.1812E+03 STD 5.4088E+09 1.3565E+04 7.3344E+03 1.2296E+04 1.4234E+04 5.6768E+03 9.3133E+03 F2 AVG 1.6879E+117 4.1155E+102 2.9505E+84 2.0344E+71 3.9933E+68 6.0119E+62 1.9875E+108 STD 9.1480E+117 2.2540E+103 1.6161E+85 1.1142E+72 2.1872E+69 2.8414E+63 1.0886E+109 F3 AVG 8.0614E+05 3.2088E+05 1.7117E+05 2.4094E+05 3.0007E+05 3.4393E+05 4.2434E+05 STD 1.3236E+05 1.6731E+05 5.2316E+04 6.5200E+04 6.8758E+04 9.4540E+04 8.1802E+04 F4 AVG 1.6091E+03 8.7567E+02 7.8847E+02 7.4569E+02 7.4751E+02 6.9740E+02 6.9020E+02 STD 3.6239E+02 1.5055E+02 9.3875E+01 8.9137E+01 7.9240E+01 6.8406E+01 6.1617E+01 F5 AVG 1.3360E+03 1.2051E+03 1.1313E+03 1.0797E+03 1.1001E+03 1.0685E+03 1.0845E+03 STD 9.0122E+01 7.5637E+01 7.8424E+01 6.6965E+01 9.2841E+01 7.5740E+01 1.0163E+02 F6 AVG 6.5957E+02 6.5151E+02 6.4563E+02 6.3645E+02 6.3036E+02 6.2871E+02 6.2948E+02 STD 3.5052E+00 4.1109E+00 4.4569E+00 6.8871E+00 6.7447E+00 7.2641E+00 8.0682E+00 F7 AVG 3.0663E+03 2.6014E+03 2.3913E+03 2.1716E+03 2.0881E+03 2.0554E+03 2.0082E+03 STD 2.0101E+02 1.6121E+02 1.9519E+02 1.9221E+02 2.5886E+02 1.8246E+02 1.8334E+02 F8 AVG 1.7448E+03 1.5844E+03 1.4598E+03 1.3876E+03 1.3995E+03 1.3716E+03 1.3755E+03 STD 1.0279E+02 1.0661E+02 8.2951E+01 9.3012E+01 1.3786E+02 8.2917E+01 7.9233E+01 F9 AVG 2.4590E+04 2.3007E+04 2.3722E+04 2.2598E+04 2.3260E+04 2.2611E+04 2.2596E+04 STD 3.0034E+03 3.3783E+03 4.5861E+03 2.7892E+03 4.3199E+03 4.0715E+03 4.4909E+03 F10 AVG 1.6598E+04 1.5804E+04 1.6329E+04 1.7291E+04 1.6833E+04 1.7532E+04 1.7258E+04 STD 1.7383E+03 1.5440E+03 1.7496E+03 1.4613E+03 1.0571E+03 1.3410E+03 1.3224E+03 F11 AVG 9.3035E+04 2.7613E+04 1.5496E+04 7.1644E+03 4.4574E+03 3.5331E+03 3.0142E+03 STD 3.4925E+04 1.2544E+04 9.2731E+03 6.4614E+03 2.2261E+03 8.0321E+02 5.3579E+02 F12 AVG 2.7758E+08 1.9218E+07 1.1814E+07 9.2409E+06 5.3477E+06 7.5569E+06 6.4178E+06 STD 4.3611E+08 2.4459E+07 1.6710E+07 1.3488E+07 4.8010E+06 1.4285E+07 7.3343E+06 F13 AVG 1.1184E+05 4.3365E+04 2.8164E+04 1.3749E+04 1.5457E+04 2.3299E+04 9.4844E+03 STD 3.6282E+04 1.9678E+04 6.0474E+04 6.8155E+03 8.3252E+03 6.5433E+04 6.9073E+03 F14 AVG 1.7751E+06 1.4709E+06 1.0776E+06 6.7843E+05 4.3442E+05 3.8413E+05 5.5463E+05 STD 1.2208E+06 7.7293E+05 8.1086E+05 5.3584E+05 2.0929E+05 1.9925E+05 5.6678E+05 F15 AVG 7.4718E+04 4.2772E+04 2.3866E+04 2.0771E+04 2.9160E+04 1.2730E+04 7.1162E+03 STD 5.5953E+04 8.0024E+04 7.0886E+04 4.8992E+04 8.5171E+04 4.0644E+04 5.5599E+03 F16 AVG 6.4497E+03 6.1165E+03 5.7215E+03 5.6920E+03 5.8327E+03 6.1294E+03 6.4905E+03 STD 8.9718E+02 8.0772E+02 7.4823E+02 8.6622E+02 9.5451E+02 9.9792E+02 1.1286E+03 F17 AVG 6.4634E+03 6.2552E+03 5.6976E+03 5.2670E+03 5.4252E+03 5.4645E+03 5.5989E+03 STD 7.9534E+02 8.1125E+02 7.8391E+02 6.3973E+02 5.9873E+02 7.9492E+02 7.4707E+02 F18 AVG 1.8836E+06 1.6637E+06 1.1950E+06 1.4119E+06 1.3872E+06 1.7249E+06 1.6466E+06 STD 9.9606E+05 9.2139E+05 5.6851E+05 5.8794E+05 7.9922E+05 1.4242E+06 7.9161E+05 F19 AVG 1.7701E+04 3.0590E+04 1.1784E+04 1.5925E+04 8.6091E+03 6.3173E+03 5.9897E+03 STD 2.1471E+04 1.3584E+05 3.0732E+04 4.4640E+04 6.5532E+03 5.8492E+03 5.0915E+03 F20 AVG 5.7008E+03 5.9165E+03 5.4408E+03 5.8210E+03 5.6719E+03 5.6949E+03 5.9163E+03 STD 6.7873E+02 6.3756E+02 6.3485E+02 5.3380E+02 5.4259E+02 5.9978E+02 5.5936E+02 F21 AVG 3.6475E+03 3.1866E+03 3.0035E+03 2.9271E+03 2.8429E+03 2.8806E+03 2.8411E+03 STD 3.4330E+02 1.5336E+02 9.4240E+01 9.3150E+01 8.9407E+01 8.1129E+01 8.5704E+01 F22 AVG 1.9082E+04 1.8131E+04 1.9082E+04 1.9121E+04 1.9529E+04 1.9292E+04 1.9414E+04 STD 1.5800E+03 1.7786E+03 1.5116E+03 1.7940E+03 1.3685E+03 1.4222E+03 1.2100E+03 F23 AVG 4.5578E+03 4.0427E+03 3.8404E+03 3.6848E+03 3.6228E+03 3.5075E+03 3.4353E+03 STD 2.5970E+02 1.9348E+02 1.8389E+02 1.9275E+02 1.6264E+02 1.4044E+02 1.3760E+02 F24 AVG 6.2129E+03 5.1950E+03 4.6864E+03 4.4478E+03 4.1874E+03 4.0361E+03 3.9765E+03 STD 5.3096E+02 4.6604E+02 2.9826E+02 3.0567E+02 2.1216E+02 1.7093E+02 1.5981E+02 F25 AVG 4.5951E+03 3.7186E+03 3.5412E+03 3.4841E+03 3.4402E+03 3.4081E+03 3.3902E+03 STD 4.0886E+02 1.4575E+02 1.4991E+02 8.0945E+01 8.7436E+01 8.6940E+01 9.0235E+01 F26 AVG 2.7687E+04 2.0863E+04 1.6056E+04 1.4387E+04 1.3073E+04 1.1802E+04 1.1667E+04 STD 3.2515E+03 3.5464E+03 2.4413E+03 1.9014E+03 1.5027E+03 1.3063E+03 1.5034E+03 F27 AVG 5.1033E+03 4.0649E+03 3.8027E+03 3.7210E+03 3.6330E+03 3.5986E+03 3.5919E+03 STD 9.5742E+02 2.2184E+02 1.7896E+02 1.4162E+02 1.1269E+02 1.2315E+02 1.2182E+02 F28 AVG 5.7850E+03 3.7325E+03 3.5575E+03 3.5249E+03 3.4870E+03 3.4948E+03 3.8440E+03 STD 8.5128E+02 1.7265E+02 6.4074E+01 5.1161E+01 4.8977E+01 4.6886E+01 2.0245E+03 F29 AVG 8.6416E+03 7.7365E+03 7.6587E+03 7.1360E+03 6.9983E+03 6.7558E+03 6.7501E+03 STD 7.0136E+02 7.4767E+02 6.9488E+02 5.3438E+02 7.1650E+02 5.1479E+02 7.4395E+02 F30 AVG 1.8430E+06 1.4989E+05 1.1158E+05 1.7986E+04 4.8317E+04 1.4804E+04 1.2655E+04 STD 1.4094E+06 1.7872E+05 1.8724E+05 6.8275E+03 1.0530E+05 5.9214E+03 5.4702E+03 Avg 11.573 9.394 7.680 6.818 6.250 5.747 5.757 Rank 14 12 10 8 6 1 3 Fun Item 9 10 11 12 13 m 2*m F1 AVG 9.0369E+03 6.9012E+03 6.1618E+03 6.0730E+03 8.1622E+03 7.3594E+08 1.0836E+10 STD 1.0548E+04 9.7268E+03 7.0016E+03 6.9873E+03 1.2778E+04 7.2589E+08 2.0999E+10 F2 AVG 2.2865E+99 1.3053E+101 4.9971E+110 2.5328E+127 3.2047E+120 4.4023E+136 6.9465E+146 STD 1.2524E+100 7.1268E+101 2.4864E+111 1.3873E+128 1.7530E+121 2.4108E+137 3.8029E+147 F3 AVG 4.3394E+05 4.3811E+05 5.0447E+05 5.1956E+05 5.4894E+05 6.9552E+05 8.2104E+05 STD 9.4997E+04 9.8550E+04 7.7476E+04 1.0707E+05 8.7441E+04 7.4016E+04 1.1296E+05 F4 AVG 6.9430E+02 7.1122E+02 6.9581E+02 7.1864E+02 7.4141E+02 1.2427E+03 2.7616E+03 STD 4.9275E+01 5.8479E+01 5.3181E+01 5.9310E+01 6.3111E+01 2.8544E+02 9.6750E+02 F5 AVG 1.0490E+03 1.0279E+03 1.0651E+03 1.0593E+03 1.0710E+03 1.1301E+03 1.3305E+03 STD 6.0311E+01 7.9387E+01 8.8449E+01 6.0890E+01 7.9501E+01 8.1460E+01 1.1592E+02 F6 AVG 6.2513E+02 6.2632E+02 6.2345E+02 6.2421E+02 6.2343E+02 6.3338E+02 6.4977E+02 STD 1.0386E+01 7.3776E+00 5.0661E+00 6.3056E+00 6.0107E+00 7.7141E+00 6.9125E+00 F7 AVG 1.9345E+03 1.9153E+03 1.8145E+03 1.8949E+03 1.8031E+03 1.6713E+03 1.5460E+03 STD 1.7240E+02 1.6694E+02 1.7511E+02 1.3402E+02 2.0136E+02 1.6895E+02 1.5674E+02 F8 AVG 1.3852E+03 1.3383E+03 1.3331E+03 1.3165E+03 1.3348E+03 1.4242E+03 1.6381E+03 STD 9.8592E+01 8.7670E+01 5.9035E+01 1.0280E+02 6.1706E+01 7.8331E+01 9.3751E+01 F9 AVG 2.3696E+04 2.3422E+04 2.2924E+04 2.3198E+04 2.3096E+04 2.7227E+04 3.4603E+04 STD 6.2334E+03 5.4137E+03 9.2735E+03 7.2277E+03 7.7298E+03 9.1945E+03 8.2326E+03 F10 AVG 1.7045E+04 1.7248E+04 1.7642E+04 1.7251E+04 1.7854E+04 1.8543E+04 1.9698E+04 STD 1.3249E+03 1.4194E+03 9.6921E+02 1.3424E+03 1.1929E+03 1.0228E+03 1.0305E+03 F11 AVG 3.1737E+03 4.6846E+03 8.3573E+03 1.2829E+04 2.3009E+04 7.6195E+04 1.3919E+05 STD 8.3708E+02 3.7793E+03 6.0282E+03 8.5488E+03 8.7973E+03 2.1956E+04 3.1991E+04 F12 AVG 1.0143E+07 5.8599E+06 5.8153E+06 1.5087E+07 1.5085E+07 2.4365E+08 4.1569E+09 STD 1.8458E+07 8.0539E+06 6.3937E+06 2.2991E+07 1.0279E+07 2.5523E+08 1.9486E+09 F13 AVG 2.2684E+04 2.4871E+04 8.4200E+03 2.1854E+04 1.1785E+04 4.2100E+04 4.2468E+04 STD 6.5593E+04 7.4253E+04 7.5411E+03 7.3280E+04 1.0431E+04 1.2002E+05 2.4654E+04 F14 AVG 7.6569E+05 5.1922E+05 7.4413E+05 1.2964E+06 1.8241E+06 6.6127E+06 1.1347E+07 STD 1.0378E+06 5.9510E+05 5.4741E+05 1.1490E+06 1.2247E+06 4.0234E+06 7.3522E+06 F15 AVG 1.6046E+04 2.1950E+04 1.6727E+04 1.6701E+04 1.4987E+04 1.7684E+04 1.0649E+04 STD 4.7291E+04 6.6229E+04 5.1893E+04 4.7647E+04 5.3897E+04 5.4946E+04 1.0282E+04 F16 AVG 6.2705E+03 6.4812E+03 6.6390E+03 6.5394E+03 6.6394E+03 7.2110E+03 7.4178E+03 STD 1.0306E+03 7.8505E+02 9.7237E+02 7.3847E+02 6.1689E+02 7.2422E+02 6.2755E+02 F17 AVG 5.7245E+03 5.8350E+03 5.8167E+03 5.8920E+03 5.6917E+03 5.9155E+03 6.1354E+03 STD 8.0389E+02 6.9572E+02 5.7676E+02 6.5784E+02 5.9097E+02 5.6716E+02 6.8967E+02 F18 AVG 1.9576E+06 2.7016E+06 3.5492E+06 4.4467E+06 6.4497E+06 1.2330E+07 1.6580E+07 STD 1.0148E+06 1.4311E+06 1.9187E+06 3.0298E+06 5.5555E+06 9.2955E+06 1.0307E+07 F19 AVG 8.6680E+03 7.1669E+03 8.1501E+03 1.4831E+04 9.2364E+03 1.4771E+04 4.5532E+05 STD 6.3252E+03 8.6001E+03 4.9781E+03 3.6482E+04 8.9352E+03 1.3781E+04 2.3511E+06 F20 AVG 5.6925E+03 5.9227E+03 5.9940E+03 5.7750E+03 5.9300E+03 5.9179E+03 6.0097E+03 STD 5.2418E+02 5.6020E+02 5.5003E+02 5.2303E+02 5.2844E+02 6.5216E+02 5.3580E+02 F21 AVG 2.8490E+03 2.8571E+03 2.8407E+03 2.8638E+03 2.8844E+03 2.9974E+03 3.2289E+03 STD 8.8457E+01 5.9545E+01 7.2296E+01 6.5192E+01 7.9936E+01 8.0000E+01 7.0348E+01 F22 AVG 1.9806E+04 1.9561E+04 1.9374E+04 1.9775E+04 1.9444E+04 2.0563E+04 2.2546E+04 STD 1.1720E+03 9.8467E+02 1.3263E+03 1.2058E+03 1.0574E+03 9.7573E+02 1.1730E+03 F23 AVG 3.3586E+03 3.3678E+03 3.3792E+03 3.3900E+03 3.4362E+03 3.5215E+03 3.6047E+03 STD 1.1409E+02 1.0621E+02 1.2973E+02 1.1469E+02 9.2403E+01 6.1049E+01 5.2735E+01 F24 AVG 3.9112E+03 3.9717E+03 3.9025E+03 3.8697E+03 3.8859E+03 3.9046E+03 4.0170E+03 STD 1.8323E+02 1.7559E+02 1.2429E+02 8.7540E+01 1.0458E+02 6.1411E+01 5.0683E+01 F25 AVG 3.3737E+03 3.3870E+03 3.3758E+03 3.3933E+03 3.4355E+03 3.8943E+03 4.9258E+03 STD 7.4242E+01 7.0720E+01 8.5621E+01 7.8764E+01 7.2810E+01 2.6210E+02 6.8592E+02 F26 AVG 1.2001E+04 1.1607E+04 1.1624E+04 1.1721E+04 1.2146E+04 1.2858E+04 1.3813E+04 STD 1.4118E+03 9.1440E+02 6.3715E+02 9.0176E+02 6.6466E+02 8.1247E+02 5.5354E+02 F27 AVG 3.5402E+03 3.5656E+03 3.4943E+03 3.5355E+03 3.4929E+03 3.4235E+03 3.4845E+03 STD 1.0721E+02 8.3709E+01 6.3851E+01 7.1976E+01 6.5933E+01 3.8909E+01 5.6213E+01 F28 AVG 4.6494E+03 4.8960E+03 4.5710E+03 5.3127E+03 7.1886E+03 1.3257E+04 1.5074E+04 STD 3.5966E+03 3.6935E+03 3.3636E+03 4.1910E+03 5.2921E+03 3.3913E+03 9.4930E+02 F29 AVG 6.5446E+03 6.5298E+03 6.8516E+03 7.0426E+03 7.3777E+03 7.8648E+03 8.2344E+03 STD 9.5339E+02 9.1810E+02 1.1785E+03 8.7025E+02 9.4837E+02 6.9074E+02 6.4989E+02 F30 AVG 1.8891E+04 1.4259E+04 1.3664E+04 1.4264E+04 1.1200E+04 3.2763E+04 3.4358E+05 STD 2.1036E+04 5.5468E+03 6.0615E+03 6.4128E+03 4.5468E+03 1.3235E+04 1.6077E+05 Avg 5.753 5.833 6.083 6.464 6.894 9.372 11.380 Rank 2 4 5 7 9 11 13 Open in new tab Table A5: The relevant experimental results of the size of the archive. Fun . Item . 2 . 3 . 4 . 5 . 6 . 7 . 8 . F1 AVG 7.1804E+09 1.0104E+04 6.5408E+03 8.2055E+03 1.0053E+04 6.2719E+03 7.1812E+03 STD 5.4088E+09 1.3565E+04 7.3344E+03 1.2296E+04 1.4234E+04 5.6768E+03 9.3133E+03 F2 AVG 1.6879E+117 4.1155E+102 2.9505E+84 2.0344E+71 3.9933E+68 6.0119E+62 1.9875E+108 STD 9.1480E+117 2.2540E+103 1.6161E+85 1.1142E+72 2.1872E+69 2.8414E+63 1.0886E+109 F3 AVG 8.0614E+05 3.2088E+05 1.7117E+05 2.4094E+05 3.0007E+05 3.4393E+05 4.2434E+05 STD 1.3236E+05 1.6731E+05 5.2316E+04 6.5200E+04 6.8758E+04 9.4540E+04 8.1802E+04 F4 AVG 1.6091E+03 8.7567E+02 7.8847E+02 7.4569E+02 7.4751E+02 6.9740E+02 6.9020E+02 STD 3.6239E+02 1.5055E+02 9.3875E+01 8.9137E+01 7.9240E+01 6.8406E+01 6.1617E+01 F5 AVG 1.3360E+03 1.2051E+03 1.1313E+03 1.0797E+03 1.1001E+03 1.0685E+03 1.0845E+03 STD 9.0122E+01 7.5637E+01 7.8424E+01 6.6965E+01 9.2841E+01 7.5740E+01 1.0163E+02 F6 AVG 6.5957E+02 6.5151E+02 6.4563E+02 6.3645E+02 6.3036E+02 6.2871E+02 6.2948E+02 STD 3.5052E+00 4.1109E+00 4.4569E+00 6.8871E+00 6.7447E+00 7.2641E+00 8.0682E+00 F7 AVG 3.0663E+03 2.6014E+03 2.3913E+03 2.1716E+03 2.0881E+03 2.0554E+03 2.0082E+03 STD 2.0101E+02 1.6121E+02 1.9519E+02 1.9221E+02 2.5886E+02 1.8246E+02 1.8334E+02 F8 AVG 1.7448E+03 1.5844E+03 1.4598E+03 1.3876E+03 1.3995E+03 1.3716E+03 1.3755E+03 STD 1.0279E+02 1.0661E+02 8.2951E+01 9.3012E+01 1.3786E+02 8.2917E+01 7.9233E+01 F9 AVG 2.4590E+04 2.3007E+04 2.3722E+04 2.2598E+04 2.3260E+04 2.2611E+04 2.2596E+04 STD 3.0034E+03 3.3783E+03 4.5861E+03 2.7892E+03 4.3199E+03 4.0715E+03 4.4909E+03 F10 AVG 1.6598E+04 1.5804E+04 1.6329E+04 1.7291E+04 1.6833E+04 1.7532E+04 1.7258E+04 STD 1.7383E+03 1.5440E+03 1.7496E+03 1.4613E+03 1.0571E+03 1.3410E+03 1.3224E+03 F11 AVG 9.3035E+04 2.7613E+04 1.5496E+04 7.1644E+03 4.4574E+03 3.5331E+03 3.0142E+03 STD 3.4925E+04 1.2544E+04 9.2731E+03 6.4614E+03 2.2261E+03 8.0321E+02 5.3579E+02 F12 AVG 2.7758E+08 1.9218E+07 1.1814E+07 9.2409E+06 5.3477E+06 7.5569E+06 6.4178E+06 STD 4.3611E+08 2.4459E+07 1.6710E+07 1.3488E+07 4.8010E+06 1.4285E+07 7.3343E+06 F13 AVG 1.1184E+05 4.3365E+04 2.8164E+04 1.3749E+04 1.5457E+04 2.3299E+04 9.4844E+03 STD 3.6282E+04 1.9678E+04 6.0474E+04 6.8155E+03 8.3252E+03 6.5433E+04 6.9073E+03 F14 AVG 1.7751E+06 1.4709E+06 1.0776E+06 6.7843E+05 4.3442E+05 3.8413E+05 5.5463E+05 STD 1.2208E+06 7.7293E+05 8.1086E+05 5.3584E+05 2.0929E+05 1.9925E+05 5.6678E+05 F15 AVG 7.4718E+04 4.2772E+04 2.3866E+04 2.0771E+04 2.9160E+04 1.2730E+04 7.1162E+03 STD 5.5953E+04 8.0024E+04 7.0886E+04 4.8992E+04 8.5171E+04 4.0644E+04 5.5599E+03 F16 AVG 6.4497E+03 6.1165E+03 5.7215E+03 5.6920E+03 5.8327E+03 6.1294E+03 6.4905E+03 STD 8.9718E+02 8.0772E+02 7.4823E+02 8.6622E+02 9.5451E+02 9.9792E+02 1.1286E+03 F17 AVG 6.4634E+03 6.2552E+03 5.6976E+03 5.2670E+03 5.4252E+03 5.4645E+03 5.5989E+03 STD 7.9534E+02 8.1125E+02 7.8391E+02 6.3973E+02 5.9873E+02 7.9492E+02 7.4707E+02 F18 AVG 1.8836E+06 1.6637E+06 1.1950E+06 1.4119E+06 1.3872E+06 1.7249E+06 1.6466E+06 STD 9.9606E+05 9.2139E+05 5.6851E+05 5.8794E+05 7.9922E+05 1.4242E+06 7.9161E+05 F19 AVG 1.7701E+04 3.0590E+04 1.1784E+04 1.5925E+04 8.6091E+03 6.3173E+03 5.9897E+03 STD 2.1471E+04 1.3584E+05 3.0732E+04 4.4640E+04 6.5532E+03 5.8492E+03 5.0915E+03 F20 AVG 5.7008E+03 5.9165E+03 5.4408E+03 5.8210E+03 5.6719E+03 5.6949E+03 5.9163E+03 STD 6.7873E+02 6.3756E+02 6.3485E+02 5.3380E+02 5.4259E+02 5.9978E+02 5.5936E+02 F21 AVG 3.6475E+03 3.1866E+03 3.0035E+03 2.9271E+03 2.8429E+03 2.8806E+03 2.8411E+03 STD 3.4330E+02 1.5336E+02 9.4240E+01 9.3150E+01 8.9407E+01 8.1129E+01 8.5704E+01 F22 AVG 1.9082E+04 1.8131E+04 1.9082E+04 1.9121E+04 1.9529E+04 1.9292E+04 1.9414E+04 STD 1.5800E+03 1.7786E+03 1.5116E+03 1.7940E+03 1.3685E+03 1.4222E+03 1.2100E+03 F23 AVG 4.5578E+03 4.0427E+03 3.8404E+03 3.6848E+03 3.6228E+03 3.5075E+03 3.4353E+03 STD 2.5970E+02 1.9348E+02 1.8389E+02 1.9275E+02 1.6264E+02 1.4044E+02 1.3760E+02 F24 AVG 6.2129E+03 5.1950E+03 4.6864E+03 4.4478E+03 4.1874E+03 4.0361E+03 3.9765E+03 STD 5.3096E+02 4.6604E+02 2.9826E+02 3.0567E+02 2.1216E+02 1.7093E+02 1.5981E+02 F25 AVG 4.5951E+03 3.7186E+03 3.5412E+03 3.4841E+03 3.4402E+03 3.4081E+03 3.3902E+03 STD 4.0886E+02 1.4575E+02 1.4991E+02 8.0945E+01 8.7436E+01 8.6940E+01 9.0235E+01 F26 AVG 2.7687E+04 2.0863E+04 1.6056E+04 1.4387E+04 1.3073E+04 1.1802E+04 1.1667E+04 STD 3.2515E+03 3.5464E+03 2.4413E+03 1.9014E+03 1.5027E+03 1.3063E+03 1.5034E+03 F27 AVG 5.1033E+03 4.0649E+03 3.8027E+03 3.7210E+03 3.6330E+03 3.5986E+03 3.5919E+03 STD 9.5742E+02 2.2184E+02 1.7896E+02 1.4162E+02 1.1269E+02 1.2315E+02 1.2182E+02 F28 AVG 5.7850E+03 3.7325E+03 3.5575E+03 3.5249E+03 3.4870E+03 3.4948E+03 3.8440E+03 STD 8.5128E+02 1.7265E+02 6.4074E+01 5.1161E+01 4.8977E+01 4.6886E+01 2.0245E+03 F29 AVG 8.6416E+03 7.7365E+03 7.6587E+03 7.1360E+03 6.9983E+03 6.7558E+03 6.7501E+03 STD 7.0136E+02 7.4767E+02 6.9488E+02 5.3438E+02 7.1650E+02 5.1479E+02 7.4395E+02 F30 AVG 1.8430E+06 1.4989E+05 1.1158E+05 1.7986E+04 4.8317E+04 1.4804E+04 1.2655E+04 STD 1.4094E+06 1.7872E+05 1.8724E+05 6.8275E+03 1.0530E+05 5.9214E+03 5.4702E+03 Avg 11.573 9.394 7.680 6.818 6.250 5.747 5.757 Rank 14 12 10 8 6 1 3 Fun Item 9 10 11 12 13 m 2*m F1 AVG 9.0369E+03 6.9012E+03 6.1618E+03 6.0730E+03 8.1622E+03 7.3594E+08 1.0836E+10 STD 1.0548E+04 9.7268E+03 7.0016E+03 6.9873E+03 1.2778E+04 7.2589E+08 2.0999E+10 F2 AVG 2.2865E+99 1.3053E+101 4.9971E+110 2.5328E+127 3.2047E+120 4.4023E+136 6.9465E+146 STD 1.2524E+100 7.1268E+101 2.4864E+111 1.3873E+128 1.7530E+121 2.4108E+137 3.8029E+147 F3 AVG 4.3394E+05 4.3811E+05 5.0447E+05 5.1956E+05 5.4894E+05 6.9552E+05 8.2104E+05 STD 9.4997E+04 9.8550E+04 7.7476E+04 1.0707E+05 8.7441E+04 7.4016E+04 1.1296E+05 F4 AVG 6.9430E+02 7.1122E+02 6.9581E+02 7.1864E+02 7.4141E+02 1.2427E+03 2.7616E+03 STD 4.9275E+01 5.8479E+01 5.3181E+01 5.9310E+01 6.3111E+01 2.8544E+02 9.6750E+02 F5 AVG 1.0490E+03 1.0279E+03 1.0651E+03 1.0593E+03 1.0710E+03 1.1301E+03 1.3305E+03 STD 6.0311E+01 7.9387E+01 8.8449E+01 6.0890E+01 7.9501E+01 8.1460E+01 1.1592E+02 F6 AVG 6.2513E+02 6.2632E+02 6.2345E+02 6.2421E+02 6.2343E+02 6.3338E+02 6.4977E+02 STD 1.0386E+01 7.3776E+00 5.0661E+00 6.3056E+00 6.0107E+00 7.7141E+00 6.9125E+00 F7 AVG 1.9345E+03 1.9153E+03 1.8145E+03 1.8949E+03 1.8031E+03 1.6713E+03 1.5460E+03 STD 1.7240E+02 1.6694E+02 1.7511E+02 1.3402E+02 2.0136E+02 1.6895E+02 1.5674E+02 F8 AVG 1.3852E+03 1.3383E+03 1.3331E+03 1.3165E+03 1.3348E+03 1.4242E+03 1.6381E+03 STD 9.8592E+01 8.7670E+01 5.9035E+01 1.0280E+02 6.1706E+01 7.8331E+01 9.3751E+01 F9 AVG 2.3696E+04 2.3422E+04 2.2924E+04 2.3198E+04 2.3096E+04 2.7227E+04 3.4603E+04 STD 6.2334E+03 5.4137E+03 9.2735E+03 7.2277E+03 7.7298E+03 9.1945E+03 8.2326E+03 F10 AVG 1.7045E+04 1.7248E+04 1.7642E+04 1.7251E+04 1.7854E+04 1.8543E+04 1.9698E+04 STD 1.3249E+03 1.4194E+03 9.6921E+02 1.3424E+03 1.1929E+03 1.0228E+03 1.0305E+03 F11 AVG 3.1737E+03 4.6846E+03 8.3573E+03 1.2829E+04 2.3009E+04 7.6195E+04 1.3919E+05 STD 8.3708E+02 3.7793E+03 6.0282E+03 8.5488E+03 8.7973E+03 2.1956E+04 3.1991E+04 F12 AVG 1.0143E+07 5.8599E+06 5.8153E+06 1.5087E+07 1.5085E+07 2.4365E+08 4.1569E+09 STD 1.8458E+07 8.0539E+06 6.3937E+06 2.2991E+07 1.0279E+07 2.5523E+08 1.9486E+09 F13 AVG 2.2684E+04 2.4871E+04 8.4200E+03 2.1854E+04 1.1785E+04 4.2100E+04 4.2468E+04 STD 6.5593E+04 7.4253E+04 7.5411E+03 7.3280E+04 1.0431E+04 1.2002E+05 2.4654E+04 F14 AVG 7.6569E+05 5.1922E+05 7.4413E+05 1.2964E+06 1.8241E+06 6.6127E+06 1.1347E+07 STD 1.0378E+06 5.9510E+05 5.4741E+05 1.1490E+06 1.2247E+06 4.0234E+06 7.3522E+06 F15 AVG 1.6046E+04 2.1950E+04 1.6727E+04 1.6701E+04 1.4987E+04 1.7684E+04 1.0649E+04 STD 4.7291E+04 6.6229E+04 5.1893E+04 4.7647E+04 5.3897E+04 5.4946E+04 1.0282E+04 F16 AVG 6.2705E+03 6.4812E+03 6.6390E+03 6.5394E+03 6.6394E+03 7.2110E+03 7.4178E+03 STD 1.0306E+03 7.8505E+02 9.7237E+02 7.3847E+02 6.1689E+02 7.2422E+02 6.2755E+02 F17 AVG 5.7245E+03 5.8350E+03 5.8167E+03 5.8920E+03 5.6917E+03 5.9155E+03 6.1354E+03 STD 8.0389E+02 6.9572E+02 5.7676E+02 6.5784E+02 5.9097E+02 5.6716E+02 6.8967E+02 F18 AVG 1.9576E+06 2.7016E+06 3.5492E+06 4.4467E+06 6.4497E+06 1.2330E+07 1.6580E+07 STD 1.0148E+06 1.4311E+06 1.9187E+06 3.0298E+06 5.5555E+06 9.2955E+06 1.0307E+07 F19 AVG 8.6680E+03 7.1669E+03 8.1501E+03 1.4831E+04 9.2364E+03 1.4771E+04 4.5532E+05 STD 6.3252E+03 8.6001E+03 4.9781E+03 3.6482E+04 8.9352E+03 1.3781E+04 2.3511E+06 F20 AVG 5.6925E+03 5.9227E+03 5.9940E+03 5.7750E+03 5.9300E+03 5.9179E+03 6.0097E+03 STD 5.2418E+02 5.6020E+02 5.5003E+02 5.2303E+02 5.2844E+02 6.5216E+02 5.3580E+02 F21 AVG 2.8490E+03 2.8571E+03 2.8407E+03 2.8638E+03 2.8844E+03 2.9974E+03 3.2289E+03 STD 8.8457E+01 5.9545E+01 7.2296E+01 6.5192E+01 7.9936E+01 8.0000E+01 7.0348E+01 F22 AVG 1.9806E+04 1.9561E+04 1.9374E+04 1.9775E+04 1.9444E+04 2.0563E+04 2.2546E+04 STD 1.1720E+03 9.8467E+02 1.3263E+03 1.2058E+03 1.0574E+03 9.7573E+02 1.1730E+03 F23 AVG 3.3586E+03 3.3678E+03 3.3792E+03 3.3900E+03 3.4362E+03 3.5215E+03 3.6047E+03 STD 1.1409E+02 1.0621E+02 1.2973E+02 1.1469E+02 9.2403E+01 6.1049E+01 5.2735E+01 F24 AVG 3.9112E+03 3.9717E+03 3.9025E+03 3.8697E+03 3.8859E+03 3.9046E+03 4.0170E+03 STD 1.8323E+02 1.7559E+02 1.2429E+02 8.7540E+01 1.0458E+02 6.1411E+01 5.0683E+01 F25 AVG 3.3737E+03 3.3870E+03 3.3758E+03 3.3933E+03 3.4355E+03 3.8943E+03 4.9258E+03 STD 7.4242E+01 7.0720E+01 8.5621E+01 7.8764E+01 7.2810E+01 2.6210E+02 6.8592E+02 F26 AVG 1.2001E+04 1.1607E+04 1.1624E+04 1.1721E+04 1.2146E+04 1.2858E+04 1.3813E+04 STD 1.4118E+03 9.1440E+02 6.3715E+02 9.0176E+02 6.6466E+02 8.1247E+02 5.5354E+02 F27 AVG 3.5402E+03 3.5656E+03 3.4943E+03 3.5355E+03 3.4929E+03 3.4235E+03 3.4845E+03 STD 1.0721E+02 8.3709E+01 6.3851E+01 7.1976E+01 6.5933E+01 3.8909E+01 5.6213E+01 F28 AVG 4.6494E+03 4.8960E+03 4.5710E+03 5.3127E+03 7.1886E+03 1.3257E+04 1.5074E+04 STD 3.5966E+03 3.6935E+03 3.3636E+03 4.1910E+03 5.2921E+03 3.3913E+03 9.4930E+02 F29 AVG 6.5446E+03 6.5298E+03 6.8516E+03 7.0426E+03 7.3777E+03 7.8648E+03 8.2344E+03 STD 9.5339E+02 9.1810E+02 1.1785E+03 8.7025E+02 9.4837E+02 6.9074E+02 6.4989E+02 F30 AVG 1.8891E+04 1.4259E+04 1.3664E+04 1.4264E+04 1.1200E+04 3.2763E+04 3.4358E+05 STD 2.1036E+04 5.5468E+03 6.0615E+03 6.4128E+03 4.5468E+03 1.3235E+04 1.6077E+05 Avg 5.753 5.833 6.083 6.464 6.894 9.372 11.380 Rank 2 4 5 7 9 11 13 Fun . Item . 2 . 3 . 4 . 5 . 6 . 7 . 8 . F1 AVG 7.1804E+09 1.0104E+04 6.5408E+03 8.2055E+03 1.0053E+04 6.2719E+03 7.1812E+03 STD 5.4088E+09 1.3565E+04 7.3344E+03 1.2296E+04 1.4234E+04 5.6768E+03 9.3133E+03 F2 AVG 1.6879E+117 4.1155E+102 2.9505E+84 2.0344E+71 3.9933E+68 6.0119E+62 1.9875E+108 STD 9.1480E+117 2.2540E+103 1.6161E+85 1.1142E+72 2.1872E+69 2.8414E+63 1.0886E+109 F3 AVG 8.0614E+05 3.2088E+05 1.7117E+05 2.4094E+05 3.0007E+05 3.4393E+05 4.2434E+05 STD 1.3236E+05 1.6731E+05 5.2316E+04 6.5200E+04 6.8758E+04 9.4540E+04 8.1802E+04 F4 AVG 1.6091E+03 8.7567E+02 7.8847E+02 7.4569E+02 7.4751E+02 6.9740E+02 6.9020E+02 STD 3.6239E+02 1.5055E+02 9.3875E+01 8.9137E+01 7.9240E+01 6.8406E+01 6.1617E+01 F5 AVG 1.3360E+03 1.2051E+03 1.1313E+03 1.0797E+03 1.1001E+03 1.0685E+03 1.0845E+03 STD 9.0122E+01 7.5637E+01 7.8424E+01 6.6965E+01 9.2841E+01 7.5740E+01 1.0163E+02 F6 AVG 6.5957E+02 6.5151E+02 6.4563E+02 6.3645E+02 6.3036E+02 6.2871E+02 6.2948E+02 STD 3.5052E+00 4.1109E+00 4.4569E+00 6.8871E+00 6.7447E+00 7.2641E+00 8.0682E+00 F7 AVG 3.0663E+03 2.6014E+03 2.3913E+03 2.1716E+03 2.0881E+03 2.0554E+03 2.0082E+03 STD 2.0101E+02 1.6121E+02 1.9519E+02 1.9221E+02 2.5886E+02 1.8246E+02 1.8334E+02 F8 AVG 1.7448E+03 1.5844E+03 1.4598E+03 1.3876E+03 1.3995E+03 1.3716E+03 1.3755E+03 STD 1.0279E+02 1.0661E+02 8.2951E+01 9.3012E+01 1.3786E+02 8.2917E+01 7.9233E+01 F9 AVG 2.4590E+04 2.3007E+04 2.3722E+04 2.2598E+04 2.3260E+04 2.2611E+04 2.2596E+04 STD 3.0034E+03 3.3783E+03 4.5861E+03 2.7892E+03 4.3199E+03 4.0715E+03 4.4909E+03 F10 AVG 1.6598E+04 1.5804E+04 1.6329E+04 1.7291E+04 1.6833E+04 1.7532E+04 1.7258E+04 STD 1.7383E+03 1.5440E+03 1.7496E+03 1.4613E+03 1.0571E+03 1.3410E+03 1.3224E+03 F11 AVG 9.3035E+04 2.7613E+04 1.5496E+04 7.1644E+03 4.4574E+03 3.5331E+03 3.0142E+03 STD 3.4925E+04 1.2544E+04 9.2731E+03 6.4614E+03 2.2261E+03 8.0321E+02 5.3579E+02 F12 AVG 2.7758E+08 1.9218E+07 1.1814E+07 9.2409E+06 5.3477E+06 7.5569E+06 6.4178E+06 STD 4.3611E+08 2.4459E+07 1.6710E+07 1.3488E+07 4.8010E+06 1.4285E+07 7.3343E+06 F13 AVG 1.1184E+05 4.3365E+04 2.8164E+04 1.3749E+04 1.5457E+04 2.3299E+04 9.4844E+03 STD 3.6282E+04 1.9678E+04 6.0474E+04 6.8155E+03 8.3252E+03 6.5433E+04 6.9073E+03 F14 AVG 1.7751E+06 1.4709E+06 1.0776E+06 6.7843E+05 4.3442E+05 3.8413E+05 5.5463E+05 STD 1.2208E+06 7.7293E+05 8.1086E+05 5.3584E+05 2.0929E+05 1.9925E+05 5.6678E+05 F15 AVG 7.4718E+04 4.2772E+04 2.3866E+04 2.0771E+04 2.9160E+04 1.2730E+04 7.1162E+03 STD 5.5953E+04 8.0024E+04 7.0886E+04 4.8992E+04 8.5171E+04 4.0644E+04 5.5599E+03 F16 AVG 6.4497E+03 6.1165E+03 5.7215E+03 5.6920E+03 5.8327E+03 6.1294E+03 6.4905E+03 STD 8.9718E+02 8.0772E+02 7.4823E+02 8.6622E+02 9.5451E+02 9.9792E+02 1.1286E+03 F17 AVG 6.4634E+03 6.2552E+03 5.6976E+03 5.2670E+03 5.4252E+03 5.4645E+03 5.5989E+03 STD 7.9534E+02 8.1125E+02 7.8391E+02 6.3973E+02 5.9873E+02 7.9492E+02 7.4707E+02 F18 AVG 1.8836E+06 1.6637E+06 1.1950E+06 1.4119E+06 1.3872E+06 1.7249E+06 1.6466E+06 STD 9.9606E+05 9.2139E+05 5.6851E+05 5.8794E+05 7.9922E+05 1.4242E+06 7.9161E+05 F19 AVG 1.7701E+04 3.0590E+04 1.1784E+04 1.5925E+04 8.6091E+03 6.3173E+03 5.9897E+03 STD 2.1471E+04 1.3584E+05 3.0732E+04 4.4640E+04 6.5532E+03 5.8492E+03 5.0915E+03 F20 AVG 5.7008E+03 5.9165E+03 5.4408E+03 5.8210E+03 5.6719E+03 5.6949E+03 5.9163E+03 STD 6.7873E+02 6.3756E+02 6.3485E+02 5.3380E+02 5.4259E+02 5.9978E+02 5.5936E+02 F21 AVG 3.6475E+03 3.1866E+03 3.0035E+03 2.9271E+03 2.8429E+03 2.8806E+03 2.8411E+03 STD 3.4330E+02 1.5336E+02 9.4240E+01 9.3150E+01 8.9407E+01 8.1129E+01 8.5704E+01 F22 AVG 1.9082E+04 1.8131E+04 1.9082E+04 1.9121E+04 1.9529E+04 1.9292E+04 1.9414E+04 STD 1.5800E+03 1.7786E+03 1.5116E+03 1.7940E+03 1.3685E+03 1.4222E+03 1.2100E+03 F23 AVG 4.5578E+03 4.0427E+03 3.8404E+03 3.6848E+03 3.6228E+03 3.5075E+03 3.4353E+03 STD 2.5970E+02 1.9348E+02 1.8389E+02 1.9275E+02 1.6264E+02 1.4044E+02 1.3760E+02 F24 AVG 6.2129E+03 5.1950E+03 4.6864E+03 4.4478E+03 4.1874E+03 4.0361E+03 3.9765E+03 STD 5.3096E+02 4.6604E+02 2.9826E+02 3.0567E+02 2.1216E+02 1.7093E+02 1.5981E+02 F25 AVG 4.5951E+03 3.7186E+03 3.5412E+03 3.4841E+03 3.4402E+03 3.4081E+03 3.3902E+03 STD 4.0886E+02 1.4575E+02 1.4991E+02 8.0945E+01 8.7436E+01 8.6940E+01 9.0235E+01 F26 AVG 2.7687E+04 2.0863E+04 1.6056E+04 1.4387E+04 1.3073E+04 1.1802E+04 1.1667E+04 STD 3.2515E+03 3.5464E+03 2.4413E+03 1.9014E+03 1.5027E+03 1.3063E+03 1.5034E+03 F27 AVG 5.1033E+03 4.0649E+03 3.8027E+03 3.7210E+03 3.6330E+03 3.5986E+03 3.5919E+03 STD 9.5742E+02 2.2184E+02 1.7896E+02 1.4162E+02 1.1269E+02 1.2315E+02 1.2182E+02 F28 AVG 5.7850E+03 3.7325E+03 3.5575E+03 3.5249E+03 3.4870E+03 3.4948E+03 3.8440E+03 STD 8.5128E+02 1.7265E+02 6.4074E+01 5.1161E+01 4.8977E+01 4.6886E+01 2.0245E+03 F29 AVG 8.6416E+03 7.7365E+03 7.6587E+03 7.1360E+03 6.9983E+03 6.7558E+03 6.7501E+03 STD 7.0136E+02 7.4767E+02 6.9488E+02 5.3438E+02 7.1650E+02 5.1479E+02 7.4395E+02 F30 AVG 1.8430E+06 1.4989E+05 1.1158E+05 1.7986E+04 4.8317E+04 1.4804E+04 1.2655E+04 STD 1.4094E+06 1.7872E+05 1.8724E+05 6.8275E+03 1.0530E+05 5.9214E+03 5.4702E+03 Avg 11.573 9.394 7.680 6.818 6.250 5.747 5.757 Rank 14 12 10 8 6 1 3 Fun Item 9 10 11 12 13 m 2*m F1 AVG 9.0369E+03 6.9012E+03 6.1618E+03 6.0730E+03 8.1622E+03 7.3594E+08 1.0836E+10 STD 1.0548E+04 9.7268E+03 7.0016E+03 6.9873E+03 1.2778E+04 7.2589E+08 2.0999E+10 F2 AVG 2.2865E+99 1.3053E+101 4.9971E+110 2.5328E+127 3.2047E+120 4.4023E+136 6.9465E+146 STD 1.2524E+100 7.1268E+101 2.4864E+111 1.3873E+128 1.7530E+121 2.4108E+137 3.8029E+147 F3 AVG 4.3394E+05 4.3811E+05 5.0447E+05 5.1956E+05 5.4894E+05 6.9552E+05 8.2104E+05 STD 9.4997E+04 9.8550E+04 7.7476E+04 1.0707E+05 8.7441E+04 7.4016E+04 1.1296E+05 F4 AVG 6.9430E+02 7.1122E+02 6.9581E+02 7.1864E+02 7.4141E+02 1.2427E+03 2.7616E+03 STD 4.9275E+01 5.8479E+01 5.3181E+01 5.9310E+01 6.3111E+01 2.8544E+02 9.6750E+02 F5 AVG 1.0490E+03 1.0279E+03 1.0651E+03 1.0593E+03 1.0710E+03 1.1301E+03 1.3305E+03 STD 6.0311E+01 7.9387E+01 8.8449E+01 6.0890E+01 7.9501E+01 8.1460E+01 1.1592E+02 F6 AVG 6.2513E+02 6.2632E+02 6.2345E+02 6.2421E+02 6.2343E+02 6.3338E+02 6.4977E+02 STD 1.0386E+01 7.3776E+00 5.0661E+00 6.3056E+00 6.0107E+00 7.7141E+00 6.9125E+00 F7 AVG 1.9345E+03 1.9153E+03 1.8145E+03 1.8949E+03 1.8031E+03 1.6713E+03 1.5460E+03 STD 1.7240E+02 1.6694E+02 1.7511E+02 1.3402E+02 2.0136E+02 1.6895E+02 1.5674E+02 F8 AVG 1.3852E+03 1.3383E+03 1.3331E+03 1.3165E+03 1.3348E+03 1.4242E+03 1.6381E+03 STD 9.8592E+01 8.7670E+01 5.9035E+01 1.0280E+02 6.1706E+01 7.8331E+01 9.3751E+01 F9 AVG 2.3696E+04 2.3422E+04 2.2924E+04 2.3198E+04 2.3096E+04 2.7227E+04 3.4603E+04 STD 6.2334E+03 5.4137E+03 9.2735E+03 7.2277E+03 7.7298E+03 9.1945E+03 8.2326E+03 F10 AVG 1.7045E+04 1.7248E+04 1.7642E+04 1.7251E+04 1.7854E+04 1.8543E+04 1.9698E+04 STD 1.3249E+03 1.4194E+03 9.6921E+02 1.3424E+03 1.1929E+03 1.0228E+03 1.0305E+03 F11 AVG 3.1737E+03 4.6846E+03 8.3573E+03 1.2829E+04 2.3009E+04 7.6195E+04 1.3919E+05 STD 8.3708E+02 3.7793E+03 6.0282E+03 8.5488E+03 8.7973E+03 2.1956E+04 3.1991E+04 F12 AVG 1.0143E+07 5.8599E+06 5.8153E+06 1.5087E+07 1.5085E+07 2.4365E+08 4.1569E+09 STD 1.8458E+07 8.0539E+06 6.3937E+06 2.2991E+07 1.0279E+07 2.5523E+08 1.9486E+09 F13 AVG 2.2684E+04 2.4871E+04 8.4200E+03 2.1854E+04 1.1785E+04 4.2100E+04 4.2468E+04 STD 6.5593E+04 7.4253E+04 7.5411E+03 7.3280E+04 1.0431E+04 1.2002E+05 2.4654E+04 F14 AVG 7.6569E+05 5.1922E+05 7.4413E+05 1.2964E+06 1.8241E+06 6.6127E+06 1.1347E+07 STD 1.0378E+06 5.9510E+05 5.4741E+05 1.1490E+06 1.2247E+06 4.0234E+06 7.3522E+06 F15 AVG 1.6046E+04 2.1950E+04 1.6727E+04 1.6701E+04 1.4987E+04 1.7684E+04 1.0649E+04 STD 4.7291E+04 6.6229E+04 5.1893E+04 4.7647E+04 5.3897E+04 5.4946E+04 1.0282E+04 F16 AVG 6.2705E+03 6.4812E+03 6.6390E+03 6.5394E+03 6.6394E+03 7.2110E+03 7.4178E+03 STD 1.0306E+03 7.8505E+02 9.7237E+02 7.3847E+02 6.1689E+02 7.2422E+02 6.2755E+02 F17 AVG 5.7245E+03 5.8350E+03 5.8167E+03 5.8920E+03 5.6917E+03 5.9155E+03 6.1354E+03 STD 8.0389E+02 6.9572E+02 5.7676E+02 6.5784E+02 5.9097E+02 5.6716E+02 6.8967E+02 F18 AVG 1.9576E+06 2.7016E+06 3.5492E+06 4.4467E+06 6.4497E+06 1.2330E+07 1.6580E+07 STD 1.0148E+06 1.4311E+06 1.9187E+06 3.0298E+06 5.5555E+06 9.2955E+06 1.0307E+07 F19 AVG 8.6680E+03 7.1669E+03 8.1501E+03 1.4831E+04 9.2364E+03 1.4771E+04 4.5532E+05 STD 6.3252E+03 8.6001E+03 4.9781E+03 3.6482E+04 8.9352E+03 1.3781E+04 2.3511E+06 F20 AVG 5.6925E+03 5.9227E+03 5.9940E+03 5.7750E+03 5.9300E+03 5.9179E+03 6.0097E+03 STD 5.2418E+02 5.6020E+02 5.5003E+02 5.2303E+02 5.2844E+02 6.5216E+02 5.3580E+02 F21 AVG 2.8490E+03 2.8571E+03 2.8407E+03 2.8638E+03 2.8844E+03 2.9974E+03 3.2289E+03 STD 8.8457E+01 5.9545E+01 7.2296E+01 6.5192E+01 7.9936E+01 8.0000E+01 7.0348E+01 F22 AVG 1.9806E+04 1.9561E+04 1.9374E+04 1.9775E+04 1.9444E+04 2.0563E+04 2.2546E+04 STD 1.1720E+03 9.8467E+02 1.3263E+03 1.2058E+03 1.0574E+03 9.7573E+02 1.1730E+03 F23 AVG 3.3586E+03 3.3678E+03 3.3792E+03 3.3900E+03 3.4362E+03 3.5215E+03 3.6047E+03 STD 1.1409E+02 1.0621E+02 1.2973E+02 1.1469E+02 9.2403E+01 6.1049E+01 5.2735E+01 F24 AVG 3.9112E+03 3.9717E+03 3.9025E+03 3.8697E+03 3.8859E+03 3.9046E+03 4.0170E+03 STD 1.8323E+02 1.7559E+02 1.2429E+02 8.7540E+01 1.0458E+02 6.1411E+01 5.0683E+01 F25 AVG 3.3737E+03 3.3870E+03 3.3758E+03 3.3933E+03 3.4355E+03 3.8943E+03 4.9258E+03 STD 7.4242E+01 7.0720E+01 8.5621E+01 7.8764E+01 7.2810E+01 2.6210E+02 6.8592E+02 F26 AVG 1.2001E+04 1.1607E+04 1.1624E+04 1.1721E+04 1.2146E+04 1.2858E+04 1.3813E+04 STD 1.4118E+03 9.1440E+02 6.3715E+02 9.0176E+02 6.6466E+02 8.1247E+02 5.5354E+02 F27 AVG 3.5402E+03 3.5656E+03 3.4943E+03 3.5355E+03 3.4929E+03 3.4235E+03 3.4845E+03 STD 1.0721E+02 8.3709E+01 6.3851E+01 7.1976E+01 6.5933E+01 3.8909E+01 5.6213E+01 F28 AVG 4.6494E+03 4.8960E+03 4.5710E+03 5.3127E+03 7.1886E+03 1.3257E+04 1.5074E+04 STD 3.5966E+03 3.6935E+03 3.3636E+03 4.1910E+03 5.2921E+03 3.3913E+03 9.4930E+02 F29 AVG 6.5446E+03 6.5298E+03 6.8516E+03 7.0426E+03 7.3777E+03 7.8648E+03 8.2344E+03 STD 9.5339E+02 9.1810E+02 1.1785E+03 8.7025E+02 9.4837E+02 6.9074E+02 6.4989E+02 F30 AVG 1.8891E+04 1.4259E+04 1.3664E+04 1.4264E+04 1.1200E+04 3.2763E+04 3.4358E+05 STD 2.1036E+04 5.5468E+03 6.0615E+03 6.4128E+03 4.5468E+03 1.3235E+04 1.6077E+05 Avg 5.753 5.833 6.083 6.464 6.894 9.372 11.380 Rank 2 4 5 7 9 11 13 Open in new tab Table A6: The relevant experimental results of pheromone evaporation rate. Fun . Item . 0.5 . 0.6 . 0.7 . 0.8 . 0.9 . 1 . 1.1 . 1.2 . 1.3 . 1.4 . 1.5 . F1 AVG 9.960E+10 3.065E+10 2.401E+04 4.241E+03 6.909E+03 7.309E+03 5.976E+03 1.283E+07 1.116E+09 3.370E+09 5.416E+09 STD 1.384E+10 9.129E+09 1.058E+05 4.504E+03 1.019E+04 9.085E+03 7.335E+03 3.036E+07 6.707E+08 1.494E+09 1.900E+09 F2 AVG 3.421E+131 1.530E+121 1.053E+117 4.306E+85 6.038E+84 1.081E+69 2.626E+114 1.485E+136 5.787E+139 2.377E+142 5.347E+146 STD 1.720E+132 8.286E+121 5.747E+117 2.358E+86 3.307E+85 5.923E+69 1.438E+115 8.131E+136 2.724E+140 1.302E+143 2.074E+147 F3 AVG 4.167E+05 3.019E+05 2.288E+05 1.631E+05 2.608E+05 3.614E+05 4.017E+05 4.576E+05 5.313E+05 5.837E+05 6.244E+05 STD 1.747E+05 8.591E+04 6.013E+04 1.959E+04 6.656E+04 7.925E+04 7.302E+04 8.063E+04 1.190E+05 1.304E+05 1.428E+05 F4 AVG 1.278E+04 3.959E+03 1.102E+03 8.208E+02 7.129E+02 7.066E+02 7.432E+02 8.679E+02 1.163E+03 1.350E+03 1.735E+03 STD 2.622E+03 1.307E+03 2.305E+02 9.704E+01 7.232E+01 6.293E+01 6.339E+01 1.240E+02 1.888E+02 1.741E+02 4.078E+02 F5 AVG 1.295E+03 1.217E+03 1.179E+03 1.082E+03 1.034E+03 1.065E+03 1.084E+03 1.120E+03 1.181E+03 1.216E+03 1.235E+03 STD 5.292E+01 6.436E+01 6.907E+01 7.977E+01 8.308E+01 6.962E+01 8.031E+01 7.565E+01 9.610E+01 7.664E+01 9.415E+01 F6 AVG 6.597E+02 6.529E+02 6.523E+02 6.414E+02 6.335E+02 6.300E+02 6.363E+02 6.440E+02 6.512E+02 6.542E+02 6.570E+02 STD 2.225E+00 3.789E+00 4.703E+00 3.749E+00 5.715E+00 8.221E+00 8.594E+00 6.299E+00 7.237E+00 1.035E+01 8.109E+00 F7 AVG 2.923E+03 2.772E+03 2.580E+03 2.327E+03 2.075E+03 2.034E+03 2.079E+03 2.188E+03 2.342E+03 2.328E+03 2.455E+03 STD 1.478E+02 1.666E+02 1.929E+02 1.577E+02 2.172E+02 2.110E+02 1.836E+02 2.495E+02 1.773E+02 2.457E+02 2.641E+02 F8 AVG 1.697E+03 1.632E+03 1.528E+03 1.434E+03 1.327E+03 1.383E+03 1.390E+03 1.429E+03 1.487E+03 1.495E+03 1.537E+03 STD 8.951E+01 7.377E+01 1.053E+02 1.023E+02 6.811E+01 9.873E+01 9.919E+01 7.765E+01 9.488E+01 8.495E+01 6.870E+01 F9 AVG 2.241E+04 2.125E+04 2.194E+04 2.119E+04 2.074E+04 2.109E+04 2.531E+04 2.730E+04 2.777E+04 3.081E+04 3.106E+04 STD 1.879E+03 3.028E+03 2.716E+03 3.604E+03 4.387E+03 4.398E+03 6.374E+03 7.103E+03 7.141E+03 7.473E+03 7.173E+03 F10 AVG 1.552E+04 1.528E+04 1.568E+04 1.619E+04 1.715E+04 1.737E+04 1.745E+04 1.774E+04 1.748E+04 1.792E+04 1.789E+04 STD 1.433E+03 1.514E+03 1.520E+03 1.909E+03 1.171E+03 9.974E+02 1.246E+03 1.252E+03 1.163E+03 1.411E+03 1.028E+03 F11 AVG 1.464E+05 9.459E+04 3.111E+04 2.023E+04 5.689E+03 3.076E+03 4.140E+03 2.165E+04 5.401E+04 8.655E+04 1.050E+05 STD 3.729E+04 3.697E+04 1.152E+04 8.654E+03 3.551E+03 4.419E+02 1.209E+03 1.009E+04 1.927E+04 3.162E+04 3.050E+04 F12 AVG 1.695E+10 1.665E+09 3.034E+07 6.202E+06 5.476E+06 6.449E+06 1.003E+07 2.219E+07 1.040E+08 3.094E+08 7.058E+08 STD 7.926E+09 2.080E+09 5.443E+07 4.475E+06 5.121E+06 1.151E+07 1.470E+07 1.865E+07 1.121E+08 2.437E+08 3.804E+08 F13 AVG 3.277E+07 1.202E+05 9.140E+04 3.304E+04 2.870E+04 4.421E+04 3.371E+04 9.169E+03 2.936E+04 4.504E+04 1.658E+05 STD 1.139E+08 3.774E+04 4.605E+04 1.486E+04 7.177E+04 1.131E+05 1.003E+05 5.901E+03 7.205E+04 1.322E+04 6.229E+04 F14 AVG 1.896E+06 1.561E+06 1.342E+06 1.232E+06 5.877E+05 3.686E+05 8.159E+05 2.173E+06 3.415E+06 5.356E+06 7.193E+06 STD 7.518E+05 1.116E+06 8.398E+05 4.759E+05 2.801E+05 1.846E+05 8.509E+05 2.043E+06 2.583E+06 4.388E+06 7.969E+06 F15 AVG 8.393E+04 7.950E+04 7.664E+04 9.574E+03 6.460E+03 6.086E+03 1.462E+04 3.278E+04 1.878E+04 2.576E+04 2.095E+04 STD 2.645E+04 2.750E+04 6.888E+04 8.199E+03 4.513E+03 4.943E+03 3.800E+04 9.819E+04 6.708E+04 6.043E+04 4.194E+04 F16 AVG 6.920E+03 6.289E+03 6.016E+03 5.668E+03 5.348E+03 5.924E+03 6.724E+03 6.700E+03 7.113E+03 7.298E+03 7.421E+03 STD 7.439E+02 8.380E+02 6.214E+02 7.759E+02 8.370E+02 1.049E+03 7.609E+02 8.161E+02 6.320E+02 8.515E+02 5.791E+02 F17 AVG 6.800E+03 6.365E+03 5.955E+03 5.618E+03 5.413E+03 5.594E+03 6.011E+03 6.075E+03 6.246E+03 6.314E+03 6.249E+03 STD 6.943E+02 8.492E+02 6.722E+02 6.398E+02 7.268E+02 7.542E+02 7.050E+02 5.409E+02 6.563E+02 5.550E+02 5.441E+02 F18 AVG 2.026E+06 1.904E+06 1.863E+06 1.500E+06 1.290E+06 1.507E+06 3.541E+06 4.462E+06 6.234E+06 6.504E+06 1.060E+07 STD 6.074E+05 7.596E+05 8.407E+05 6.108E+05 6.376E+05 6.459E+05 2.536E+06 2.267E+06 5.037E+06 6.148E+06 7.007E+06 F19 AVG 2.801E+05 3.191E+04 1.613E+04 1.512E+04 1.593E+04 3.269E+04 1.461E+04 1.154E+04 1.031E+04 1.268E+04 9.816E+04 STD 5.838E+05 4.391E+04 2.775E+04 1.958E+04 5.166E+04 9.770E+04 3.495E+04 1.073E+04 9.029E+03 9.227E+03 7.001E+04 F20 AVG 5.134E+03 5.102E+03 5.418E+03 5.550E+03 5.632E+03 5.797E+03 5.906E+03 6.210E+03 6.311E+03 6.063E+03 6.189E+03 STD 3.923E+02 5.914E+02 6.999E+02 7.569E+02 4.797E+02 5.541E+02 4.371E+02 5.977E+02 5.534E+02 4.855E+02 6.158E+02 F21 AVG 3.739E+03 3.446E+03 3.200E+03 3.035E+03 2.864E+03 2.832E+03 2.865E+03 2.942E+03 2.945E+03 3.008E+03 3.053E+03 STD 2.345E+02 2.345E+02 1.406E+02 1.176E+02 9.146E+01 8.806E+01 8.089E+01 9.915E+01 9.563E+01 1.065E+02 1.063E+02 F22 AVG 1.909E+04 1.859E+04 1.774E+04 1.814E+04 1.873E+04 1.917E+04 1.962E+04 1.947E+04 1.933E+04 1.960E+04 1.941E+04 STD 1.693E+03 1.531E+03 3.543E+03 2.108E+03 1.891E+03 1.188E+03 1.262E+03 1.519E+03 1.332E+03 1.332E+03 1.502E+03 F23 AVG 4.889E+03 4.412E+03 4.103E+03 3.836E+03 3.669E+03 3.487E+03 3.423E+03 3.487E+03 3.516E+03 3.582E+03 3.601E+03 STD 3.052E+02 2.333E+02 1.763E+02 1.413E+02 1.508E+02 1.410E+02 1.127E+02 8.480E+01 8.006E+01 8.809E+01 6.876E+01 F24 AVG 7.181E+03 6.328E+03 5.270E+03 4.722E+03 4.388E+03 4.035E+03 3.897E+03 3.919E+03 3.962E+03 4.027E+03 4.094E+03 STD 6.075E+02 4.909E+02 3.844E+02 3.069E+02 2.475E+02 2.154E+02 1.210E+02 1.216E+02 8.631E+01 1.044E+02 1.114E+02 F25 AVG 8.355E+03 5.461E+03 4.046E+03 3.589E+03 3.434E+03 3.425E+03 3.463E+03 3.660E+03 3.872E+03 4.152E+03 4.472E+03 STD 5.858E+02 4.121E+02 2.713E+02 1.167E+02 1.098E+02 7.410E+01 6.797E+01 1.577E+02 1.706E+02 2.049E+02 3.319E+02 F26 AVG 3.075E+04 2.805E+04 2.381E+04 1.947E+04 1.371E+04 1.211E+04 1.188E+04 1.226E+04 1.301E+04 1.289E+04 1.354E+04 STD 3.116E+03 2.756E+03 2.669E+03 2.755E+03 1.688E+03 1.397E+03 1.230E+03 9.012E+02 1.093E+03 1.252E+03 1.286E+03 F27 AVG 6.557E+03 5.171E+03 4.471E+03 4.002E+03 3.748E+03 3.571E+03 3.548E+03 3.515E+03 3.542E+03 3.552E+03 3.643E+03 STD 9.832E+02 4.193E+02 3.473E+02 2.344E+02 1.391E+02 8.738E+01 8.408E+01 8.253E+01 8.997E+01 8.927E+01 8.530E+01 F28 AVG 1.318E+04 8.071E+03 4.696E+03 3.650E+03 3.508E+03 3.481E+03 5.329E+03 6.513E+03 6.603E+03 9.715E+03 1.132E+04 STD 1.340E+03 1.221E+03 1.117E+03 6.102E+01 4.642E+01 5.467E+01 4.157E+03 4.887E+03 4.802E+03 5.354E+03 5.122E+03 F29 AVG 1.088E+04 9.285E+03 8.261E+03 7.484E+03 6.929E+03 6.749E+03 7.465E+03 7.939E+03 8.372E+03 8.609E+03 9.134E+03 STD 1.639E+03 1.108E+03 7.723E+02 5.802E+02 5.311E+02 7.165E+02 9.875E+02 8.928E+02 6.819E+02 7.066E+02 8.418E+02 F30 AVG 3.155E+08 1.284E+07 4.840E+05 1.355E+05 1.848E+04 1.299E+04 1.349E+04 1.723E+04 4.385E+04 4.864E+05 2.085E+06 STD 3.238E+08 1.243E+07 6.963E+05 1.666E+05 2.076E+04 5.289E+03 4.728E+03 6.461E+03 2.149E+04 8.486E+05 1.827E+06 Avg 9.086 7.797 6.338 4.793 3.529 3.397 4.099 5.294 6.312 7.233 8.122 Rank 11 9 7 4 2 1 3 5 6 8 10 Fun . Item . 0.5 . 0.6 . 0.7 . 0.8 . 0.9 . 1 . 1.1 . 1.2 . 1.3 . 1.4 . 1.5 . F1 AVG 9.960E+10 3.065E+10 2.401E+04 4.241E+03 6.909E+03 7.309E+03 5.976E+03 1.283E+07 1.116E+09 3.370E+09 5.416E+09 STD 1.384E+10 9.129E+09 1.058E+05 4.504E+03 1.019E+04 9.085E+03 7.335E+03 3.036E+07 6.707E+08 1.494E+09 1.900E+09 F2 AVG 3.421E+131 1.530E+121 1.053E+117 4.306E+85 6.038E+84 1.081E+69 2.626E+114 1.485E+136 5.787E+139 2.377E+142 5.347E+146 STD 1.720E+132 8.286E+121 5.747E+117 2.358E+86 3.307E+85 5.923E+69 1.438E+115 8.131E+136 2.724E+140 1.302E+143 2.074E+147 F3 AVG 4.167E+05 3.019E+05 2.288E+05 1.631E+05 2.608E+05 3.614E+05 4.017E+05 4.576E+05 5.313E+05 5.837E+05 6.244E+05 STD 1.747E+05 8.591E+04 6.013E+04 1.959E+04 6.656E+04 7.925E+04 7.302E+04 8.063E+04 1.190E+05 1.304E+05 1.428E+05 F4 AVG 1.278E+04 3.959E+03 1.102E+03 8.208E+02 7.129E+02 7.066E+02 7.432E+02 8.679E+02 1.163E+03 1.350E+03 1.735E+03 STD 2.622E+03 1.307E+03 2.305E+02 9.704E+01 7.232E+01 6.293E+01 6.339E+01 1.240E+02 1.888E+02 1.741E+02 4.078E+02 F5 AVG 1.295E+03 1.217E+03 1.179E+03 1.082E+03 1.034E+03 1.065E+03 1.084E+03 1.120E+03 1.181E+03 1.216E+03 1.235E+03 STD 5.292E+01 6.436E+01 6.907E+01 7.977E+01 8.308E+01 6.962E+01 8.031E+01 7.565E+01 9.610E+01 7.664E+01 9.415E+01 F6 AVG 6.597E+02 6.529E+02 6.523E+02 6.414E+02 6.335E+02 6.300E+02 6.363E+02 6.440E+02 6.512E+02 6.542E+02 6.570E+02 STD 2.225E+00 3.789E+00 4.703E+00 3.749E+00 5.715E+00 8.221E+00 8.594E+00 6.299E+00 7.237E+00 1.035E+01 8.109E+00 F7 AVG 2.923E+03 2.772E+03 2.580E+03 2.327E+03 2.075E+03 2.034E+03 2.079E+03 2.188E+03 2.342E+03 2.328E+03 2.455E+03 STD 1.478E+02 1.666E+02 1.929E+02 1.577E+02 2.172E+02 2.110E+02 1.836E+02 2.495E+02 1.773E+02 2.457E+02 2.641E+02 F8 AVG 1.697E+03 1.632E+03 1.528E+03 1.434E+03 1.327E+03 1.383E+03 1.390E+03 1.429E+03 1.487E+03 1.495E+03 1.537E+03 STD 8.951E+01 7.377E+01 1.053E+02 1.023E+02 6.811E+01 9.873E+01 9.919E+01 7.765E+01 9.488E+01 8.495E+01 6.870E+01 F9 AVG 2.241E+04 2.125E+04 2.194E+04 2.119E+04 2.074E+04 2.109E+04 2.531E+04 2.730E+04 2.777E+04 3.081E+04 3.106E+04 STD 1.879E+03 3.028E+03 2.716E+03 3.604E+03 4.387E+03 4.398E+03 6.374E+03 7.103E+03 7.141E+03 7.473E+03 7.173E+03 F10 AVG 1.552E+04 1.528E+04 1.568E+04 1.619E+04 1.715E+04 1.737E+04 1.745E+04 1.774E+04 1.748E+04 1.792E+04 1.789E+04 STD 1.433E+03 1.514E+03 1.520E+03 1.909E+03 1.171E+03 9.974E+02 1.246E+03 1.252E+03 1.163E+03 1.411E+03 1.028E+03 F11 AVG 1.464E+05 9.459E+04 3.111E+04 2.023E+04 5.689E+03 3.076E+03 4.140E+03 2.165E+04 5.401E+04 8.655E+04 1.050E+05 STD 3.729E+04 3.697E+04 1.152E+04 8.654E+03 3.551E+03 4.419E+02 1.209E+03 1.009E+04 1.927E+04 3.162E+04 3.050E+04 F12 AVG 1.695E+10 1.665E+09 3.034E+07 6.202E+06 5.476E+06 6.449E+06 1.003E+07 2.219E+07 1.040E+08 3.094E+08 7.058E+08 STD 7.926E+09 2.080E+09 5.443E+07 4.475E+06 5.121E+06 1.151E+07 1.470E+07 1.865E+07 1.121E+08 2.437E+08 3.804E+08 F13 AVG 3.277E+07 1.202E+05 9.140E+04 3.304E+04 2.870E+04 4.421E+04 3.371E+04 9.169E+03 2.936E+04 4.504E+04 1.658E+05 STD 1.139E+08 3.774E+04 4.605E+04 1.486E+04 7.177E+04 1.131E+05 1.003E+05 5.901E+03 7.205E+04 1.322E+04 6.229E+04 F14 AVG 1.896E+06 1.561E+06 1.342E+06 1.232E+06 5.877E+05 3.686E+05 8.159E+05 2.173E+06 3.415E+06 5.356E+06 7.193E+06 STD 7.518E+05 1.116E+06 8.398E+05 4.759E+05 2.801E+05 1.846E+05 8.509E+05 2.043E+06 2.583E+06 4.388E+06 7.969E+06 F15 AVG 8.393E+04 7.950E+04 7.664E+04 9.574E+03 6.460E+03 6.086E+03 1.462E+04 3.278E+04 1.878E+04 2.576E+04 2.095E+04 STD 2.645E+04 2.750E+04 6.888E+04 8.199E+03 4.513E+03 4.943E+03 3.800E+04 9.819E+04 6.708E+04 6.043E+04 4.194E+04 F16 AVG 6.920E+03 6.289E+03 6.016E+03 5.668E+03 5.348E+03 5.924E+03 6.724E+03 6.700E+03 7.113E+03 7.298E+03 7.421E+03 STD 7.439E+02 8.380E+02 6.214E+02 7.759E+02 8.370E+02 1.049E+03 7.609E+02 8.161E+02 6.320E+02 8.515E+02 5.791E+02 F17 AVG 6.800E+03 6.365E+03 5.955E+03 5.618E+03 5.413E+03 5.594E+03 6.011E+03 6.075E+03 6.246E+03 6.314E+03 6.249E+03 STD 6.943E+02 8.492E+02 6.722E+02 6.398E+02 7.268E+02 7.542E+02 7.050E+02 5.409E+02 6.563E+02 5.550E+02 5.441E+02 F18 AVG 2.026E+06 1.904E+06 1.863E+06 1.500E+06 1.290E+06 1.507E+06 3.541E+06 4.462E+06 6.234E+06 6.504E+06 1.060E+07 STD 6.074E+05 7.596E+05 8.407E+05 6.108E+05 6.376E+05 6.459E+05 2.536E+06 2.267E+06 5.037E+06 6.148E+06 7.007E+06 F19 AVG 2.801E+05 3.191E+04 1.613E+04 1.512E+04 1.593E+04 3.269E+04 1.461E+04 1.154E+04 1.031E+04 1.268E+04 9.816E+04 STD 5.838E+05 4.391E+04 2.775E+04 1.958E+04 5.166E+04 9.770E+04 3.495E+04 1.073E+04 9.029E+03 9.227E+03 7.001E+04 F20 AVG 5.134E+03 5.102E+03 5.418E+03 5.550E+03 5.632E+03 5.797E+03 5.906E+03 6.210E+03 6.311E+03 6.063E+03 6.189E+03 STD 3.923E+02 5.914E+02 6.999E+02 7.569E+02 4.797E+02 5.541E+02 4.371E+02 5.977E+02 5.534E+02 4.855E+02 6.158E+02 F21 AVG 3.739E+03 3.446E+03 3.200E+03 3.035E+03 2.864E+03 2.832E+03 2.865E+03 2.942E+03 2.945E+03 3.008E+03 3.053E+03 STD 2.345E+02 2.345E+02 1.406E+02 1.176E+02 9.146E+01 8.806E+01 8.089E+01 9.915E+01 9.563E+01 1.065E+02 1.063E+02 F22 AVG 1.909E+04 1.859E+04 1.774E+04 1.814E+04 1.873E+04 1.917E+04 1.962E+04 1.947E+04 1.933E+04 1.960E+04 1.941E+04 STD 1.693E+03 1.531E+03 3.543E+03 2.108E+03 1.891E+03 1.188E+03 1.262E+03 1.519E+03 1.332E+03 1.332E+03 1.502E+03 F23 AVG 4.889E+03 4.412E+03 4.103E+03 3.836E+03 3.669E+03 3.487E+03 3.423E+03 3.487E+03 3.516E+03 3.582E+03 3.601E+03 STD 3.052E+02 2.333E+02 1.763E+02 1.413E+02 1.508E+02 1.410E+02 1.127E+02 8.480E+01 8.006E+01 8.809E+01 6.876E+01 F24 AVG 7.181E+03 6.328E+03 5.270E+03 4.722E+03 4.388E+03 4.035E+03 3.897E+03 3.919E+03 3.962E+03 4.027E+03 4.094E+03 STD 6.075E+02 4.909E+02 3.844E+02 3.069E+02 2.475E+02 2.154E+02 1.210E+02 1.216E+02 8.631E+01 1.044E+02 1.114E+02 F25 AVG 8.355E+03 5.461E+03 4.046E+03 3.589E+03 3.434E+03 3.425E+03 3.463E+03 3.660E+03 3.872E+03 4.152E+03 4.472E+03 STD 5.858E+02 4.121E+02 2.713E+02 1.167E+02 1.098E+02 7.410E+01 6.797E+01 1.577E+02 1.706E+02 2.049E+02 3.319E+02 F26 AVG 3.075E+04 2.805E+04 2.381E+04 1.947E+04 1.371E+04 1.211E+04 1.188E+04 1.226E+04 1.301E+04 1.289E+04 1.354E+04 STD 3.116E+03 2.756E+03 2.669E+03 2.755E+03 1.688E+03 1.397E+03 1.230E+03 9.012E+02 1.093E+03 1.252E+03 1.286E+03 F27 AVG 6.557E+03 5.171E+03 4.471E+03 4.002E+03 3.748E+03 3.571E+03 3.548E+03 3.515E+03 3.542E+03 3.552E+03 3.643E+03 STD 9.832E+02 4.193E+02 3.473E+02 2.344E+02 1.391E+02 8.738E+01 8.408E+01 8.253E+01 8.997E+01 8.927E+01 8.530E+01 F28 AVG 1.318E+04 8.071E+03 4.696E+03 3.650E+03 3.508E+03 3.481E+03 5.329E+03 6.513E+03 6.603E+03 9.715E+03 1.132E+04 STD 1.340E+03 1.221E+03 1.117E+03 6.102E+01 4.642E+01 5.467E+01 4.157E+03 4.887E+03 4.802E+03 5.354E+03 5.122E+03 F29 AVG 1.088E+04 9.285E+03 8.261E+03 7.484E+03 6.929E+03 6.749E+03 7.465E+03 7.939E+03 8.372E+03 8.609E+03 9.134E+03 STD 1.639E+03 1.108E+03 7.723E+02 5.802E+02 5.311E+02 7.165E+02 9.875E+02 8.928E+02 6.819E+02 7.066E+02 8.418E+02 F30 AVG 3.155E+08 1.284E+07 4.840E+05 1.355E+05 1.848E+04 1.299E+04 1.349E+04 1.723E+04 4.385E+04 4.864E+05 2.085E+06 STD 3.238E+08 1.243E+07 6.963E+05 1.666E+05 2.076E+04 5.289E+03 4.728E+03 6.461E+03 2.149E+04 8.486E+05 1.827E+06 Avg 9.086 7.797 6.338 4.793 3.529 3.397 4.099 5.294 6.312 7.233 8.122 Rank 11 9 7 4 2 1 3 5 6 8 10 Open in new tab Table A6: The relevant experimental results of pheromone evaporation rate. Fun . Item . 0.5 . 0.6 . 0.7 . 0.8 . 0.9 . 1 . 1.1 . 1.2 . 1.3 . 1.4 . 1.5 . F1 AVG 9.960E+10 3.065E+10 2.401E+04 4.241E+03 6.909E+03 7.309E+03 5.976E+03 1.283E+07 1.116E+09 3.370E+09 5.416E+09 STD 1.384E+10 9.129E+09 1.058E+05 4.504E+03 1.019E+04 9.085E+03 7.335E+03 3.036E+07 6.707E+08 1.494E+09 1.900E+09 F2 AVG 3.421E+131 1.530E+121 1.053E+117 4.306E+85 6.038E+84 1.081E+69 2.626E+114 1.485E+136 5.787E+139 2.377E+142 5.347E+146 STD 1.720E+132 8.286E+121 5.747E+117 2.358E+86 3.307E+85 5.923E+69 1.438E+115 8.131E+136 2.724E+140 1.302E+143 2.074E+147 F3 AVG 4.167E+05 3.019E+05 2.288E+05 1.631E+05 2.608E+05 3.614E+05 4.017E+05 4.576E+05 5.313E+05 5.837E+05 6.244E+05 STD 1.747E+05 8.591E+04 6.013E+04 1.959E+04 6.656E+04 7.925E+04 7.302E+04 8.063E+04 1.190E+05 1.304E+05 1.428E+05 F4 AVG 1.278E+04 3.959E+03 1.102E+03 8.208E+02 7.129E+02 7.066E+02 7.432E+02 8.679E+02 1.163E+03 1.350E+03 1.735E+03 STD 2.622E+03 1.307E+03 2.305E+02 9.704E+01 7.232E+01 6.293E+01 6.339E+01 1.240E+02 1.888E+02 1.741E+02 4.078E+02 F5 AVG 1.295E+03 1.217E+03 1.179E+03 1.082E+03 1.034E+03 1.065E+03 1.084E+03 1.120E+03 1.181E+03 1.216E+03 1.235E+03 STD 5.292E+01 6.436E+01 6.907E+01 7.977E+01 8.308E+01 6.962E+01 8.031E+01 7.565E+01 9.610E+01 7.664E+01 9.415E+01 F6 AVG 6.597E+02 6.529E+02 6.523E+02 6.414E+02 6.335E+02 6.300E+02 6.363E+02 6.440E+02 6.512E+02 6.542E+02 6.570E+02 STD 2.225E+00 3.789E+00 4.703E+00 3.749E+00 5.715E+00 8.221E+00 8.594E+00 6.299E+00 7.237E+00 1.035E+01 8.109E+00 F7 AVG 2.923E+03 2.772E+03 2.580E+03 2.327E+03 2.075E+03 2.034E+03 2.079E+03 2.188E+03 2.342E+03 2.328E+03 2.455E+03 STD 1.478E+02 1.666E+02 1.929E+02 1.577E+02 2.172E+02 2.110E+02 1.836E+02 2.495E+02 1.773E+02 2.457E+02 2.641E+02 F8 AVG 1.697E+03 1.632E+03 1.528E+03 1.434E+03 1.327E+03 1.383E+03 1.390E+03 1.429E+03 1.487E+03 1.495E+03 1.537E+03 STD 8.951E+01 7.377E+01 1.053E+02 1.023E+02 6.811E+01 9.873E+01 9.919E+01 7.765E+01 9.488E+01 8.495E+01 6.870E+01 F9 AVG 2.241E+04 2.125E+04 2.194E+04 2.119E+04 2.074E+04 2.109E+04 2.531E+04 2.730E+04 2.777E+04 3.081E+04 3.106E+04 STD 1.879E+03 3.028E+03 2.716E+03 3.604E+03 4.387E+03 4.398E+03 6.374E+03 7.103E+03 7.141E+03 7.473E+03 7.173E+03 F10 AVG 1.552E+04 1.528E+04 1.568E+04 1.619E+04 1.715E+04 1.737E+04 1.745E+04 1.774E+04 1.748E+04 1.792E+04 1.789E+04 STD 1.433E+03 1.514E+03 1.520E+03 1.909E+03 1.171E+03 9.974E+02 1.246E+03 1.252E+03 1.163E+03 1.411E+03 1.028E+03 F11 AVG 1.464E+05 9.459E+04 3.111E+04 2.023E+04 5.689E+03 3.076E+03 4.140E+03 2.165E+04 5.401E+04 8.655E+04 1.050E+05 STD 3.729E+04 3.697E+04 1.152E+04 8.654E+03 3.551E+03 4.419E+02 1.209E+03 1.009E+04 1.927E+04 3.162E+04 3.050E+04 F12 AVG 1.695E+10 1.665E+09 3.034E+07 6.202E+06 5.476E+06 6.449E+06 1.003E+07 2.219E+07 1.040E+08 3.094E+08 7.058E+08 STD 7.926E+09 2.080E+09 5.443E+07 4.475E+06 5.121E+06 1.151E+07 1.470E+07 1.865E+07 1.121E+08 2.437E+08 3.804E+08 F13 AVG 3.277E+07 1.202E+05 9.140E+04 3.304E+04 2.870E+04 4.421E+04 3.371E+04 9.169E+03 2.936E+04 4.504E+04 1.658E+05 STD 1.139E+08 3.774E+04 4.605E+04 1.486E+04 7.177E+04 1.131E+05 1.003E+05 5.901E+03 7.205E+04 1.322E+04 6.229E+04 F14 AVG 1.896E+06 1.561E+06 1.342E+06 1.232E+06 5.877E+05 3.686E+05 8.159E+05 2.173E+06 3.415E+06 5.356E+06 7.193E+06 STD 7.518E+05 1.116E+06 8.398E+05 4.759E+05 2.801E+05 1.846E+05 8.509E+05 2.043E+06 2.583E+06 4.388E+06 7.969E+06 F15 AVG 8.393E+04 7.950E+04 7.664E+04 9.574E+03 6.460E+03 6.086E+03 1.462E+04 3.278E+04 1.878E+04 2.576E+04 2.095E+04 STD 2.645E+04 2.750E+04 6.888E+04 8.199E+03 4.513E+03 4.943E+03 3.800E+04 9.819E+04 6.708E+04 6.043E+04 4.194E+04 F16 AVG 6.920E+03 6.289E+03 6.016E+03 5.668E+03 5.348E+03 5.924E+03 6.724E+03 6.700E+03 7.113E+03 7.298E+03 7.421E+03 STD 7.439E+02 8.380E+02 6.214E+02 7.759E+02 8.370E+02 1.049E+03 7.609E+02 8.161E+02 6.320E+02 8.515E+02 5.791E+02 F17 AVG 6.800E+03 6.365E+03 5.955E+03 5.618E+03 5.413E+03 5.594E+03 6.011E+03 6.075E+03 6.246E+03 6.314E+03 6.249E+03 STD 6.943E+02 8.492E+02 6.722E+02 6.398E+02 7.268E+02 7.542E+02 7.050E+02 5.409E+02 6.563E+02 5.550E+02 5.441E+02 F18 AVG 2.026E+06 1.904E+06 1.863E+06 1.500E+06 1.290E+06 1.507E+06 3.541E+06 4.462E+06 6.234E+06 6.504E+06 1.060E+07 STD 6.074E+05 7.596E+05 8.407E+05 6.108E+05 6.376E+05 6.459E+05 2.536E+06 2.267E+06 5.037E+06 6.148E+06 7.007E+06 F19 AVG 2.801E+05 3.191E+04 1.613E+04 1.512E+04 1.593E+04 3.269E+04 1.461E+04 1.154E+04 1.031E+04 1.268E+04 9.816E+04 STD 5.838E+05 4.391E+04 2.775E+04 1.958E+04 5.166E+04 9.770E+04 3.495E+04 1.073E+04 9.029E+03 9.227E+03 7.001E+04 F20 AVG 5.134E+03 5.102E+03 5.418E+03 5.550E+03 5.632E+03 5.797E+03 5.906E+03 6.210E+03 6.311E+03 6.063E+03 6.189E+03 STD 3.923E+02 5.914E+02 6.999E+02 7.569E+02 4.797E+02 5.541E+02 4.371E+02 5.977E+02 5.534E+02 4.855E+02 6.158E+02 F21 AVG 3.739E+03 3.446E+03 3.200E+03 3.035E+03 2.864E+03 2.832E+03 2.865E+03 2.942E+03 2.945E+03 3.008E+03 3.053E+03 STD 2.345E+02 2.345E+02 1.406E+02 1.176E+02 9.146E+01 8.806E+01 8.089E+01 9.915E+01 9.563E+01 1.065E+02 1.063E+02 F22 AVG 1.909E+04 1.859E+04 1.774E+04 1.814E+04 1.873E+04 1.917E+04 1.962E+04 1.947E+04 1.933E+04 1.960E+04 1.941E+04 STD 1.693E+03 1.531E+03 3.543E+03 2.108E+03 1.891E+03 1.188E+03 1.262E+03 1.519E+03 1.332E+03 1.332E+03 1.502E+03 F23 AVG 4.889E+03 4.412E+03 4.103E+03 3.836E+03 3.669E+03 3.487E+03 3.423E+03 3.487E+03 3.516E+03 3.582E+03 3.601E+03 STD 3.052E+02 2.333E+02 1.763E+02 1.413E+02 1.508E+02 1.410E+02 1.127E+02 8.480E+01 8.006E+01 8.809E+01 6.876E+01 F24 AVG 7.181E+03 6.328E+03 5.270E+03 4.722E+03 4.388E+03 4.035E+03 3.897E+03 3.919E+03 3.962E+03 4.027E+03 4.094E+03 STD 6.075E+02 4.909E+02 3.844E+02 3.069E+02 2.475E+02 2.154E+02 1.210E+02 1.216E+02 8.631E+01 1.044E+02 1.114E+02 F25 AVG 8.355E+03 5.461E+03 4.046E+03 3.589E+03 3.434E+03 3.425E+03 3.463E+03 3.660E+03 3.872E+03 4.152E+03 4.472E+03 STD 5.858E+02 4.121E+02 2.713E+02 1.167E+02 1.098E+02 7.410E+01 6.797E+01 1.577E+02 1.706E+02 2.049E+02 3.319E+02 F26 AVG 3.075E+04 2.805E+04 2.381E+04 1.947E+04 1.371E+04 1.211E+04 1.188E+04 1.226E+04 1.301E+04 1.289E+04 1.354E+04 STD 3.116E+03 2.756E+03 2.669E+03 2.755E+03 1.688E+03 1.397E+03 1.230E+03 9.012E+02 1.093E+03 1.252E+03 1.286E+03 F27 AVG 6.557E+03 5.171E+03 4.471E+03 4.002E+03 3.748E+03 3.571E+03 3.548E+03 3.515E+03 3.542E+03 3.552E+03 3.643E+03 STD 9.832E+02 4.193E+02 3.473E+02 2.344E+02 1.391E+02 8.738E+01 8.408E+01 8.253E+01 8.997E+01 8.927E+01 8.530E+01 F28 AVG 1.318E+04 8.071E+03 4.696E+03 3.650E+03 3.508E+03 3.481E+03 5.329E+03 6.513E+03 6.603E+03 9.715E+03 1.132E+04 STD 1.340E+03 1.221E+03 1.117E+03 6.102E+01 4.642E+01 5.467E+01 4.157E+03 4.887E+03 4.802E+03 5.354E+03 5.122E+03 F29 AVG 1.088E+04 9.285E+03 8.261E+03 7.484E+03 6.929E+03 6.749E+03 7.465E+03 7.939E+03 8.372E+03 8.609E+03 9.134E+03 STD 1.639E+03 1.108E+03 7.723E+02 5.802E+02 5.311E+02 7.165E+02 9.875E+02 8.928E+02 6.819E+02 7.066E+02 8.418E+02 F30 AVG 3.155E+08 1.284E+07 4.840E+05 1.355E+05 1.848E+04 1.299E+04 1.349E+04 1.723E+04 4.385E+04 4.864E+05 2.085E+06 STD 3.238E+08 1.243E+07 6.963E+05 1.666E+05 2.076E+04 5.289E+03 4.728E+03 6.461E+03 2.149E+04 8.486E+05 1.827E+06 Avg 9.086 7.797 6.338 4.793 3.529 3.397 4.099 5.294 6.312 7.233 8.122 Rank 11 9 7 4 2 1 3 5 6 8 10 Fun . Item . 0.5 . 0.6 . 0.7 . 0.8 . 0.9 . 1 . 1.1 . 1.2 . 1.3 . 1.4 . 1.5 . F1 AVG 9.960E+10 3.065E+10 2.401E+04 4.241E+03 6.909E+03 7.309E+03 5.976E+03 1.283E+07 1.116E+09 3.370E+09 5.416E+09 STD 1.384E+10 9.129E+09 1.058E+05 4.504E+03 1.019E+04 9.085E+03 7.335E+03 3.036E+07 6.707E+08 1.494E+09 1.900E+09 F2 AVG 3.421E+131 1.530E+121 1.053E+117 4.306E+85 6.038E+84 1.081E+69 2.626E+114 1.485E+136 5.787E+139 2.377E+142 5.347E+146 STD 1.720E+132 8.286E+121 5.747E+117 2.358E+86 3.307E+85 5.923E+69 1.438E+115 8.131E+136 2.724E+140 1.302E+143 2.074E+147 F3 AVG 4.167E+05 3.019E+05 2.288E+05 1.631E+05 2.608E+05 3.614E+05 4.017E+05 4.576E+05 5.313E+05 5.837E+05 6.244E+05 STD 1.747E+05 8.591E+04 6.013E+04 1.959E+04 6.656E+04 7.925E+04 7.302E+04 8.063E+04 1.190E+05 1.304E+05 1.428E+05 F4 AVG 1.278E+04 3.959E+03 1.102E+03 8.208E+02 7.129E+02 7.066E+02 7.432E+02 8.679E+02 1.163E+03 1.350E+03 1.735E+03 STD 2.622E+03 1.307E+03 2.305E+02 9.704E+01 7.232E+01 6.293E+01 6.339E+01 1.240E+02 1.888E+02 1.741E+02 4.078E+02 F5 AVG 1.295E+03 1.217E+03 1.179E+03 1.082E+03 1.034E+03 1.065E+03 1.084E+03 1.120E+03 1.181E+03 1.216E+03 1.235E+03 STD 5.292E+01 6.436E+01 6.907E+01 7.977E+01 8.308E+01 6.962E+01 8.031E+01 7.565E+01 9.610E+01 7.664E+01 9.415E+01 F6 AVG 6.597E+02 6.529E+02 6.523E+02 6.414E+02 6.335E+02 6.300E+02 6.363E+02 6.440E+02 6.512E+02 6.542E+02 6.570E+02 STD 2.225E+00 3.789E+00 4.703E+00 3.749E+00 5.715E+00 8.221E+00 8.594E+00 6.299E+00 7.237E+00 1.035E+01 8.109E+00 F7 AVG 2.923E+03 2.772E+03 2.580E+03 2.327E+03 2.075E+03 2.034E+03 2.079E+03 2.188E+03 2.342E+03 2.328E+03 2.455E+03 STD 1.478E+02 1.666E+02 1.929E+02 1.577E+02 2.172E+02 2.110E+02 1.836E+02 2.495E+02 1.773E+02 2.457E+02 2.641E+02 F8 AVG 1.697E+03 1.632E+03 1.528E+03 1.434E+03 1.327E+03 1.383E+03 1.390E+03 1.429E+03 1.487E+03 1.495E+03 1.537E+03 STD 8.951E+01 7.377E+01 1.053E+02 1.023E+02 6.811E+01 9.873E+01 9.919E+01 7.765E+01 9.488E+01 8.495E+01 6.870E+01 F9 AVG 2.241E+04 2.125E+04 2.194E+04 2.119E+04 2.074E+04 2.109E+04 2.531E+04 2.730E+04 2.777E+04 3.081E+04 3.106E+04 STD 1.879E+03 3.028E+03 2.716E+03 3.604E+03 4.387E+03 4.398E+03 6.374E+03 7.103E+03 7.141E+03 7.473E+03 7.173E+03 F10 AVG 1.552E+04 1.528E+04 1.568E+04 1.619E+04 1.715E+04 1.737E+04 1.745E+04 1.774E+04 1.748E+04 1.792E+04 1.789E+04 STD 1.433E+03 1.514E+03 1.520E+03 1.909E+03 1.171E+03 9.974E+02 1.246E+03 1.252E+03 1.163E+03 1.411E+03 1.028E+03 F11 AVG 1.464E+05 9.459E+04 3.111E+04 2.023E+04 5.689E+03 3.076E+03 4.140E+03 2.165E+04 5.401E+04 8.655E+04 1.050E+05 STD 3.729E+04 3.697E+04 1.152E+04 8.654E+03 3.551E+03 4.419E+02 1.209E+03 1.009E+04 1.927E+04 3.162E+04 3.050E+04 F12 AVG 1.695E+10 1.665E+09 3.034E+07 6.202E+06 5.476E+06 6.449E+06 1.003E+07 2.219E+07 1.040E+08 3.094E+08 7.058E+08 STD 7.926E+09 2.080E+09 5.443E+07 4.475E+06 5.121E+06 1.151E+07 1.470E+07 1.865E+07 1.121E+08 2.437E+08 3.804E+08 F13 AVG 3.277E+07 1.202E+05 9.140E+04 3.304E+04 2.870E+04 4.421E+04 3.371E+04 9.169E+03 2.936E+04 4.504E+04 1.658E+05 STD 1.139E+08 3.774E+04 4.605E+04 1.486E+04 7.177E+04 1.131E+05 1.003E+05 5.901E+03 7.205E+04 1.322E+04 6.229E+04 F14 AVG 1.896E+06 1.561E+06 1.342E+06 1.232E+06 5.877E+05 3.686E+05 8.159E+05 2.173E+06 3.415E+06 5.356E+06 7.193E+06 STD 7.518E+05 1.116E+06 8.398E+05 4.759E+05 2.801E+05 1.846E+05 8.509E+05 2.043E+06 2.583E+06 4.388E+06 7.969E+06 F15 AVG 8.393E+04 7.950E+04 7.664E+04 9.574E+03 6.460E+03 6.086E+03 1.462E+04 3.278E+04 1.878E+04 2.576E+04 2.095E+04 STD 2.645E+04 2.750E+04 6.888E+04 8.199E+03 4.513E+03 4.943E+03 3.800E+04 9.819E+04 6.708E+04 6.043E+04 4.194E+04 F16 AVG 6.920E+03 6.289E+03 6.016E+03 5.668E+03 5.348E+03 5.924E+03 6.724E+03 6.700E+03 7.113E+03 7.298E+03 7.421E+03 STD 7.439E+02 8.380E+02 6.214E+02 7.759E+02 8.370E+02 1.049E+03 7.609E+02 8.161E+02 6.320E+02 8.515E+02 5.791E+02 F17 AVG 6.800E+03 6.365E+03 5.955E+03 5.618E+03 5.413E+03 5.594E+03 6.011E+03 6.075E+03 6.246E+03 6.314E+03 6.249E+03 STD 6.943E+02 8.492E+02 6.722E+02 6.398E+02 7.268E+02 7.542E+02 7.050E+02 5.409E+02 6.563E+02 5.550E+02 5.441E+02 F18 AVG 2.026E+06 1.904E+06 1.863E+06 1.500E+06 1.290E+06 1.507E+06 3.541E+06 4.462E+06 6.234E+06 6.504E+06 1.060E+07 STD 6.074E+05 7.596E+05 8.407E+05 6.108E+05 6.376E+05 6.459E+05 2.536E+06 2.267E+06 5.037E+06 6.148E+06 7.007E+06 F19 AVG 2.801E+05 3.191E+04 1.613E+04 1.512E+04 1.593E+04 3.269E+04 1.461E+04 1.154E+04 1.031E+04 1.268E+04 9.816E+04 STD 5.838E+05 4.391E+04 2.775E+04 1.958E+04 5.166E+04 9.770E+04 3.495E+04 1.073E+04 9.029E+03 9.227E+03 7.001E+04 F20 AVG 5.134E+03 5.102E+03 5.418E+03 5.550E+03 5.632E+03 5.797E+03 5.906E+03 6.210E+03 6.311E+03 6.063E+03 6.189E+03 STD 3.923E+02 5.914E+02 6.999E+02 7.569E+02 4.797E+02 5.541E+02 4.371E+02 5.977E+02 5.534E+02 4.855E+02 6.158E+02 F21 AVG 3.739E+03 3.446E+03 3.200E+03 3.035E+03 2.864E+03 2.832E+03 2.865E+03 2.942E+03 2.945E+03 3.008E+03 3.053E+03 STD 2.345E+02 2.345E+02 1.406E+02 1.176E+02 9.146E+01 8.806E+01 8.089E+01 9.915E+01 9.563E+01 1.065E+02 1.063E+02 F22 AVG 1.909E+04 1.859E+04 1.774E+04 1.814E+04 1.873E+04 1.917E+04 1.962E+04 1.947E+04 1.933E+04 1.960E+04 1.941E+04 STD 1.693E+03 1.531E+03 3.543E+03 2.108E+03 1.891E+03 1.188E+03 1.262E+03 1.519E+03 1.332E+03 1.332E+03 1.502E+03 F23 AVG 4.889E+03 4.412E+03 4.103E+03 3.836E+03 3.669E+03 3.487E+03 3.423E+03 3.487E+03 3.516E+03 3.582E+03 3.601E+03 STD 3.052E+02 2.333E+02 1.763E+02 1.413E+02 1.508E+02 1.410E+02 1.127E+02 8.480E+01 8.006E+01 8.809E+01 6.876E+01 F24 AVG 7.181E+03 6.328E+03 5.270E+03 4.722E+03 4.388E+03 4.035E+03 3.897E+03 3.919E+03 3.962E+03 4.027E+03 4.094E+03 STD 6.075E+02 4.909E+02 3.844E+02 3.069E+02 2.475E+02 2.154E+02 1.210E+02 1.216E+02 8.631E+01 1.044E+02 1.114E+02 F25 AVG 8.355E+03 5.461E+03 4.046E+03 3.589E+03 3.434E+03 3.425E+03 3.463E+03 3.660E+03 3.872E+03 4.152E+03 4.472E+03 STD 5.858E+02 4.121E+02 2.713E+02 1.167E+02 1.098E+02 7.410E+01 6.797E+01 1.577E+02 1.706E+02 2.049E+02 3.319E+02 F26 AVG 3.075E+04 2.805E+04 2.381E+04 1.947E+04 1.371E+04 1.211E+04 1.188E+04 1.226E+04 1.301E+04 1.289E+04 1.354E+04 STD 3.116E+03 2.756E+03 2.669E+03 2.755E+03 1.688E+03 1.397E+03 1.230E+03 9.012E+02 1.093E+03 1.252E+03 1.286E+03 F27 AVG 6.557E+03 5.171E+03 4.471E+03 4.002E+03 3.748E+03 3.571E+03 3.548E+03 3.515E+03 3.542E+03 3.552E+03 3.643E+03 STD 9.832E+02 4.193E+02 3.473E+02 2.344E+02 1.391E+02 8.738E+01 8.408E+01 8.253E+01 8.997E+01 8.927E+01 8.530E+01 F28 AVG 1.318E+04 8.071E+03 4.696E+03 3.650E+03 3.508E+03 3.481E+03 5.329E+03 6.513E+03 6.603E+03 9.715E+03 1.132E+04 STD 1.340E+03 1.221E+03 1.117E+03 6.102E+01 4.642E+01 5.467E+01 4.157E+03 4.887E+03 4.802E+03 5.354E+03 5.122E+03 F29 AVG 1.088E+04 9.285E+03 8.261E+03 7.484E+03 6.929E+03 6.749E+03 7.465E+03 7.939E+03 8.372E+03 8.609E+03 9.134E+03 STD 1.639E+03 1.108E+03 7.723E+02 5.802E+02 5.311E+02 7.165E+02 9.875E+02 8.928E+02 6.819E+02 7.066E+02 8.418E+02 F30 AVG 3.155E+08 1.284E+07 4.840E+05 1.355E+05 1.848E+04 1.299E+04 1.349E+04 1.723E+04 4.385E+04 4.864E+05 2.085E+06 STD 3.238E+08 1.243E+07 6.963E+05 1.666E+05 2.076E+04 5.289E+03 4.728E+03 6.461E+03 2.149E+04 8.486E+05 1.827E+06 Avg 9.086 7.797 6.338 4.793 3.529 3.397 4.099 5.294 6.312 7.233 8.122 Rank 11 9 7 4 2 1 3 5 6 8 10 Open in new tab Table A7: The results of the comparison between ADNOLACO and the nine basic algorithms. Fun . Item . ADNOLACO . ACOR . DE . FA . GWO . HHO . MFO . PSO . SCA . WOA . F1 AVG 6.0028E+03 3.4681E+10 1.7658E+04 1.2949E+11 5.0111E+10 4.4339E+08 1.4254E+11 1.5681E+09 1.6467E+11 1.1180E+09 STD 7.1452E+03 2.2201E+10 2.1066E+04 7.2370E+09 1.2645E+10 4.4414E+07 5.5320E+10 7.7777E+07 8.3098E+09 3.8262E+08 F2 AVG 5.7958E+118 1.6942E+130 9.1443E+137 5.4672E+151 2.9123E+133 6.6775E+103 2.2054E+159 5.1230E+74 3.6166E+152 2.8596E+155 STD 3.1717E+119 9.2796E+130 1.8000E+138 1.8714E+152 1.5948E+134 3.6500E+104 6.5535E+04 1.4610E+75 1.9730E+153 6.5535E+04 F3 AVG 4.9279E+05 5.8116E+05 6.0882E+05 4.3741E+05 2.2657E+05 1.9781E+05 6.8058E+05 8.6298E+04 3.3177E+05 7.5807E+05 STD 8.7639E+04 9.9045E+04 5.2925E+04 3.3924E+04 2.3338E+04 2.3223E+04 1.7517E+05 1.9896E+04 2.9638E+04 1.4312E+05 F4 AVG 7.1229E+02 3.7573E+03 6.1876E+02 1.7742E+04 4.8887E+03 1.0150E+03 2.1892E+04 7.9574E+02 3.2477E+04 1.4872E+03 STD 6.2538E+01 1.9373E+03 1.2862E+01 1.5144E+03 1.6184E+03 9.7609E+01 1.0254E+04 8.9391E+01 4.5857E+03 2.3372E+02 F5 AVG 1.0593E+03 1.6355E+03 1.4075E+03 1.7420E+03 1.1396E+03 1.5005E+03 1.8253E+03 1.7081E+03 1.8967E+03 1.5152E+03 STD 7.8108E+01 2.1814E+02 2.2668E+01 2.2588E+01 6.0751E+01 5.2321E+01 1.4382E+02 5.6627E+01 5.0301E+01 1.1288E+02 F6 AVG 6.2657E+02 6.2740E+02 6.0000E+02 6.7534E+02 6.3917E+02 6.8186E+02 6.7345E+02 6.8873E+02 6.9306E+02 6.8497E+02 STD 7.1335E+00 5.9942E+00 3.7110E-13 2.7275E+00 4.7465E+00 4.0279E+00 7.6487E+00 5.5109E+00 4.4485E+00 1.0067E+01 F7 AVG 1.8375E+03 3.3471E+03 1.7299E+03 4.9710E+03 1.9955E+03 3.6463E+03 5.2192E+03 1.8374E+03 3.5462E+03 3.3740E+03 STD 1.7278E+02 4.6117E+02 3.5364E+01 1.4839E+02 1.2162E+02 1.0829E+02 6.3278E+02 6.7718E+01 1.2757E+02 1.0477E+02 F8 AVG 1.3388E+03 1.8605E+03 1.7048E+03 2.0612E+03 1.4222E+03 1.9292E+03 2.1356E+03 2.0812E+03 2.2603E+03 1.9854E+03 STD 7.8388E+01 2.8228E+02 2.7598E+01 2.5188E+01 5.6934E+01 5.6765E+01 1.7764E+02 7.7798E+01 6.5793E+01 1.0999E+02 F9 AVG 2.3411E+04 6.5620E+04 1.3749E+03 4.9326E+04 3.2759E+04 4.5838E+04 4.6720E+04 6.3802E+04 7.2560E+04 4.4790E+04 STD 6.2391E+03 1.7250E+04 2.4034E+02 4.7311E+03 1.3687E+04 3.8661E+03 6.2995E+03 7.3951E+03 6.7079E+03 8.8246E+03 F10 AVG 1.7581E+04 3.1369E+04 2.9735E+04 3.1427E+04 1.5072E+04 2.0315E+04 1.7734E+04 2.4920E+04 3.1592E+04 2.1783E+04 STD 1.2405E+03 7.8428E+02 4.6280E+02 5.9761E+02 1.6201E+03 1.2499E+03 1.4476E+03 1.2090E+03 4.2462E+02 2.5626E+03 F11 AVG 1.2152E+04 3.0970E+04 8.0990E+03 1.2830E+05 5.4998E+04 4.6423E+03 1.2332E+05 3.5105E+03 8.9477E+04 4.8954E+04 STD 9.2459E+03 3.2613E+04 1.6155E+03 1.8123E+04 1.2011E+04 7.3468E+02 9.1345E+04 2.3180E+02 1.4815E+04 2.1687E+04 F12 AVG 1.0189E+07 3.1848E+09 2.5107E+08 4.6312E+10 7.8253E+09 4.7446E+08 4.5509E+10 1.1006E+09 6.1380E+10 1.2151E+09 STD 1.7671E+07 4.3719E+09 4.0708E+07 3.9711E+09 3.8718E+09 1.1631E+08 2.4756E+10 1.9338E+08 8.5173E+09 3.9133E+08 F13 AVG 2.2693E+04 8.0360E+06 7.8591E+03 9.7288E+09 1.0466E+09 7.0536E+06 7.3340E+09 9.4664E+07 1.0032E+10 1.3350E+06 STD 7.8098E+04 3.8295E+07 1.0613E+04 9.4723E+08 9.6283E+08 1.4568E+06 3.9823E+09 1.0226E+07 1.9366E+09 1.3703E+06 F14 AVG 1.4990E+06 1.0512E+06 1.3287E+07 3.8009E+07 4.7065E+06 2.1451E+06 1.0518E+07 1.4759E+06 2.3444E+07 4.1118E+06 STD 1.2951E+06 9.5249E+05 3.7747E+06 1.0248E+07 3.3519E+06 5.1768E+05 1.2731E+07 4.0402E+05 1.0701E+07 2.4404E+06 F15 AVG 2.5377E+04 2.4397E+04 2.8849E+04 4.0827E+09 2.1062E+08 2.2179E+06 1.2710E+09 3.4048E+07 3.1769E+09 1.7726E+05 STD 7.1797E+04 1.5083E+04 2.4375E+04 5.6323E+08 3.1777E+08 1.4173E+06 1.3981E+09 4.7972E+06 6.7020E+08 1.6438E+05 F16 AVG 6.7997E+03 6.6953E+03 8.9770E+03 1.1729E+04 5.8484E+03 7.3403E+03 8.1767E+03 7.9589E+03 1.3350E+04 1.0888E+04 STD 8.2300E+02 2.3674E+03 3.5980E+02 4.4502E+02 7.3143E+02 7.1049E+02 8.9032E+02 7.0004E+02 6.7657E+02 1.4993E+03 F17 AVG 6.0091E+03 5.7638E+03 5.5197E+03 1.2537E+04 4.8080E+03 6.3590E+03 3.1665E+04 6.1660E+03 1.4525E+04 7.3525E+03 STD 6.2750E+02 1.4790E+03 2.9158E+02 1.2617E+03 7.8534E+02 6.1244E+02 1.0178E+05 5.0955E+02 4.9052E+03 8.0057E+02 F18 AVG 3.4706E+06 4.0566E+06 2.3162E+07 7.0953E+07 4.9053E+06 3.1637E+06 1.8693E+07 2.8095E+06 5.0197E+07 3.3844E+06 STD 2.4617E+06 3.9401E+06 6.2128E+06 1.4606E+07 3.2047E+06 1.1178E+06 2.5716E+07 1.2376E+06 1.8014E+07 1.3426E+06 F19 AVG 7.3798E+03 8.7749E+05 2.2961E+04 3.9014E+09 1.8530E+08 8.2954E+06 1.5764E+09 4.5438E+07 2.7156E+09 2.6032E+07 STD 6.7516E+03 2.0986E+06 3.0036E+04 4.4975E+08 2.8642E+08 2.4947E+06 1.7318E+09 9.2647E+06 7.7693E+08 1.4209E+07 F20 AVG 5.6076E+03 7.1459E+03 5.6582E+03 7.0323E+03 4.4686E+03 5.9749E+03 5.8870E+03 5.9158E+03 7.4043E+03 6.3353E+03 STD 5.6437E+02 3.2783E+02 2.5337E+02 2.7372E+02 6.3624E+02 5.8048E+02 5.4213E+02 3.8649E+02 2.0336E+02 6.8298E+02 F21 AVG 2.8543E+03 3.4238E+03 3.2436E+03 3.5965E+03 2.9256E+03 4.0772E+03 3.6904E+03 3.7535E+03 3.9915E+03 3.9672E+03 STD 6.2248E+01 2.5269E+02 2.0733E+01 2.0879E+01 7.8128E+01 2.3425E+02 1.4184E+02 1.1775E+02 8.5239E+01 1.9786E+02 F22 AVG 1.9610E+04 3.2126E+04 3.1761E+04 3.3420E+04 1.8177E+04 2.3593E+04 2.0628E+04 2.8108E+04 3.4042E+04 2.5706E+04 STD 1.2271E+03 3.9533E+03 5.6175E+02 5.7973E+02 3.1822E+03 1.4776E+03 1.6283E+03 1.4072E+03 7.1057E+02 2.4122E+03 F23 AVG 3.4037E+03 3.4696E+03 3.5493E+03 4.1209E+03 3.5710E+03 5.1291E+03 3.8743E+03 4.9284E+03 4.8865E+03 4.8079E+03 STD 1.1017E+02 9.4916E+01 2.4421E+01 3.4337E+01 1.0557E+02 3.9899E+02 9.7304E+01 3.2978E+02 1.0623E+02 1.9911E+02 F24 AVG 3.8529E+03 3.9268E+03 4.1157E+03 4.8692E+03 4.2046E+03 6.4972E+03 4.5209E+03 5.8941E+03 6.5166E+03 6.0739E+03 STD 1.0470E+02 1.4384E+02 2.0280E+01 5.5349E+01 1.4727E+02 4.5163E+02 1.8798E+02 3.9033E+02 2.3030E+02 4.0886E+02 F25 AVG 3.3823E+03 5.3114E+03 3.2633E+03 1.7819E+04 6.6504E+03 3.6688E+03 1.1777E+04 3.4473E+03 1.5883E+04 3.9791E+03 STD 7.7397E+01 1.2725E+03 3.5037E+01 1.0290E+03 8.3302E+02 8.1348E+01 5.1280E+03 4.1371E+01 1.5794E+03 1.8233E+02 F26 AVG 1.1418E+04 1.4994E+04 1.4759E+04 2.1533E+04 1.5128E+04 2.5071E+04 2.0853E+04 1.3040E+04 3.4214E+04 3.3254E+04 STD 7.8480E+02 2.4911E+03 2.3334E+02 5.3819E+02 1.0696E+03 2.1667E+03 1.9910E+03 9.1341E+03 1.7788E+03 3.5350E+03 F27 AVG 3.5053E+03 3.6093E+03 3.5357E+03 5.2225E+03 4.0100E+03 4.3352E+03 4.1042E+03 3.2692E+03 7.1278E+03 5.1854E+03 STD 7.5694E+01 1.2404E+02 6.0460E+01 1.6804E+02 1.3073E+02 3.8685E+02 1.6847E+02 3.0602E+01 3.0711E+02 7.6058E+02 F28 AVG 5.9840E+03 1.5456E+04 3.3996E+03 1.6095E+04 8.3312E+03 3.6704E+03 2.0117E+04 3.4218E+03 2.0292E+04 4.3533E+03 STD 4.6234E+03 2.0170E+03 2.4487E+02 1.1591E+03 1.2888E+03 6.4903E+01 3.1192E+03 3.9249E+01 1.7978E+03 1.9545E+02 F29 AVG 6.8783E+03 6.9171E+03 7.3326E+03 1.8728E+04 8.4144E+03 9.5532E+03 1.3382E+04 9.8320E+03 1.8435E+04 1.4206E+04 STD 1.1093E+03 7.0208E+02 3.2169E+02 1.4056E+03 9.0906E+02 7.8726E+02 1.0409E+04 6.0570E+02 3.2067E+03 2.0848E+03 F30 AVG 2.2316E+04 1.0261E+08 2.2270E+04 6.1417E+09 6.0335E+08 4.5978E+07 3.2365E+09 1.6485E+08 7.3188E+09 3.4958E+08 STD 4.5522E+04 3.1685E+08 6.9884E+03 7.4022E+08 6.3399E+08 1.5173E+07 2.6693E+09 4.7447E+07 1.3730E+09 1.5622E+08 Fun . Item . ADNOLACO . ACOR . DE . FA . GWO . HHO . MFO . PSO . SCA . WOA . F1 AVG 6.0028E+03 3.4681E+10 1.7658E+04 1.2949E+11 5.0111E+10 4.4339E+08 1.4254E+11 1.5681E+09 1.6467E+11 1.1180E+09 STD 7.1452E+03 2.2201E+10 2.1066E+04 7.2370E+09 1.2645E+10 4.4414E+07 5.5320E+10 7.7777E+07 8.3098E+09 3.8262E+08 F2 AVG 5.7958E+118 1.6942E+130 9.1443E+137 5.4672E+151 2.9123E+133 6.6775E+103 2.2054E+159 5.1230E+74 3.6166E+152 2.8596E+155 STD 3.1717E+119 9.2796E+130 1.8000E+138 1.8714E+152 1.5948E+134 3.6500E+104 6.5535E+04 1.4610E+75 1.9730E+153 6.5535E+04 F3 AVG 4.9279E+05 5.8116E+05 6.0882E+05 4.3741E+05 2.2657E+05 1.9781E+05 6.8058E+05 8.6298E+04 3.3177E+05 7.5807E+05 STD 8.7639E+04 9.9045E+04 5.2925E+04 3.3924E+04 2.3338E+04 2.3223E+04 1.7517E+05 1.9896E+04 2.9638E+04 1.4312E+05 F4 AVG 7.1229E+02 3.7573E+03 6.1876E+02 1.7742E+04 4.8887E+03 1.0150E+03 2.1892E+04 7.9574E+02 3.2477E+04 1.4872E+03 STD 6.2538E+01 1.9373E+03 1.2862E+01 1.5144E+03 1.6184E+03 9.7609E+01 1.0254E+04 8.9391E+01 4.5857E+03 2.3372E+02 F5 AVG 1.0593E+03 1.6355E+03 1.4075E+03 1.7420E+03 1.1396E+03 1.5005E+03 1.8253E+03 1.7081E+03 1.8967E+03 1.5152E+03 STD 7.8108E+01 2.1814E+02 2.2668E+01 2.2588E+01 6.0751E+01 5.2321E+01 1.4382E+02 5.6627E+01 5.0301E+01 1.1288E+02 F6 AVG 6.2657E+02 6.2740E+02 6.0000E+02 6.7534E+02 6.3917E+02 6.8186E+02 6.7345E+02 6.8873E+02 6.9306E+02 6.8497E+02 STD 7.1335E+00 5.9942E+00 3.7110E-13 2.7275E+00 4.7465E+00 4.0279E+00 7.6487E+00 5.5109E+00 4.4485E+00 1.0067E+01 F7 AVG 1.8375E+03 3.3471E+03 1.7299E+03 4.9710E+03 1.9955E+03 3.6463E+03 5.2192E+03 1.8374E+03 3.5462E+03 3.3740E+03 STD 1.7278E+02 4.6117E+02 3.5364E+01 1.4839E+02 1.2162E+02 1.0829E+02 6.3278E+02 6.7718E+01 1.2757E+02 1.0477E+02 F8 AVG 1.3388E+03 1.8605E+03 1.7048E+03 2.0612E+03 1.4222E+03 1.9292E+03 2.1356E+03 2.0812E+03 2.2603E+03 1.9854E+03 STD 7.8388E+01 2.8228E+02 2.7598E+01 2.5188E+01 5.6934E+01 5.6765E+01 1.7764E+02 7.7798E+01 6.5793E+01 1.0999E+02 F9 AVG 2.3411E+04 6.5620E+04 1.3749E+03 4.9326E+04 3.2759E+04 4.5838E+04 4.6720E+04 6.3802E+04 7.2560E+04 4.4790E+04 STD 6.2391E+03 1.7250E+04 2.4034E+02 4.7311E+03 1.3687E+04 3.8661E+03 6.2995E+03 7.3951E+03 6.7079E+03 8.8246E+03 F10 AVG 1.7581E+04 3.1369E+04 2.9735E+04 3.1427E+04 1.5072E+04 2.0315E+04 1.7734E+04 2.4920E+04 3.1592E+04 2.1783E+04 STD 1.2405E+03 7.8428E+02 4.6280E+02 5.9761E+02 1.6201E+03 1.2499E+03 1.4476E+03 1.2090E+03 4.2462E+02 2.5626E+03 F11 AVG 1.2152E+04 3.0970E+04 8.0990E+03 1.2830E+05 5.4998E+04 4.6423E+03 1.2332E+05 3.5105E+03 8.9477E+04 4.8954E+04 STD 9.2459E+03 3.2613E+04 1.6155E+03 1.8123E+04 1.2011E+04 7.3468E+02 9.1345E+04 2.3180E+02 1.4815E+04 2.1687E+04 F12 AVG 1.0189E+07 3.1848E+09 2.5107E+08 4.6312E+10 7.8253E+09 4.7446E+08 4.5509E+10 1.1006E+09 6.1380E+10 1.2151E+09 STD 1.7671E+07 4.3719E+09 4.0708E+07 3.9711E+09 3.8718E+09 1.1631E+08 2.4756E+10 1.9338E+08 8.5173E+09 3.9133E+08 F13 AVG 2.2693E+04 8.0360E+06 7.8591E+03 9.7288E+09 1.0466E+09 7.0536E+06 7.3340E+09 9.4664E+07 1.0032E+10 1.3350E+06 STD 7.8098E+04 3.8295E+07 1.0613E+04 9.4723E+08 9.6283E+08 1.4568E+06 3.9823E+09 1.0226E+07 1.9366E+09 1.3703E+06 F14 AVG 1.4990E+06 1.0512E+06 1.3287E+07 3.8009E+07 4.7065E+06 2.1451E+06 1.0518E+07 1.4759E+06 2.3444E+07 4.1118E+06 STD 1.2951E+06 9.5249E+05 3.7747E+06 1.0248E+07 3.3519E+06 5.1768E+05 1.2731E+07 4.0402E+05 1.0701E+07 2.4404E+06 F15 AVG 2.5377E+04 2.4397E+04 2.8849E+04 4.0827E+09 2.1062E+08 2.2179E+06 1.2710E+09 3.4048E+07 3.1769E+09 1.7726E+05 STD 7.1797E+04 1.5083E+04 2.4375E+04 5.6323E+08 3.1777E+08 1.4173E+06 1.3981E+09 4.7972E+06 6.7020E+08 1.6438E+05 F16 AVG 6.7997E+03 6.6953E+03 8.9770E+03 1.1729E+04 5.8484E+03 7.3403E+03 8.1767E+03 7.9589E+03 1.3350E+04 1.0888E+04 STD 8.2300E+02 2.3674E+03 3.5980E+02 4.4502E+02 7.3143E+02 7.1049E+02 8.9032E+02 7.0004E+02 6.7657E+02 1.4993E+03 F17 AVG 6.0091E+03 5.7638E+03 5.5197E+03 1.2537E+04 4.8080E+03 6.3590E+03 3.1665E+04 6.1660E+03 1.4525E+04 7.3525E+03 STD 6.2750E+02 1.4790E+03 2.9158E+02 1.2617E+03 7.8534E+02 6.1244E+02 1.0178E+05 5.0955E+02 4.9052E+03 8.0057E+02 F18 AVG 3.4706E+06 4.0566E+06 2.3162E+07 7.0953E+07 4.9053E+06 3.1637E+06 1.8693E+07 2.8095E+06 5.0197E+07 3.3844E+06 STD 2.4617E+06 3.9401E+06 6.2128E+06 1.4606E+07 3.2047E+06 1.1178E+06 2.5716E+07 1.2376E+06 1.8014E+07 1.3426E+06 F19 AVG 7.3798E+03 8.7749E+05 2.2961E+04 3.9014E+09 1.8530E+08 8.2954E+06 1.5764E+09 4.5438E+07 2.7156E+09 2.6032E+07 STD 6.7516E+03 2.0986E+06 3.0036E+04 4.4975E+08 2.8642E+08 2.4947E+06 1.7318E+09 9.2647E+06 7.7693E+08 1.4209E+07 F20 AVG 5.6076E+03 7.1459E+03 5.6582E+03 7.0323E+03 4.4686E+03 5.9749E+03 5.8870E+03 5.9158E+03 7.4043E+03 6.3353E+03 STD 5.6437E+02 3.2783E+02 2.5337E+02 2.7372E+02 6.3624E+02 5.8048E+02 5.4213E+02 3.8649E+02 2.0336E+02 6.8298E+02 F21 AVG 2.8543E+03 3.4238E+03 3.2436E+03 3.5965E+03 2.9256E+03 4.0772E+03 3.6904E+03 3.7535E+03 3.9915E+03 3.9672E+03 STD 6.2248E+01 2.5269E+02 2.0733E+01 2.0879E+01 7.8128E+01 2.3425E+02 1.4184E+02 1.1775E+02 8.5239E+01 1.9786E+02 F22 AVG 1.9610E+04 3.2126E+04 3.1761E+04 3.3420E+04 1.8177E+04 2.3593E+04 2.0628E+04 2.8108E+04 3.4042E+04 2.5706E+04 STD 1.2271E+03 3.9533E+03 5.6175E+02 5.7973E+02 3.1822E+03 1.4776E+03 1.6283E+03 1.4072E+03 7.1057E+02 2.4122E+03 F23 AVG 3.4037E+03 3.4696E+03 3.5493E+03 4.1209E+03 3.5710E+03 5.1291E+03 3.8743E+03 4.9284E+03 4.8865E+03 4.8079E+03 STD 1.1017E+02 9.4916E+01 2.4421E+01 3.4337E+01 1.0557E+02 3.9899E+02 9.7304E+01 3.2978E+02 1.0623E+02 1.9911E+02 F24 AVG 3.8529E+03 3.9268E+03 4.1157E+03 4.8692E+03 4.2046E+03 6.4972E+03 4.5209E+03 5.8941E+03 6.5166E+03 6.0739E+03 STD 1.0470E+02 1.4384E+02 2.0280E+01 5.5349E+01 1.4727E+02 4.5163E+02 1.8798E+02 3.9033E+02 2.3030E+02 4.0886E+02 F25 AVG 3.3823E+03 5.3114E+03 3.2633E+03 1.7819E+04 6.6504E+03 3.6688E+03 1.1777E+04 3.4473E+03 1.5883E+04 3.9791E+03 STD 7.7397E+01 1.2725E+03 3.5037E+01 1.0290E+03 8.3302E+02 8.1348E+01 5.1280E+03 4.1371E+01 1.5794E+03 1.8233E+02 F26 AVG 1.1418E+04 1.4994E+04 1.4759E+04 2.1533E+04 1.5128E+04 2.5071E+04 2.0853E+04 1.3040E+04 3.4214E+04 3.3254E+04 STD 7.8480E+02 2.4911E+03 2.3334E+02 5.3819E+02 1.0696E+03 2.1667E+03 1.9910E+03 9.1341E+03 1.7788E+03 3.5350E+03 F27 AVG 3.5053E+03 3.6093E+03 3.5357E+03 5.2225E+03 4.0100E+03 4.3352E+03 4.1042E+03 3.2692E+03 7.1278E+03 5.1854E+03 STD 7.5694E+01 1.2404E+02 6.0460E+01 1.6804E+02 1.3073E+02 3.8685E+02 1.6847E+02 3.0602E+01 3.0711E+02 7.6058E+02 F28 AVG 5.9840E+03 1.5456E+04 3.3996E+03 1.6095E+04 8.3312E+03 3.6704E+03 2.0117E+04 3.4218E+03 2.0292E+04 4.3533E+03 STD 4.6234E+03 2.0170E+03 2.4487E+02 1.1591E+03 1.2888E+03 6.4903E+01 3.1192E+03 3.9249E+01 1.7978E+03 1.9545E+02 F29 AVG 6.8783E+03 6.9171E+03 7.3326E+03 1.8728E+04 8.4144E+03 9.5532E+03 1.3382E+04 9.8320E+03 1.8435E+04 1.4206E+04 STD 1.1093E+03 7.0208E+02 3.2169E+02 1.4056E+03 9.0906E+02 7.8726E+02 1.0409E+04 6.0570E+02 3.2067E+03 2.0848E+03 F30 AVG 2.2316E+04 1.0261E+08 2.2270E+04 6.1417E+09 6.0335E+08 4.5978E+07 3.2365E+09 1.6485E+08 7.3188E+09 3.4958E+08 STD 4.5522E+04 3.1685E+08 6.9884E+03 7.4022E+08 6.3399E+08 1.5173E+07 2.6693E+09 4.7447E+07 1.3730E+09 1.5622E+08 Open in new tab Table A7: The results of the comparison between ADNOLACO and the nine basic algorithms. Fun . Item . ADNOLACO . ACOR . DE . FA . GWO . HHO . MFO . PSO . SCA . WOA . F1 AVG 6.0028E+03 3.4681E+10 1.7658E+04 1.2949E+11 5.0111E+10 4.4339E+08 1.4254E+11 1.5681E+09 1.6467E+11 1.1180E+09 STD 7.1452E+03 2.2201E+10 2.1066E+04 7.2370E+09 1.2645E+10 4.4414E+07 5.5320E+10 7.7777E+07 8.3098E+09 3.8262E+08 F2 AVG 5.7958E+118 1.6942E+130 9.1443E+137 5.4672E+151 2.9123E+133 6.6775E+103 2.2054E+159 5.1230E+74 3.6166E+152 2.8596E+155 STD 3.1717E+119 9.2796E+130 1.8000E+138 1.8714E+152 1.5948E+134 3.6500E+104 6.5535E+04 1.4610E+75 1.9730E+153 6.5535E+04 F3 AVG 4.9279E+05 5.8116E+05 6.0882E+05 4.3741E+05 2.2657E+05 1.9781E+05 6.8058E+05 8.6298E+04 3.3177E+05 7.5807E+05 STD 8.7639E+04 9.9045E+04 5.2925E+04 3.3924E+04 2.3338E+04 2.3223E+04 1.7517E+05 1.9896E+04 2.9638E+04 1.4312E+05 F4 AVG 7.1229E+02 3.7573E+03 6.1876E+02 1.7742E+04 4.8887E+03 1.0150E+03 2.1892E+04 7.9574E+02 3.2477E+04 1.4872E+03 STD 6.2538E+01 1.9373E+03 1.2862E+01 1.5144E+03 1.6184E+03 9.7609E+01 1.0254E+04 8.9391E+01 4.5857E+03 2.3372E+02 F5 AVG 1.0593E+03 1.6355E+03 1.4075E+03 1.7420E+03 1.1396E+03 1.5005E+03 1.8253E+03 1.7081E+03 1.8967E+03 1.5152E+03 STD 7.8108E+01 2.1814E+02 2.2668E+01 2.2588E+01 6.0751E+01 5.2321E+01 1.4382E+02 5.6627E+01 5.0301E+01 1.1288E+02 F6 AVG 6.2657E+02 6.2740E+02 6.0000E+02 6.7534E+02 6.3917E+02 6.8186E+02 6.7345E+02 6.8873E+02 6.9306E+02 6.8497E+02 STD 7.1335E+00 5.9942E+00 3.7110E-13 2.7275E+00 4.7465E+00 4.0279E+00 7.6487E+00 5.5109E+00 4.4485E+00 1.0067E+01 F7 AVG 1.8375E+03 3.3471E+03 1.7299E+03 4.9710E+03 1.9955E+03 3.6463E+03 5.2192E+03 1.8374E+03 3.5462E+03 3.3740E+03 STD 1.7278E+02 4.6117E+02 3.5364E+01 1.4839E+02 1.2162E+02 1.0829E+02 6.3278E+02 6.7718E+01 1.2757E+02 1.0477E+02 F8 AVG 1.3388E+03 1.8605E+03 1.7048E+03 2.0612E+03 1.4222E+03 1.9292E+03 2.1356E+03 2.0812E+03 2.2603E+03 1.9854E+03 STD 7.8388E+01 2.8228E+02 2.7598E+01 2.5188E+01 5.6934E+01 5.6765E+01 1.7764E+02 7.7798E+01 6.5793E+01 1.0999E+02 F9 AVG 2.3411E+04 6.5620E+04 1.3749E+03 4.9326E+04 3.2759E+04 4.5838E+04 4.6720E+04 6.3802E+04 7.2560E+04 4.4790E+04 STD 6.2391E+03 1.7250E+04 2.4034E+02 4.7311E+03 1.3687E+04 3.8661E+03 6.2995E+03 7.3951E+03 6.7079E+03 8.8246E+03 F10 AVG 1.7581E+04 3.1369E+04 2.9735E+04 3.1427E+04 1.5072E+04 2.0315E+04 1.7734E+04 2.4920E+04 3.1592E+04 2.1783E+04 STD 1.2405E+03 7.8428E+02 4.6280E+02 5.9761E+02 1.6201E+03 1.2499E+03 1.4476E+03 1.2090E+03 4.2462E+02 2.5626E+03 F11 AVG 1.2152E+04 3.0970E+04 8.0990E+03 1.2830E+05 5.4998E+04 4.6423E+03 1.2332E+05 3.5105E+03 8.9477E+04 4.8954E+04 STD 9.2459E+03 3.2613E+04 1.6155E+03 1.8123E+04 1.2011E+04 7.3468E+02 9.1345E+04 2.3180E+02 1.4815E+04 2.1687E+04 F12 AVG 1.0189E+07 3.1848E+09 2.5107E+08 4.6312E+10 7.8253E+09 4.7446E+08 4.5509E+10 1.1006E+09 6.1380E+10 1.2151E+09 STD 1.7671E+07 4.3719E+09 4.0708E+07 3.9711E+09 3.8718E+09 1.1631E+08 2.4756E+10 1.9338E+08 8.5173E+09 3.9133E+08 F13 AVG 2.2693E+04 8.0360E+06 7.8591E+03 9.7288E+09 1.0466E+09 7.0536E+06 7.3340E+09 9.4664E+07 1.0032E+10 1.3350E+06 STD 7.8098E+04 3.8295E+07 1.0613E+04 9.4723E+08 9.6283E+08 1.4568E+06 3.9823E+09 1.0226E+07 1.9366E+09 1.3703E+06 F14 AVG 1.4990E+06 1.0512E+06 1.3287E+07 3.8009E+07 4.7065E+06 2.1451E+06 1.0518E+07 1.4759E+06 2.3444E+07 4.1118E+06 STD 1.2951E+06 9.5249E+05 3.7747E+06 1.0248E+07 3.3519E+06 5.1768E+05 1.2731E+07 4.0402E+05 1.0701E+07 2.4404E+06 F15 AVG 2.5377E+04 2.4397E+04 2.8849E+04 4.0827E+09 2.1062E+08 2.2179E+06 1.2710E+09 3.4048E+07 3.1769E+09 1.7726E+05 STD 7.1797E+04 1.5083E+04 2.4375E+04 5.6323E+08 3.1777E+08 1.4173E+06 1.3981E+09 4.7972E+06 6.7020E+08 1.6438E+05 F16 AVG 6.7997E+03 6.6953E+03 8.9770E+03 1.1729E+04 5.8484E+03 7.3403E+03 8.1767E+03 7.9589E+03 1.3350E+04 1.0888E+04 STD 8.2300E+02 2.3674E+03 3.5980E+02 4.4502E+02 7.3143E+02 7.1049E+02 8.9032E+02 7.0004E+02 6.7657E+02 1.4993E+03 F17 AVG 6.0091E+03 5.7638E+03 5.5197E+03 1.2537E+04 4.8080E+03 6.3590E+03 3.1665E+04 6.1660E+03 1.4525E+04 7.3525E+03 STD 6.2750E+02 1.4790E+03 2.9158E+02 1.2617E+03 7.8534E+02 6.1244E+02 1.0178E+05 5.0955E+02 4.9052E+03 8.0057E+02 F18 AVG 3.4706E+06 4.0566E+06 2.3162E+07 7.0953E+07 4.9053E+06 3.1637E+06 1.8693E+07 2.8095E+06 5.0197E+07 3.3844E+06 STD 2.4617E+06 3.9401E+06 6.2128E+06 1.4606E+07 3.2047E+06 1.1178E+06 2.5716E+07 1.2376E+06 1.8014E+07 1.3426E+06 F19 AVG 7.3798E+03 8.7749E+05 2.2961E+04 3.9014E+09 1.8530E+08 8.2954E+06 1.5764E+09 4.5438E+07 2.7156E+09 2.6032E+07 STD 6.7516E+03 2.0986E+06 3.0036E+04 4.4975E+08 2.8642E+08 2.4947E+06 1.7318E+09 9.2647E+06 7.7693E+08 1.4209E+07 F20 AVG 5.6076E+03 7.1459E+03 5.6582E+03 7.0323E+03 4.4686E+03 5.9749E+03 5.8870E+03 5.9158E+03 7.4043E+03 6.3353E+03 STD 5.6437E+02 3.2783E+02 2.5337E+02 2.7372E+02 6.3624E+02 5.8048E+02 5.4213E+02 3.8649E+02 2.0336E+02 6.8298E+02 F21 AVG 2.8543E+03 3.4238E+03 3.2436E+03 3.5965E+03 2.9256E+03 4.0772E+03 3.6904E+03 3.7535E+03 3.9915E+03 3.9672E+03 STD 6.2248E+01 2.5269E+02 2.0733E+01 2.0879E+01 7.8128E+01 2.3425E+02 1.4184E+02 1.1775E+02 8.5239E+01 1.9786E+02 F22 AVG 1.9610E+04 3.2126E+04 3.1761E+04 3.3420E+04 1.8177E+04 2.3593E+04 2.0628E+04 2.8108E+04 3.4042E+04 2.5706E+04 STD 1.2271E+03 3.9533E+03 5.6175E+02 5.7973E+02 3.1822E+03 1.4776E+03 1.6283E+03 1.4072E+03 7.1057E+02 2.4122E+03 F23 AVG 3.4037E+03 3.4696E+03 3.5493E+03 4.1209E+03 3.5710E+03 5.1291E+03 3.8743E+03 4.9284E+03 4.8865E+03 4.8079E+03 STD 1.1017E+02 9.4916E+01 2.4421E+01 3.4337E+01 1.0557E+02 3.9899E+02 9.7304E+01 3.2978E+02 1.0623E+02 1.9911E+02 F24 AVG 3.8529E+03 3.9268E+03 4.1157E+03 4.8692E+03 4.2046E+03 6.4972E+03 4.5209E+03 5.8941E+03 6.5166E+03 6.0739E+03 STD 1.0470E+02 1.4384E+02 2.0280E+01 5.5349E+01 1.4727E+02 4.5163E+02 1.8798E+02 3.9033E+02 2.3030E+02 4.0886E+02 F25 AVG 3.3823E+03 5.3114E+03 3.2633E+03 1.7819E+04 6.6504E+03 3.6688E+03 1.1777E+04 3.4473E+03 1.5883E+04 3.9791E+03 STD 7.7397E+01 1.2725E+03 3.5037E+01 1.0290E+03 8.3302E+02 8.1348E+01 5.1280E+03 4.1371E+01 1.5794E+03 1.8233E+02 F26 AVG 1.1418E+04 1.4994E+04 1.4759E+04 2.1533E+04 1.5128E+04 2.5071E+04 2.0853E+04 1.3040E+04 3.4214E+04 3.3254E+04 STD 7.8480E+02 2.4911E+03 2.3334E+02 5.3819E+02 1.0696E+03 2.1667E+03 1.9910E+03 9.1341E+03 1.7788E+03 3.5350E+03 F27 AVG 3.5053E+03 3.6093E+03 3.5357E+03 5.2225E+03 4.0100E+03 4.3352E+03 4.1042E+03 3.2692E+03 7.1278E+03 5.1854E+03 STD 7.5694E+01 1.2404E+02 6.0460E+01 1.6804E+02 1.3073E+02 3.8685E+02 1.6847E+02 3.0602E+01 3.0711E+02 7.6058E+02 F28 AVG 5.9840E+03 1.5456E+04 3.3996E+03 1.6095E+04 8.3312E+03 3.6704E+03 2.0117E+04 3.4218E+03 2.0292E+04 4.3533E+03 STD 4.6234E+03 2.0170E+03 2.4487E+02 1.1591E+03 1.2888E+03 6.4903E+01 3.1192E+03 3.9249E+01 1.7978E+03 1.9545E+02 F29 AVG 6.8783E+03 6.9171E+03 7.3326E+03 1.8728E+04 8.4144E+03 9.5532E+03 1.3382E+04 9.8320E+03 1.8435E+04 1.4206E+04 STD 1.1093E+03 7.0208E+02 3.2169E+02 1.4056E+03 9.0906E+02 7.8726E+02 1.0409E+04 6.0570E+02 3.2067E+03 2.0848E+03 F30 AVG 2.2316E+04 1.0261E+08 2.2270E+04 6.1417E+09 6.0335E+08 4.5978E+07 3.2365E+09 1.6485E+08 7.3188E+09 3.4958E+08 STD 4.5522E+04 3.1685E+08 6.9884E+03 7.4022E+08 6.3399E+08 1.5173E+07 2.6693E+09 4.7447E+07 1.3730E+09 1.5622E+08 Fun . Item . ADNOLACO . ACOR . DE . FA . GWO . HHO . MFO . PSO . SCA . WOA . F1 AVG 6.0028E+03 3.4681E+10 1.7658E+04 1.2949E+11 5.0111E+10 4.4339E+08 1.4254E+11 1.5681E+09 1.6467E+11 1.1180E+09 STD 7.1452E+03 2.2201E+10 2.1066E+04 7.2370E+09 1.2645E+10 4.4414E+07 5.5320E+10 7.7777E+07 8.3098E+09 3.8262E+08 F2 AVG 5.7958E+118 1.6942E+130 9.1443E+137 5.4672E+151 2.9123E+133 6.6775E+103 2.2054E+159 5.1230E+74 3.6166E+152 2.8596E+155 STD 3.1717E+119 9.2796E+130 1.8000E+138 1.8714E+152 1.5948E+134 3.6500E+104 6.5535E+04 1.4610E+75 1.9730E+153 6.5535E+04 F3 AVG 4.9279E+05 5.8116E+05 6.0882E+05 4.3741E+05 2.2657E+05 1.9781E+05 6.8058E+05 8.6298E+04 3.3177E+05 7.5807E+05 STD 8.7639E+04 9.9045E+04 5.2925E+04 3.3924E+04 2.3338E+04 2.3223E+04 1.7517E+05 1.9896E+04 2.9638E+04 1.4312E+05 F4 AVG 7.1229E+02 3.7573E+03 6.1876E+02 1.7742E+04 4.8887E+03 1.0150E+03 2.1892E+04 7.9574E+02 3.2477E+04 1.4872E+03 STD 6.2538E+01 1.9373E+03 1.2862E+01 1.5144E+03 1.6184E+03 9.7609E+01 1.0254E+04 8.9391E+01 4.5857E+03 2.3372E+02 F5 AVG 1.0593E+03 1.6355E+03 1.4075E+03 1.7420E+03 1.1396E+03 1.5005E+03 1.8253E+03 1.7081E+03 1.8967E+03 1.5152E+03 STD 7.8108E+01 2.1814E+02 2.2668E+01 2.2588E+01 6.0751E+01 5.2321E+01 1.4382E+02 5.6627E+01 5.0301E+01 1.1288E+02 F6 AVG 6.2657E+02 6.2740E+02 6.0000E+02 6.7534E+02 6.3917E+02 6.8186E+02 6.7345E+02 6.8873E+02 6.9306E+02 6.8497E+02 STD 7.1335E+00 5.9942E+00 3.7110E-13 2.7275E+00 4.7465E+00 4.0279E+00 7.6487E+00 5.5109E+00 4.4485E+00 1.0067E+01 F7 AVG 1.8375E+03 3.3471E+03 1.7299E+03 4.9710E+03 1.9955E+03 3.6463E+03 5.2192E+03 1.8374E+03 3.5462E+03 3.3740E+03 STD 1.7278E+02 4.6117E+02 3.5364E+01 1.4839E+02 1.2162E+02 1.0829E+02 6.3278E+02 6.7718E+01 1.2757E+02 1.0477E+02 F8 AVG 1.3388E+03 1.8605E+03 1.7048E+03 2.0612E+03 1.4222E+03 1.9292E+03 2.1356E+03 2.0812E+03 2.2603E+03 1.9854E+03 STD 7.8388E+01 2.8228E+02 2.7598E+01 2.5188E+01 5.6934E+01 5.6765E+01 1.7764E+02 7.7798E+01 6.5793E+01 1.0999E+02 F9 AVG 2.3411E+04 6.5620E+04 1.3749E+03 4.9326E+04 3.2759E+04 4.5838E+04 4.6720E+04 6.3802E+04 7.2560E+04 4.4790E+04 STD 6.2391E+03 1.7250E+04 2.4034E+02 4.7311E+03 1.3687E+04 3.8661E+03 6.2995E+03 7.3951E+03 6.7079E+03 8.8246E+03 F10 AVG 1.7581E+04 3.1369E+04 2.9735E+04 3.1427E+04 1.5072E+04 2.0315E+04 1.7734E+04 2.4920E+04 3.1592E+04 2.1783E+04 STD 1.2405E+03 7.8428E+02 4.6280E+02 5.9761E+02 1.6201E+03 1.2499E+03 1.4476E+03 1.2090E+03 4.2462E+02 2.5626E+03 F11 AVG 1.2152E+04 3.0970E+04 8.0990E+03 1.2830E+05 5.4998E+04 4.6423E+03 1.2332E+05 3.5105E+03 8.9477E+04 4.8954E+04 STD 9.2459E+03 3.2613E+04 1.6155E+03 1.8123E+04 1.2011E+04 7.3468E+02 9.1345E+04 2.3180E+02 1.4815E+04 2.1687E+04 F12 AVG 1.0189E+07 3.1848E+09 2.5107E+08 4.6312E+10 7.8253E+09 4.7446E+08 4.5509E+10 1.1006E+09 6.1380E+10 1.2151E+09 STD 1.7671E+07 4.3719E+09 4.0708E+07 3.9711E+09 3.8718E+09 1.1631E+08 2.4756E+10 1.9338E+08 8.5173E+09 3.9133E+08 F13 AVG 2.2693E+04 8.0360E+06 7.8591E+03 9.7288E+09 1.0466E+09 7.0536E+06 7.3340E+09 9.4664E+07 1.0032E+10 1.3350E+06 STD 7.8098E+04 3.8295E+07 1.0613E+04 9.4723E+08 9.6283E+08 1.4568E+06 3.9823E+09 1.0226E+07 1.9366E+09 1.3703E+06 F14 AVG 1.4990E+06 1.0512E+06 1.3287E+07 3.8009E+07 4.7065E+06 2.1451E+06 1.0518E+07 1.4759E+06 2.3444E+07 4.1118E+06 STD 1.2951E+06 9.5249E+05 3.7747E+06 1.0248E+07 3.3519E+06 5.1768E+05 1.2731E+07 4.0402E+05 1.0701E+07 2.4404E+06 F15 AVG 2.5377E+04 2.4397E+04 2.8849E+04 4.0827E+09 2.1062E+08 2.2179E+06 1.2710E+09 3.4048E+07 3.1769E+09 1.7726E+05 STD 7.1797E+04 1.5083E+04 2.4375E+04 5.6323E+08 3.1777E+08 1.4173E+06 1.3981E+09 4.7972E+06 6.7020E+08 1.6438E+05 F16 AVG 6.7997E+03 6.6953E+03 8.9770E+03 1.1729E+04 5.8484E+03 7.3403E+03 8.1767E+03 7.9589E+03 1.3350E+04 1.0888E+04 STD 8.2300E+02 2.3674E+03 3.5980E+02 4.4502E+02 7.3143E+02 7.1049E+02 8.9032E+02 7.0004E+02 6.7657E+02 1.4993E+03 F17 AVG 6.0091E+03 5.7638E+03 5.5197E+03 1.2537E+04 4.8080E+03 6.3590E+03 3.1665E+04 6.1660E+03 1.4525E+04 7.3525E+03 STD 6.2750E+02 1.4790E+03 2.9158E+02 1.2617E+03 7.8534E+02 6.1244E+02 1.0178E+05 5.0955E+02 4.9052E+03 8.0057E+02 F18 AVG 3.4706E+06 4.0566E+06 2.3162E+07 7.0953E+07 4.9053E+06 3.1637E+06 1.8693E+07 2.8095E+06 5.0197E+07 3.3844E+06 STD 2.4617E+06 3.9401E+06 6.2128E+06 1.4606E+07 3.2047E+06 1.1178E+06 2.5716E+07 1.2376E+06 1.8014E+07 1.3426E+06 F19 AVG 7.3798E+03 8.7749E+05 2.2961E+04 3.9014E+09 1.8530E+08 8.2954E+06 1.5764E+09 4.5438E+07 2.7156E+09 2.6032E+07 STD 6.7516E+03 2.0986E+06 3.0036E+04 4.4975E+08 2.8642E+08 2.4947E+06 1.7318E+09 9.2647E+06 7.7693E+08 1.4209E+07 F20 AVG 5.6076E+03 7.1459E+03 5.6582E+03 7.0323E+03 4.4686E+03 5.9749E+03 5.8870E+03 5.9158E+03 7.4043E+03 6.3353E+03 STD 5.6437E+02 3.2783E+02 2.5337E+02 2.7372E+02 6.3624E+02 5.8048E+02 5.4213E+02 3.8649E+02 2.0336E+02 6.8298E+02 F21 AVG 2.8543E+03 3.4238E+03 3.2436E+03 3.5965E+03 2.9256E+03 4.0772E+03 3.6904E+03 3.7535E+03 3.9915E+03 3.9672E+03 STD 6.2248E+01 2.5269E+02 2.0733E+01 2.0879E+01 7.8128E+01 2.3425E+02 1.4184E+02 1.1775E+02 8.5239E+01 1.9786E+02 F22 AVG 1.9610E+04 3.2126E+04 3.1761E+04 3.3420E+04 1.8177E+04 2.3593E+04 2.0628E+04 2.8108E+04 3.4042E+04 2.5706E+04 STD 1.2271E+03 3.9533E+03 5.6175E+02 5.7973E+02 3.1822E+03 1.4776E+03 1.6283E+03 1.4072E+03 7.1057E+02 2.4122E+03 F23 AVG 3.4037E+03 3.4696E+03 3.5493E+03 4.1209E+03 3.5710E+03 5.1291E+03 3.8743E+03 4.9284E+03 4.8865E+03 4.8079E+03 STD 1.1017E+02 9.4916E+01 2.4421E+01 3.4337E+01 1.0557E+02 3.9899E+02 9.7304E+01 3.2978E+02 1.0623E+02 1.9911E+02 F24 AVG 3.8529E+03 3.9268E+03 4.1157E+03 4.8692E+03 4.2046E+03 6.4972E+03 4.5209E+03 5.8941E+03 6.5166E+03 6.0739E+03 STD 1.0470E+02 1.4384E+02 2.0280E+01 5.5349E+01 1.4727E+02 4.5163E+02 1.8798E+02 3.9033E+02 2.3030E+02 4.0886E+02 F25 AVG 3.3823E+03 5.3114E+03 3.2633E+03 1.7819E+04 6.6504E+03 3.6688E+03 1.1777E+04 3.4473E+03 1.5883E+04 3.9791E+03 STD 7.7397E+01 1.2725E+03 3.5037E+01 1.0290E+03 8.3302E+02 8.1348E+01 5.1280E+03 4.1371E+01 1.5794E+03 1.8233E+02 F26 AVG 1.1418E+04 1.4994E+04 1.4759E+04 2.1533E+04 1.5128E+04 2.5071E+04 2.0853E+04 1.3040E+04 3.4214E+04 3.3254E+04 STD 7.8480E+02 2.4911E+03 2.3334E+02 5.3819E+02 1.0696E+03 2.1667E+03 1.9910E+03 9.1341E+03 1.7788E+03 3.5350E+03 F27 AVG 3.5053E+03 3.6093E+03 3.5357E+03 5.2225E+03 4.0100E+03 4.3352E+03 4.1042E+03 3.2692E+03 7.1278E+03 5.1854E+03 STD 7.5694E+01 1.2404E+02 6.0460E+01 1.6804E+02 1.3073E+02 3.8685E+02 1.6847E+02 3.0602E+01 3.0711E+02 7.6058E+02 F28 AVG 5.9840E+03 1.5456E+04 3.3996E+03 1.6095E+04 8.3312E+03 3.6704E+03 2.0117E+04 3.4218E+03 2.0292E+04 4.3533E+03 STD 4.6234E+03 2.0170E+03 2.4487E+02 1.1591E+03 1.2888E+03 6.4903E+01 3.1192E+03 3.9249E+01 1.7978E+03 1.9545E+02 F29 AVG 6.8783E+03 6.9171E+03 7.3326E+03 1.8728E+04 8.4144E+03 9.5532E+03 1.3382E+04 9.8320E+03 1.8435E+04 1.4206E+04 STD 1.1093E+03 7.0208E+02 3.2169E+02 1.4056E+03 9.0906E+02 7.8726E+02 1.0409E+04 6.0570E+02 3.2067E+03 2.0848E+03 F30 AVG 2.2316E+04 1.0261E+08 2.2270E+04 6.1417E+09 6.0335E+08 4.5978E+07 3.2365E+09 1.6485E+08 7.3188E+09 3.4958E+08 STD 4.5522E+04 3.1685E+08 6.9884E+03 7.4022E+08 6.3399E+08 1.5173E+07 2.6693E+09 4.7447E+07 1.3730E+09 1.5622E+08 Open in new tab Table A8: The results of the p-values of the nine basic algorithms. . ACOR . DE . FA . GWO . HHO . MFO . PSO . SCA . WOA . F1 1.7344E-06 3.8723E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F2 4.5336E-04 1.7344E-06 1.7344E-06 2.1630E-05 2.3038E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F3 4.6818E-03 4.0715E-05 3.6094E-03 1.7344E-06 1.7344E-06 1.6394E-05 1.7344E-06 4.2857E-06 6.3391E-06 F4 1.7344E-06 3.1817E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 7.7122E-04 1.7344E-06 1.7344E-06 F5 1.7344E-06 1.7344E-06 1.7344E-06 2.2248E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F6 4.9080E-01 1.7344E-06 1.7344E-06 7.6909E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F7 1.7344E-06 9.8421E-03 1.7344E-06 1.1973E-03 1.7344E-06 1.7344E-06 7.8126E-01 1.7344E-06 1.7344E-06 F8 4.2857E-06 1.7344E-06 1.7344E-06 1.8910E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F9 1.7344E-06 1.7344E-06 1.7344E-06 8.3071E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F10 1.7344E-06 1.7344E-06 1.7344E-06 1.2381E-05 2.3534E-06 5.5774E-01 1.7344E-06 1.7344E-06 2.6033E-06 F11 2.7653E-03 1.9152E-01 1.7344E-06 1.7344E-06 1.7988E-05 1.1265E-05 1.9209E-06 1.7344E-06 2.6033E-06 F12 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F13 1.7344E-06 8.2206E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F14 3.5009E-02 1.7344E-06 1.7344E-06 8.1878E-05 9.2710E-03 2.6134E-04 5.3044E-01 1.7344E-06 7.5137E-05 F15 4.8969E-04 2.2551E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.6046E-04 F16 6.4352E-01 1.7344E-06 1.7344E-06 1.1138E-03 1.7518E-02 3.7243E-05 2.5967E-05 1.7344E-06 1.7344E-06 F17 3.3886E-01 4.8969E-04 1.7344E-06 8.4661E-06 5.4463E-02 1.7344E-06 2.8948E-01 1.7344E-06 7.6909E-06 F18 6.8836E-01 1.7344E-06 1.7344E-06 4.9498E-02 7.4987E-01 7.7122E-04 4.5281E-01 1.7344E-06 6.5833E-01 F19 7.6909E-06 3.8811E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F20 1.7344E-06 5.5774E-01 1.7344E-06 3.5152E-06 6.4242E-03 7.8647E-02 2.0671E-02 1.7344E-06 1.0570E-04 F21 1.7344E-06 1.7344E-06 1.7344E-06 1.1973E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F22 2.1266E-06 1.7344E-06 1.7344E-06 4.1955E-04 1.7344E-06 2.8486E-02 1.7344E-06 1.7344E-06 1.9209E-06 F23 2.0671E-02 1.0246E-05 1.7344E-06 4.4493E-05 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F24 2.0671E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F25 1.7344E-06 3.1817E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 5.7064E-04 1.7344E-06 1.7344E-06 F26 1.9209E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 4.7162E-02 1.7344E-06 1.7344E-06 F27 2.0515E-04 1.0201E-01 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F28 1.7344E-06 2.5967E-05 1.7344E-06 6.5641E-02 3.7094E-01 1.7344E-06 1.0570E-04 1.7344E-06 3.7094E-01 F29 8.9364E-01 4.7162E-02 1.7344E-06 1.4936E-05 2.3534E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F30 1.7344E-06 1.7088E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 . ACOR . DE . FA . GWO . HHO . MFO . PSO . SCA . WOA . F1 1.7344E-06 3.8723E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F2 4.5336E-04 1.7344E-06 1.7344E-06 2.1630E-05 2.3038E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F3 4.6818E-03 4.0715E-05 3.6094E-03 1.7344E-06 1.7344E-06 1.6394E-05 1.7344E-06 4.2857E-06 6.3391E-06 F4 1.7344E-06 3.1817E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 7.7122E-04 1.7344E-06 1.7344E-06 F5 1.7344E-06 1.7344E-06 1.7344E-06 2.2248E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F6 4.9080E-01 1.7344E-06 1.7344E-06 7.6909E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F7 1.7344E-06 9.8421E-03 1.7344E-06 1.1973E-03 1.7344E-06 1.7344E-06 7.8126E-01 1.7344E-06 1.7344E-06 F8 4.2857E-06 1.7344E-06 1.7344E-06 1.8910E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F9 1.7344E-06 1.7344E-06 1.7344E-06 8.3071E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F10 1.7344E-06 1.7344E-06 1.7344E-06 1.2381E-05 2.3534E-06 5.5774E-01 1.7344E-06 1.7344E-06 2.6033E-06 F11 2.7653E-03 1.9152E-01 1.7344E-06 1.7344E-06 1.7988E-05 1.1265E-05 1.9209E-06 1.7344E-06 2.6033E-06 F12 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F13 1.7344E-06 8.2206E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F14 3.5009E-02 1.7344E-06 1.7344E-06 8.1878E-05 9.2710E-03 2.6134E-04 5.3044E-01 1.7344E-06 7.5137E-05 F15 4.8969E-04 2.2551E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.6046E-04 F16 6.4352E-01 1.7344E-06 1.7344E-06 1.1138E-03 1.7518E-02 3.7243E-05 2.5967E-05 1.7344E-06 1.7344E-06 F17 3.3886E-01 4.8969E-04 1.7344E-06 8.4661E-06 5.4463E-02 1.7344E-06 2.8948E-01 1.7344E-06 7.6909E-06 F18 6.8836E-01 1.7344E-06 1.7344E-06 4.9498E-02 7.4987E-01 7.7122E-04 4.5281E-01 1.7344E-06 6.5833E-01 F19 7.6909E-06 3.8811E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F20 1.7344E-06 5.5774E-01 1.7344E-06 3.5152E-06 6.4242E-03 7.8647E-02 2.0671E-02 1.7344E-06 1.0570E-04 F21 1.7344E-06 1.7344E-06 1.7344E-06 1.1973E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F22 2.1266E-06 1.7344E-06 1.7344E-06 4.1955E-04 1.7344E-06 2.8486E-02 1.7344E-06 1.7344E-06 1.9209E-06 F23 2.0671E-02 1.0246E-05 1.7344E-06 4.4493E-05 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F24 2.0671E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F25 1.7344E-06 3.1817E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 5.7064E-04 1.7344E-06 1.7344E-06 F26 1.9209E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 4.7162E-02 1.7344E-06 1.7344E-06 F27 2.0515E-04 1.0201E-01 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F28 1.7344E-06 2.5967E-05 1.7344E-06 6.5641E-02 3.7094E-01 1.7344E-06 1.0570E-04 1.7344E-06 3.7094E-01 F29 8.9364E-01 4.7162E-02 1.7344E-06 1.4936E-05 2.3534E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F30 1.7344E-06 1.7088E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 Open in new tab Table A8: The results of the p-values of the nine basic algorithms. . ACOR . DE . FA . GWO . HHO . MFO . PSO . SCA . WOA . F1 1.7344E-06 3.8723E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F2 4.5336E-04 1.7344E-06 1.7344E-06 2.1630E-05 2.3038E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F3 4.6818E-03 4.0715E-05 3.6094E-03 1.7344E-06 1.7344E-06 1.6394E-05 1.7344E-06 4.2857E-06 6.3391E-06 F4 1.7344E-06 3.1817E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 7.7122E-04 1.7344E-06 1.7344E-06 F5 1.7344E-06 1.7344E-06 1.7344E-06 2.2248E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F6 4.9080E-01 1.7344E-06 1.7344E-06 7.6909E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F7 1.7344E-06 9.8421E-03 1.7344E-06 1.1973E-03 1.7344E-06 1.7344E-06 7.8126E-01 1.7344E-06 1.7344E-06 F8 4.2857E-06 1.7344E-06 1.7344E-06 1.8910E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F9 1.7344E-06 1.7344E-06 1.7344E-06 8.3071E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F10 1.7344E-06 1.7344E-06 1.7344E-06 1.2381E-05 2.3534E-06 5.5774E-01 1.7344E-06 1.7344E-06 2.6033E-06 F11 2.7653E-03 1.9152E-01 1.7344E-06 1.7344E-06 1.7988E-05 1.1265E-05 1.9209E-06 1.7344E-06 2.6033E-06 F12 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F13 1.7344E-06 8.2206E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F14 3.5009E-02 1.7344E-06 1.7344E-06 8.1878E-05 9.2710E-03 2.6134E-04 5.3044E-01 1.7344E-06 7.5137E-05 F15 4.8969E-04 2.2551E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.6046E-04 F16 6.4352E-01 1.7344E-06 1.7344E-06 1.1138E-03 1.7518E-02 3.7243E-05 2.5967E-05 1.7344E-06 1.7344E-06 F17 3.3886E-01 4.8969E-04 1.7344E-06 8.4661E-06 5.4463E-02 1.7344E-06 2.8948E-01 1.7344E-06 7.6909E-06 F18 6.8836E-01 1.7344E-06 1.7344E-06 4.9498E-02 7.4987E-01 7.7122E-04 4.5281E-01 1.7344E-06 6.5833E-01 F19 7.6909E-06 3.8811E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F20 1.7344E-06 5.5774E-01 1.7344E-06 3.5152E-06 6.4242E-03 7.8647E-02 2.0671E-02 1.7344E-06 1.0570E-04 F21 1.7344E-06 1.7344E-06 1.7344E-06 1.1973E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F22 2.1266E-06 1.7344E-06 1.7344E-06 4.1955E-04 1.7344E-06 2.8486E-02 1.7344E-06 1.7344E-06 1.9209E-06 F23 2.0671E-02 1.0246E-05 1.7344E-06 4.4493E-05 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F24 2.0671E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F25 1.7344E-06 3.1817E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 5.7064E-04 1.7344E-06 1.7344E-06 F26 1.9209E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 4.7162E-02 1.7344E-06 1.7344E-06 F27 2.0515E-04 1.0201E-01 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F28 1.7344E-06 2.5967E-05 1.7344E-06 6.5641E-02 3.7094E-01 1.7344E-06 1.0570E-04 1.7344E-06 3.7094E-01 F29 8.9364E-01 4.7162E-02 1.7344E-06 1.4936E-05 2.3534E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F30 1.7344E-06 1.7088E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 . ACOR . DE . FA . GWO . HHO . MFO . PSO . SCA . WOA . F1 1.7344E-06 3.8723E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F2 4.5336E-04 1.7344E-06 1.7344E-06 2.1630E-05 2.3038E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F3 4.6818E-03 4.0715E-05 3.6094E-03 1.7344E-06 1.7344E-06 1.6394E-05 1.7344E-06 4.2857E-06 6.3391E-06 F4 1.7344E-06 3.1817E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 7.7122E-04 1.7344E-06 1.7344E-06 F5 1.7344E-06 1.7344E-06 1.7344E-06 2.2248E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F6 4.9080E-01 1.7344E-06 1.7344E-06 7.6909E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F7 1.7344E-06 9.8421E-03 1.7344E-06 1.1973E-03 1.7344E-06 1.7344E-06 7.8126E-01 1.7344E-06 1.7344E-06 F8 4.2857E-06 1.7344E-06 1.7344E-06 1.8910E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F9 1.7344E-06 1.7344E-06 1.7344E-06 8.3071E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F10 1.7344E-06 1.7344E-06 1.7344E-06 1.2381E-05 2.3534E-06 5.5774E-01 1.7344E-06 1.7344E-06 2.6033E-06 F11 2.7653E-03 1.9152E-01 1.7344E-06 1.7344E-06 1.7988E-05 1.1265E-05 1.9209E-06 1.7344E-06 2.6033E-06 F12 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F13 1.7344E-06 8.2206E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F14 3.5009E-02 1.7344E-06 1.7344E-06 8.1878E-05 9.2710E-03 2.6134E-04 5.3044E-01 1.7344E-06 7.5137E-05 F15 4.8969E-04 2.2551E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.6046E-04 F16 6.4352E-01 1.7344E-06 1.7344E-06 1.1138E-03 1.7518E-02 3.7243E-05 2.5967E-05 1.7344E-06 1.7344E-06 F17 3.3886E-01 4.8969E-04 1.7344E-06 8.4661E-06 5.4463E-02 1.7344E-06 2.8948E-01 1.7344E-06 7.6909E-06 F18 6.8836E-01 1.7344E-06 1.7344E-06 4.9498E-02 7.4987E-01 7.7122E-04 4.5281E-01 1.7344E-06 6.5833E-01 F19 7.6909E-06 3.8811E-04 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F20 1.7344E-06 5.5774E-01 1.7344E-06 3.5152E-06 6.4242E-03 7.8647E-02 2.0671E-02 1.7344E-06 1.0570E-04 F21 1.7344E-06 1.7344E-06 1.7344E-06 1.1973E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F22 2.1266E-06 1.7344E-06 1.7344E-06 4.1955E-04 1.7344E-06 2.8486E-02 1.7344E-06 1.7344E-06 1.9209E-06 F23 2.0671E-02 1.0246E-05 1.7344E-06 4.4493E-05 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F24 2.0671E-02 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F25 1.7344E-06 3.1817E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 5.7064E-04 1.7344E-06 1.7344E-06 F26 1.9209E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 4.7162E-02 1.7344E-06 1.7344E-06 F27 2.0515E-04 1.0201E-01 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F28 1.7344E-06 2.5967E-05 1.7344E-06 6.5641E-02 3.7094E-01 1.7344E-06 1.0570E-04 1.7344E-06 3.7094E-01 F29 8.9364E-01 4.7162E-02 1.7344E-06 1.4936E-05 2.3534E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 F30 1.7344E-06 1.7088E-03 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 1.7344E-06 Open in new tab Table A9: The results of the comparison between ADNOLACO and the nine advanced algorithms. Fun . Item . ADNOLACO . MOFOA . CDLOBA . HGWO . OBLGWO . CGSCA . DECLS . m_SCA . ASCA . RDWOA . F1 AVG 7.4890E+03 2.6659E+11 1.1860E+08 9.8644E+10 1.6259E+09 1.8038E+11 4.3208E+04 1.1659E+11 1.7395E+11 1.6257E+09 STD 1.1500E+04 2.9163E+09 4.3436E+08 6.4337E+09 4.7170E+08 1.0208E+10 1.5420E+05 1.1924E+10 1.0889E+10 8.2562E+08 F2 AVG 2.2103E+124 1.4337E+170 5.2749E+108 2.0825E+141 2.0695E+111 2.1183E+154 9.3571E+140 1.9885E+142 8.2332E+152 3.8852E+121 STD 1.2063E+125 6.5535E+04 2.8892E+109 1.1140E+142 1.0918E+112 6.5535E+04 2.2765E+141 1.0891E+143 6.5535E+04 1.8975E+122 F3 AVG 4.8496E+05 3.3878E+05 3.5897E+05 3.4290E+05 2.7117E+05 3.0652E+05 3.6165E+05 2.3533E+05 3.0891E+05 2.4121E+05 STD 1.0611E+05 4.1893E+03 6.0769E+04 1.2289E+04 3.2659E+04 1.3205E+04 7.1351E+03 2.5490E+04 1.6684E+04 2.4056E+04 F4 AVG 7.1619E+02 9.8993E+04 1.0384E+03 1.1506E+04 1.1254E+03 3.5416E+04 6.2981E+02 1.2525E+04 3.5853E+04 1.3476E+03 STD 5.3753E+01 3.1894E+03 1.9438E+02 9.5145E+02 1.1907E+02 3.5697E+03 1.2163E+01 2.8724E+03 6.5714E+03 3.6521E+02 F5 AVG 1.0356E+03 2.1482E+03 2.0537E+03 1.7147E+03 1.4600E+03 1.9671E+03 1.4361E+03 1.4752E+03 1.9676E+03 1.5300E+03 STD 7.6523E+01 3.4233E+01 1.1649E+02 3.0433E+01 5.9878E+01 3.5841E+01 3.3791E+01 8.3796E+01 6.4216E+01 1.3757E+02 F6 AVG 6.2653E+02 7.1986E+02 6.8471E+02 6.7635E+02 6.6759E+02 6.9561E+02 6.0000E+02 6.6402E+02 6.9933E+02 6.6472E+02 STD 7.8185E+00 6.6900E-01 6.5137E+00 2.1515E+00 6.5744E+00 3.2808E+00 3.2333E-05 4.4856E+00 6.7811E+00 4.3655E+00 F7 AVG 1.8849E+03 4.0484E+03 1.0612E+04 2.7756E+03 2.0844E+03 3.4986E+03 1.7719E+03 2.9515E+03 3.4701E+03 3.0214E+03 STD 1.9674E+02 2.3049E+01 8.0636E+02 8.1691E+01 2.4210E+02 1.1878E+02 3.0608E+01 1.4885E+02 1.3148E+02 2.8194E+02 F8 AVG 1.3286E+03 2.6218E+03 2.5074E+03 2.0444E+03 1.8056E+03 2.3277E+03 1.7368E+03 1.8160E+03 2.3086E+03 1.9451E+03 STD 5.8418E+01 1.8829E+01 1.4357E+02 3.2868E+01 9.4937E+01 5.8800E+01 2.9505E+01 7.7212E+01 7.6281E+01 1.5553E+02 F9 AVG 2.4228E+04 8.4986E+04 4.6525E+04 5.4408E+04 6.3836E+04 7.4059E+04 5.5498E+03 3.9587E+04 7.5185E+04 3.7592E+04 STD 5.3088E+03 2.3539E+03 4.9506E+03 3.4835E+03 1.3177E+04 4.8473E+03 1.4774E+03 6.0003E+03 6.8227E+03 1.5683E+04 F10 AVG 1.7812E+04 3.1984E+04 1.7072E+04 2.6586E+04 1.9220E+04 3.1485E+04 3.0082E+04 1.9264E+04 3.2007E+04 2.0292E+04 STD 1.1221E+03 3.6082E+02 1.4829E+03 7.7946E+02 2.3324E+03 5.2698E+02 6.5169E+02 1.9629E+03 5.1006E+02 2.7397E+03 F11 AVG 9.9379E+03 2.0789E+05 6.7031E+03 1.6414E+05 1.0833E+04 1.0033E+05 3.1352E+04 5.1992E+04 1.0218E+05 1.7517E+04 STD 9.6729E+03 1.3716E+04 4.0965E+03 1.4250E+04 2.1040E+03 1.3367E+04 6.6190E+03 1.2490E+04 1.2713E+04 6.6262E+03 F12 AVG 7.5757E+06 2.1606E+11 4.6144E+07 3.1645E+10 7.1116E+08 7.1415E+10 4.4184E+08 2.8958E+10 6.9386E+10 6.8604E+08 STD 6.9837E+06 4.5345E+09 5.5919E+07 5.3914E+09 2.1203E+08 7.8574E+09 8.6258E+07 8.7858E+09 9.9846E+09 5.5244E+08 F13 AVG 2.0868E+04 5.2849E+10 1.0932E+05 5.9270E+09 6.9671E+06 1.2061E+10 1.3416E+04 3.5353E+09 1.1967E+10 5.3983E+06 STD 7.5373E+04 1.0352E+09 4.0055E+04 8.8136E+08 4.9318E+06 1.6166E+09 1.8069E+04 1.9116E+09 2.0502E+09 1.1036E+07 F14 AVG 1.5078E+06 1.3468E+08 1.2958E+05 1.7172E+07 3.9045E+06 1.9849E+07 1.5786E+07 6.8683E+06 2.8036E+07 1.1514E+06 STD 1.4766E+06 6.1067E+07 7.6183E+04 4.7886E+06 1.7908E+06 6.7191E+06 5.0504E+06 3.8909E+06 9.4003E+06 6.4054E+05 F15 AVG 1.6609E+04 3.0262E+10 8.4933E+04 1.4272E+09 1.9564E+06 3.5057E+09 9.0010E+04 5.7371E+08 3.3284E+09 2.1981E+05 STD 5.0583E+04 2.7362E+09 4.0391E+04 4.3787E+08 1.3876E+06 9.3572E+08 8.8746E+04 3.6495E+08 1.1273E+09 5.3550E+05 F16 AVG 6.6434E+03 2.3738E+04 8.1300E+03 1.0698E+04 7.6664E+03 1.3572E+04 9.6383E+03 7.7936E+03 1.3235E+04 8.2393E+03 STD 8.2906E+02 1.0712E+03 1.1508E+03 5.9296E+02 1.0001E+03 6.8627E+02 2.2584E+02 8.5707E+02 8.3110E+02 1.1059E+03 F17 AVG 5.6437E+03 1.7703E+07 6.5886E+03 9.1020E+03 6.0496E+03 1.5756E+04 6.0690E+03 5.9054E+03 1.4448E+04 6.2959E+03 STD 6.6753E+02 4.5571E+06 7.2372E+02 1.4102E+03 8.2625E+02 3.8147E+03 3.4936E+02 8.9765E+02 4.0679E+03 5.3886E+02 F18 AVG 5.1288E+06 3.2505E+08 3.2446E+05 2.5429E+07 5.6945E+06 3.9108E+07 2.6368E+07 7.2592E+06 5.3191E+07 2.8888E+06 STD 4.3169E+06 5.3263E+07 1.3206E+05 1.1496E+07 3.5660E+06 1.5264E+07 6.8522E+06 3.6073E+06 1.8344E+07 1.2115E+06 F19 AVG 7.8708E+03 2.9956E+10 5.3708E+05 1.5195E+09 1.2747E+07 3.1403E+09 1.2685E+05 6.3269E+08 2.9811E+09 3.5842E+05 STD 6.1693E+03 6.6276E+08 9.0180E+04 3.7044E+08 6.0691E+06 6.8995E+08 2.0389E+05 7.2790E+08 6.6316E+08 6.1825E+05 F20 AVG 6.0145E+03 8.0829E+03 6.0718E+03 6.5880E+03 5.5299E+03 7.3165E+03 6.0509E+03 5.3837E+03 7.4329E+03 5.6141E+03 STD 4.8292E+02 3.0670E+02 6.5325E+02 4.2348E+02 4.0669E+02 2.5988E+02 2.1118E+02 5.6446E+02 2.9667E+02 5.1892E+02 F21 AVG 2.8678E+03 5.3143E+03 4.2484E+03 3.5719E+03 3.2756E+03 4.0029E+03 3.2659E+03 3.3638E+03 4.0062E+03 3.7683E+03 STD 7.4927E+01 1.7921E+02 1.8973E+02 3.8397E+01 1.5595E+02 8.5515E+01 2.6046E+01 8.1485E+01 8.1329E+01 1.9551E+02 F22 AVG 1.9178E+04 3.6258E+04 1.8699E+04 1.8341E+04 2.2891E+04 3.4000E+04 3.2386E+04 2.1204E+04 3.4343E+04 2.2283E+04 STD 1.2135E+03 4.4456E+02 1.5259E+03 5.0158E+03 2.8055E+03 4.3433E+02 5.8276E+02 1.2782E+03 7.1415E+02 2.5397E+03 F23 AVG 3.3905E+03 6.8306E+03 5.3128E+03 4.3012E+03 3.7851E+03 4.7881E+03 3.5892E+03 3.9822E+03 5.0081E+03 4.0537E+03 STD 1.1848E+02 2.1284E+02 3.7581E+02 5.3491E+01 1.2112E+02 9.9330E+01 2.5562E+01 1.2181E+02 1.1627E+02 2.6177E+02 F24 AVG 3.9036E+03 1.1023E+04 7.3185E+03 5.1827E+03 4.4646E+03 6.2179E+03 4.1370E+03 4.9662E+03 6.8352E+03 4.8846E+03 STD 1.3174E+02 1.4735E+03 6.5895E+02 1.0053E+02 3.6010E+02 2.1362E+02 3.3035E+01 2.0142E+02 2.7484E+02 2.7643E+02 F25 AVG 3.4044E+03 2.6792E+04 3.7641E+03 9.4723E+03 4.0717E+03 1.6039E+04 3.3438E+03 9.8121E+03 1.6448E+04 4.0102E+03 STD 7.7846E+01 9.1658E+02 1.7697E+02 7.5318E+02 1.5222E+02 1.3168E+03 6.1314E+01 1.2513E+03 1.1414E+03 1.6916E+02 F26 AVG 1.1704E+04 5.6637E+04 4.1868E+04 2.3796E+04 1.6545E+04 3.4587E+04 1.5008E+04 2.1750E+04 3.5339E+04 2.4339E+04 STD 8.7131E+02 9.9892E+02 4.9154E+03 7.4399E+02 3.0656E+03 2.0526E+03 3.5337E+02 1.5039E+03 2.0231E+03 2.7210E+03 F27 AVG 3.5066E+03 1.7305E+04 5.4698E+03 5.4541E+03 3.8290E+03 7.1120E+03 3.6373E+03 4.6760E+03 7.3378E+03 4.2874E+03 STD 8.7869E+01 1.6806E+03 9.3749E+02 1.6707E+02 1.2738E+02 3.9532E+02 5.4933E+01 2.7216E+02 5.1179E+02 3.0870E+02 F28 AVG 4.8905E+03 3.3439E+04 5.4069E+03 1.1382E+04 4.1143E+03 2.1339E+04 3.4571E+03 1.3468E+04 2.2535E+04 4.1814E+03 STD 3.6786E+03 2.8981E+02 1.1020E+03 1.0866E+03 1.4600E+02 1.8837E+03 2.2407E+02 1.5674E+03 2.1318E+03 2.6248E+02 F29 AVG 7.0211E+03 9.7288E+05 1.3322E+04 1.5038E+04 9.2552E+03 1.9849E+04 7.9335E+03 1.0174E+04 1.9038E+04 1.0239E+04 STD 1.0329E+03 2.6234E+05 1.8358E+03 7.2458E+02 8.7445E+02 3.2160E+03 2.8961E+02 7.6378E+02 3.5497E+03 7.4440E+02 F30 AVG 1.1931E+04 4.8597E+10 6.1114E+06 4.6826E+09 1.0639E+08 7.7550E+09 6.1740E+04 1.9431E+09 8.0201E+09 4.1378E+07 STD 5.3950E+03 3.8432E+09 4.8568E+06 7.5131E+08 3.3195E+07 1.2305E+09 2.0132E+04 1.1183E+09 1.5980E+09 1.9656E+07 Fun . Item . ADNOLACO . MOFOA . CDLOBA . HGWO . OBLGWO . CGSCA . DECLS . m_SCA . ASCA . RDWOA . F1 AVG 7.4890E+03 2.6659E+11 1.1860E+08 9.8644E+10 1.6259E+09 1.8038E+11 4.3208E+04 1.1659E+11 1.7395E+11 1.6257E+09 STD 1.1500E+04 2.9163E+09 4.3436E+08 6.4337E+09 4.7170E+08 1.0208E+10 1.5420E+05 1.1924E+10 1.0889E+10 8.2562E+08 F2 AVG 2.2103E+124 1.4337E+170 5.2749E+108 2.0825E+141 2.0695E+111 2.1183E+154 9.3571E+140 1.9885E+142 8.2332E+152 3.8852E+121 STD 1.2063E+125 6.5535E+04 2.8892E+109 1.1140E+142 1.0918E+112 6.5535E+04 2.2765E+141 1.0891E+143 6.5535E+04 1.8975E+122 F3 AVG 4.8496E+05 3.3878E+05 3.5897E+05 3.4290E+05 2.7117E+05 3.0652E+05 3.6165E+05 2.3533E+05 3.0891E+05 2.4121E+05 STD 1.0611E+05 4.1893E+03 6.0769E+04 1.2289E+04 3.2659E+04 1.3205E+04 7.1351E+03 2.5490E+04 1.6684E+04 2.4056E+04 F4 AVG 7.1619E+02 9.8993E+04 1.0384E+03 1.1506E+04 1.1254E+03 3.5416E+04 6.2981E+02 1.2525E+04 3.5853E+04 1.3476E+03 STD 5.3753E+01 3.1894E+03 1.9438E+02 9.5145E+02 1.1907E+02 3.5697E+03 1.2163E+01 2.8724E+03 6.5714E+03 3.6521E+02 F5 AVG 1.0356E+03 2.1482E+03 2.0537E+03 1.7147E+03 1.4600E+03 1.9671E+03 1.4361E+03 1.4752E+03 1.9676E+03 1.5300E+03 STD 7.6523E+01 3.4233E+01 1.1649E+02 3.0433E+01 5.9878E+01 3.5841E+01 3.3791E+01 8.3796E+01 6.4216E+01 1.3757E+02 F6 AVG 6.2653E+02 7.1986E+02 6.8471E+02 6.7635E+02 6.6759E+02 6.9561E+02 6.0000E+02 6.6402E+02 6.9933E+02 6.6472E+02 STD 7.8185E+00 6.6900E-01 6.5137E+00 2.1515E+00 6.5744E+00 3.2808E+00 3.2333E-05 4.4856E+00 6.7811E+00 4.3655E+00 F7 AVG 1.8849E+03 4.0484E+03 1.0612E+04 2.7756E+03 2.0844E+03 3.4986E+03 1.7719E+03 2.9515E+03 3.4701E+03 3.0214E+03 STD 1.9674E+02 2.3049E+01 8.0636E+02 8.1691E+01 2.4210E+02 1.1878E+02 3.0608E+01 1.4885E+02 1.3148E+02 2.8194E+02 F8 AVG 1.3286E+03 2.6218E+03 2.5074E+03 2.0444E+03 1.8056E+03 2.3277E+03 1.7368E+03 1.8160E+03 2.3086E+03 1.9451E+03 STD 5.8418E+01 1.8829E+01 1.4357E+02 3.2868E+01 9.4937E+01 5.8800E+01 2.9505E+01 7.7212E+01 7.6281E+01 1.5553E+02 F9 AVG 2.4228E+04 8.4986E+04 4.6525E+04 5.4408E+04 6.3836E+04 7.4059E+04 5.5498E+03 3.9587E+04 7.5185E+04 3.7592E+04 STD 5.3088E+03 2.3539E+03 4.9506E+03 3.4835E+03 1.3177E+04 4.8473E+03 1.4774E+03 6.0003E+03 6.8227E+03 1.5683E+04 F10 AVG 1.7812E+04 3.1984E+04 1.7072E+04 2.6586E+04 1.9220E+04 3.1485E+04 3.0082E+04 1.9264E+04 3.2007E+04 2.0292E+04 STD 1.1221E+03 3.6082E+02 1.4829E+03 7.7946E+02 2.3324E+03 5.2698E+02 6.5169E+02 1.9629E+03 5.1006E+02 2.7397E+03 F11 AVG 9.9379E+03 2.0789E+05 6.7031E+03 1.6414E+05 1.0833E+04 1.0033E+05 3.1352E+04 5.1992E+04 1.0218E+05 1.7517E+04 STD 9.6729E+03 1.3716E+04 4.0965E+03 1.4250E+04 2.1040E+03 1.3367E+04 6.6190E+03 1.2490E+04 1.2713E+04 6.6262E+03 F12 AVG 7.5757E+06 2.1606E+11 4.6144E+07 3.1645E+10 7.1116E+08 7.1415E+10 4.4184E+08 2.8958E+10 6.9386E+10 6.8604E+08 STD 6.9837E+06 4.5345E+09 5.5919E+07 5.3914E+09 2.1203E+08 7.8574E+09 8.6258E+07 8.7858E+09 9.9846E+09 5.5244E+08 F13 AVG 2.0868E+04 5.2849E+10 1.0932E+05 5.9270E+09 6.9671E+06 1.2061E+10 1.3416E+04 3.5353E+09 1.1967E+10 5.3983E+06 STD 7.5373E+04 1.0352E+09 4.0055E+04 8.8136E+08 4.9318E+06 1.6166E+09 1.8069E+04 1.9116E+09 2.0502E+09 1.1036E+07 F14 AVG 1.5078E+06 1.3468E+08 1.2958E+05 1.7172E+07 3.9045E+06 1.9849E+07 1.5786E+07 6.8683E+06 2.8036E+07 1.1514E+06 STD 1.4766E+06 6.1067E+07 7.6183E+04 4.7886E+06 1.7908E+06 6.7191E+06 5.0504E+06 3.8909E+06 9.4003E+06 6.4054E+05 F15 AVG 1.6609E+04 3.0262E+10 8.4933E+04 1.4272E+09 1.9564E+06 3.5057E+09 9.0010E+04 5.7371E+08 3.3284E+09 2.1981E+05 STD 5.0583E+04 2.7362E+09 4.0391E+04 4.3787E+08 1.3876E+06 9.3572E+08 8.8746E+04 3.6495E+08 1.1273E+09 5.3550E+05 F16 AVG 6.6434E+03 2.3738E+04 8.1300E+03 1.0698E+04 7.6664E+03 1.3572E+04 9.6383E+03 7.7936E+03 1.3235E+04 8.2393E+03 STD 8.2906E+02 1.0712E+03 1.1508E+03 5.9296E+02 1.0001E+03 6.8627E+02 2.2584E+02 8.5707E+02 8.3110E+02 1.1059E+03 F17 AVG 5.6437E+03 1.7703E+07 6.5886E+03 9.1020E+03 6.0496E+03 1.5756E+04 6.0690E+03 5.9054E+03 1.4448E+04 6.2959E+03 STD 6.6753E+02 4.5571E+06 7.2372E+02 1.4102E+03 8.2625E+02 3.8147E+03 3.4936E+02 8.9765E+02 4.0679E+03 5.3886E+02 F18 AVG 5.1288E+06 3.2505E+08 3.2446E+05 2.5429E+07 5.6945E+06 3.9108E+07 2.6368E+07 7.2592E+06 5.3191E+07 2.8888E+06 STD 4.3169E+06 5.3263E+07 1.3206E+05 1.1496E+07 3.5660E+06 1.5264E+07 6.8522E+06 3.6073E+06 1.8344E+07 1.2115E+06 F19 AVG 7.8708E+03 2.9956E+10 5.3708E+05 1.5195E+09 1.2747E+07 3.1403E+09 1.2685E+05 6.3269E+08 2.9811E+09 3.5842E+05 STD 6.1693E+03 6.6276E+08 9.0180E+04 3.7044E+08 6.0691E+06 6.8995E+08 2.0389E+05 7.2790E+08 6.6316E+08 6.1825E+05 F20 AVG 6.0145E+03 8.0829E+03 6.0718E+03 6.5880E+03 5.5299E+03 7.3165E+03 6.0509E+03 5.3837E+03 7.4329E+03 5.6141E+03 STD 4.8292E+02 3.0670E+02 6.5325E+02 4.2348E+02 4.0669E+02 2.5988E+02 2.1118E+02 5.6446E+02 2.9667E+02 5.1892E+02 F21 AVG 2.8678E+03 5.3143E+03 4.2484E+03 3.5719E+03 3.2756E+03 4.0029E+03 3.2659E+03 3.3638E+03 4.0062E+03 3.7683E+03 STD 7.4927E+01 1.7921E+02 1.8973E+02 3.8397E+01 1.5595E+02 8.5515E+01 2.6046E+01 8.1485E+01 8.1329E+01 1.9551E+02 F22 AVG 1.9178E+04 3.6258E+04 1.8699E+04 1.8341E+04 2.2891E+04 3.4000E+04 3.2386E+04 2.1204E+04 3.4343E+04 2.2283E+04 STD 1.2135E+03 4.4456E+02 1.5259E+03 5.0158E+03 2.8055E+03 4.3433E+02 5.8276E+02 1.2782E+03 7.1415E+02 2.5397E+03 F23 AVG 3.3905E+03 6.8306E+03 5.3128E+03 4.3012E+03 3.7851E+03 4.7881E+03 3.5892E+03 3.9822E+03 5.0081E+03 4.0537E+03 STD 1.1848E+02 2.1284E+02 3.7581E+02 5.3491E+01 1.2112E+02 9.9330E+01 2.5562E+01 1.2181E+02 1.1627E+02 2.6177E+02 F24 AVG 3.9036E+03 1.1023E+04 7.3185E+03 5.1827E+03 4.4646E+03 6.2179E+03 4.1370E+03 4.9662E+03 6.8352E+03 4.8846E+03 STD 1.3174E+02 1.4735E+03 6.5895E+02 1.0053E+02 3.6010E+02 2.1362E+02 3.3035E+01 2.0142E+02 2.7484E+02 2.7643E+02 F25 AVG 3.4044E+03 2.6792E+04 3.7641E+03 9.4723E+03 4.0717E+03 1.6039E+04 3.3438E+03 9.8121E+03 1.6448E+04 4.0102E+03 STD 7.7846E+01 9.1658E+02 1.7697E+02 7.5318E+02 1.5222E+02 1.3168E+03 6.1314E+01 1.2513E+03 1.1414E+03 1.6916E+02 F26 AVG 1.1704E+04 5.6637E+04 4.1868E+04 2.3796E+04 1.6545E+04 3.4587E+04 1.5008E+04 2.1750E+04 3.5339E+04 2.4339E+04 STD 8.7131E+02 9.9892E+02 4.9154E+03 7.4399E+02 3.0656E+03 2.0526E+03 3.5337E+02 1.5039E+03 2.0231E+03 2.7210E+03 F27 AVG 3.5066E+03 1.7305E+04 5.4698E+03 5.4541E+03 3.8290E+03 7.1120E+03 3.6373E+03 4.6760E+03 7.3378E+03 4.2874E+03 STD 8.7869E+01 1.6806E+03 9.3749E+02 1.6707E+02 1.2738E+02 3.9532E+02 5.4933E+01 2.7216E+02 5.1179E+02 3.0870E+02 F28 AVG 4.8905E+03 3.3439E+04 5.4069E+03 1.1382E+04 4.1143E+03 2.1339E+04 3.4571E+03 1.3468E+04 2.2535E+04 4.1814E+03 STD 3.6786E+03 2.8981E+02 1.1020E+03 1.0866E+03 1.4600E+02 1.8837E+03 2.2407E+02 1.5674E+03 2.1318E+03 2.6248E+02 F29 AVG 7.0211E+03 9.7288E+05 1.3322E+04 1.5038E+04 9.2552E+03 1.9849E+04 7.9335E+03 1.0174E+04 1.9038E+04 1.0239E+04 STD 1.0329E+03 2.6234E+05 1.8358E+03 7.2458E+02 8.7445E+02 3.2160E+03 2.8961E+02 7.6378E+02 3.5497E+03 7.4440E+02 F30 AVG 1.1931E+04 4.8597E+10 6.1114E+06 4.6826E+09 1.0639E+08 7.7550E+09 6.1740E+04 1.9431E+09 8.0201E+09 4.1378E+07 STD 5.3950E+03 3.8432E+09 4.8568E+06 7.5131E+08 3.3195E+07 1.2305E+09 2.0132E+04 1.1183E+09 1.5980E+09 1.9656E+07 Open in new tab Table A9: The results of the comparison between ADNOLACO and the nine advanced algorithms. Fun . Item . ADNOLACO . MOFOA . CDLOBA . HGWO . OBLGWO . CGSCA . DECLS . m_SCA . ASCA . RDWOA . F1 AVG 7.4890E+03 2.6659E+11 1.1860E+08 9.8644E+10 1.6259E+09 1.8038E+11 4.3208E+04 1.1659E+11 1.7395E+11 1.6257E+09 STD 1.1500E+04 2.9163E+09 4.3436E+08 6.4337E+09 4.7170E+08 1.0208E+10 1.5420E+05 1.1924E+10 1.0889E+10 8.2562E+08 F2 AVG 2.2103E+124 1.4337E+170 5.2749E+108 2.0825E+141 2.0695E+111 2.1183E+154 9.3571E+140 1.9885E+142 8.2332E+152 3.8852E+121 STD 1.2063E+125 6.5535E+04 2.8892E+109 1.1140E+142 1.0918E+112 6.5535E+04 2.2765E+141 1.0891E+143 6.5535E+04 1.8975E+122 F3 AVG 4.8496E+05 3.3878E+05 3.5897E+05 3.4290E+05 2.7117E+05 3.0652E+05 3.6165E+05 2.3533E+05 3.0891E+05 2.4121E+05 STD 1.0611E+05 4.1893E+03 6.0769E+04 1.2289E+04 3.2659E+04 1.3205E+04 7.1351E+03 2.5490E+04 1.6684E+04 2.4056E+04 F4 AVG 7.1619E+02 9.8993E+04 1.0384E+03 1.1506E+04 1.1254E+03 3.5416E+04 6.2981E+02 1.2525E+04 3.5853E+04 1.3476E+03 STD 5.3753E+01 3.1894E+03 1.9438E+02 9.5145E+02 1.1907E+02 3.5697E+03 1.2163E+01 2.8724E+03 6.5714E+03 3.6521E+02 F5 AVG 1.0356E+03 2.1482E+03 2.0537E+03 1.7147E+03 1.4600E+03 1.9671E+03 1.4361E+03 1.4752E+03 1.9676E+03 1.5300E+03 STD 7.6523E+01 3.4233E+01 1.1649E+02 3.0433E+01 5.9878E+01 3.5841E+01 3.3791E+01 8.3796E+01 6.4216E+01 1.3757E+02 F6 AVG 6.2653E+02 7.1986E+02 6.8471E+02 6.7635E+02 6.6759E+02 6.9561E+02 6.0000E+02 6.6402E+02 6.9933E+02 6.6472E+02 STD 7.8185E+00 6.6900E-01 6.5137E+00 2.1515E+00 6.5744E+00 3.2808E+00 3.2333E-05 4.4856E+00 6.7811E+00 4.3655E+00 F7 AVG 1.8849E+03 4.0484E+03 1.0612E+04 2.7756E+03 2.0844E+03 3.4986E+03 1.7719E+03 2.9515E+03 3.4701E+03 3.0214E+03 STD 1.9674E+02 2.3049E+01 8.0636E+02 8.1691E+01 2.4210E+02 1.1878E+02 3.0608E+01 1.4885E+02 1.3148E+02 2.8194E+02 F8 AVG 1.3286E+03 2.6218E+03 2.5074E+03 2.0444E+03 1.8056E+03 2.3277E+03 1.7368E+03 1.8160E+03 2.3086E+03 1.9451E+03 STD 5.8418E+01 1.8829E+01 1.4357E+02 3.2868E+01 9.4937E+01 5.8800E+01 2.9505E+01 7.7212E+01 7.6281E+01 1.5553E+02 F9 AVG 2.4228E+04 8.4986E+04 4.6525E+04 5.4408E+04 6.3836E+04 7.4059E+04 5.5498E+03 3.9587E+04 7.5185E+04 3.7592E+04 STD 5.3088E+03 2.3539E+03 4.9506E+03 3.4835E+03 1.3177E+04 4.8473E+03 1.4774E+03 6.0003E+03 6.8227E+03 1.5683E+04 F10 AVG 1.7812E+04 3.1984E+04 1.7072E+04 2.6586E+04 1.9220E+04 3.1485E+04 3.0082E+04 1.9264E+04 3.2007E+04 2.0292E+04 STD 1.1221E+03 3.6082E+02 1.4829E+03 7.7946E+02 2.3324E+03 5.2698E+02 6.5169E+02 1.9629E+03 5.1006E+02 2.7397E+03 F11 AVG 9.9379E+03 2.0789E+05 6.7031E+03 1.6414E+05 1.0833E+04 1.0033E+05 3.1352E+04 5.1992E+04 1.0218E+05 1.7517E+04 STD 9.6729E+03 1.3716E+04 4.0965E+03 1.4250E+04 2.1040E+03 1.3367E+04 6.6190E+03 1.2490E+04 1.2713E+04 6.6262E+03 F12 AVG 7.5757E+06 2.1606E+11 4.6144E+07 3.1645E+10 7.1116E+08 7.1415E+10 4.4184E+08 2.8958E+10 6.9386E+10 6.8604E+08 STD 6.9837E+06 4.5345E+09 5.5919E+07 5.3914E+09 2.1203E+08 7.8574E+09 8.6258E+07 8.7858E+09 9.9846E+09 5.5244E+08 F13 AVG 2.0868E+04 5.2849E+10 1.0932E+05 5.9270E+09 6.9671E+06 1.2061E+10 1.3416E+04 3.5353E+09 1.1967E+10 5.3983E+06 STD 7.5373E+04 1.0352E+09 4.0055E+04 8.8136E+08 4.9318E+06 1.6166E+09 1.8069E+04 1.9116E+09 2.0502E+09 1.1036E+07 F14 AVG 1.5078E+06 1.3468E+08 1.2958E+05 1.7172E+07 3.9045E+06 1.9849E+07 1.5786E+07 6.8683E+06 2.8036E+07 1.1514E+06 STD 1.4766E+06 6.1067E+07 7.6183E+04 4.7886E+06 1.7908E+06 6.7191E+06 5.0504E+06 3.8909E+06 9.4003E+06 6.4054E+05 F15 AVG 1.6609E+04 3.0262E+10 8.4933E+04 1.4272E+09 1.9564E+06 3.5057E+09 9.0010E+04 5.7371E+08 3.3284E+09 2.1981E+05 STD 5.0583E+04 2.7362E+09 4.0391E+04 4.3787E+08 1.3876E+06 9.3572E+08 8.8746E+04 3.6495E+08 1.1273E+09 5.3550E+05 F16 AVG 6.6434E+03 2.3738E+04 8.1300E+03 1.0698E+04 7.6664E+03 1.3572E+04 9.6383E+03 7.7936E+03 1.3235E+04 8.2393E+03 STD 8.2906E+02 1.0712E+03 1.1508E+03 5.9296E+02 1.0001E+03 6.8627E+02 2.2584E+02 8.5707E+02 8.3110E+02 1.1059E+03 F17 AVG 5.6437E+03 1.7703E+07 6.5886E+03 9.1020E+03 6.0496E+03 1.5756E+04 6.0690E+03 5.9054E+03 1.4448E+04 6.2959E+03 STD 6.6753E+02 4.5571E+06 7.2372E+02 1.4102E+03 8.2625E+02 3.8147E+03 3.4936E+02 8.9765E+02 4.0679E+03 5.3886E+02 F18 AVG 5.1288E+06 3.2505E+08 3.2446E+05 2.5429E+07 5.6945E+06 3.9108E+07 2.6368E+07 7.2592E+06 5.3191E+07 2.8888E+06 STD 4.3169E+06 5.3263E+07 1.3206E+05 1.1496E+07 3.5660E+06 1.5264E+07 6.8522E+06 3.6073E+06 1.8344E+07 1.2115E+06 F19 AVG 7.8708E+03 2.9956E+10 5.3708E+05 1.5195E+09 1.2747E+07 3.1403E+09 1.2685E+05 6.3269E+08 2.9811E+09 3.5842E+05 STD 6.1693E+03 6.6276E+08 9.0180E+04 3.7044E+08 6.0691E+06 6.8995E+08 2.0389E+05 7.2790E+08 6.6316E+08 6.1825E+05 F20 AVG 6.0145E+03 8.0829E+03 6.0718E+03 6.5880E+03 5.5299E+03 7.3165E+03 6.0509E+03 5.3837E+03 7.4329E+03 5.6141E+03 STD 4.8292E+02 3.0670E+02 6.5325E+02 4.2348E+02 4.0669E+02 2.5988E+02 2.1118E+02 5.6446E+02 2.9667E+02 5.1892E+02 F21 AVG 2.8678E+03 5.3143E+03 4.2484E+03 3.5719E+03 3.2756E+03 4.0029E+03 3.2659E+03 3.3638E+03 4.0062E+03 3.7683E+03 STD 7.4927E+01 1.7921E+02 1.8973E+02 3.8397E+01 1.5595E+02 8.5515E+01 2.6046E+01 8.1485E+01 8.1329E+01 1.9551E+02 F22 AVG 1.9178E+04 3.6258E+04 1.8699E+04 1.8341E+04 2.2891E+04 3.4000E+04 3.2386E+04 2.1204E+04 3.4343E+04 2.2283E+04 STD 1.2135E+03 4.4456E+02 1.5259E+03 5.0158E+03 2.8055E+03 4.3433E+02 5.8276E+02 1.2782E+03 7.1415E+02 2.5397E+03 F23 AVG 3.3905E+03 6.8306E+03 5.3128E+03 4.3012E+03 3.7851E+03 4.7881E+03 3.5892E+03 3.9822E+03 5.0081E+03 4.0537E+03 STD 1.1848E+02 2.1284E+02 3.7581E+02 5.3491E+01 1.2112E+02 9.9330E+01 2.5562E+01 1.2181E+02 1.1627E+02 2.6177E+02 F24 AVG 3.9036E+03 1.1023E+04 7.3185E+03 5.1827E+03 4.4646E+03 6.2179E+03 4.1370E+03 4.9662E+03 6.8352E+03 4.8846E+03 STD 1.3174E+02 1.4735E+03 6.5895E+02 1.0053E+02 3.6010E+02 2.1362E+02 3.3035E+01 2.0142E+02 2.7484E+02 2.7643E+02 F25 AVG 3.4044E+03 2.6792E+04 3.7641E+03 9.4723E+03 4.0717E+03 1.6039E+04 3.3438E+03 9.8121E+03 1.6448E+04 4.0102E+03 STD 7.7846E+01 9.1658E+02 1.7697E+02 7.5318E+02 1.5222E+02 1.3168E+03 6.1314E+01 1.2513E+03 1.1414E+03 1.6916E+02 F26 AVG 1.1704E+04 5.6637E+04 4.1868E+04 2.3796E+04 1.6545E+04 3.4587E+04 1.5008E+04 2.1750E+04 3.5339E+04 2.4339E+04 STD 8.7131E+02 9.9892E+02 4.9154E+03 7.4399E+02 3.0656E+03 2.0526E+03 3.5337E+02 1.5039E+03 2.0231E+03 2.7210E+03 F27 AVG 3.5066E+03 1.7305E+04 5.4698E+03 5.4541E+03 3.8290E+03 7.1120E+03 3.6373E+03 4.6760E+03 7.3378E+03 4.2874E+03 STD 8.7869E+01 1.6806E+03 9.3749E+02 1.6707E+02 1.2738E+02 3.9532E+02 5.4933E+01 2.7216E+02 5.1179E+02 3.0870E+02 F28 AVG 4.8905E+03 3.3439E+04 5.4069E+03 1.1382E+04 4.1143E+03 2.1339E+04 3.4571E+03 1.3468E+04 2.2535E+04 4.1814E+03 STD 3.6786E+03 2.8981E+02 1.1020E+03 1.0866E+03 1.4600E+02 1.8837E+03 2.2407E+02 1.5674E+03 2.1318E+03 2.6248E+02 F29 AVG 7.0211E+03 9.7288E+05 1.3322E+04 1.5038E+04 9.2552E+03 1.9849E+04 7.9335E+03 1.0174E+04 1.9038E+04 1.0239E+04 STD 1.0329E+03 2.6234E+05 1.8358E+03 7.2458E+02 8.7445E+02 3.2160E+03 2.8961E+02 7.6378E+02 3.5497E+03 7.4440E+02 F30 AVG 1.1931E+04 4.8597E+10 6.1114E+06 4.6826E+09 1.0639E+08 7.7550E+09 6.1740E+04 1.9431E+09 8.0201E+09 4.1378E+07 STD 5.3950E+03 3.8432E+09 4.8568E+06 7.5131E+08 3.3195E+07 1.2305E+09 2.0132E+04 1.1183E+09 1.5980E+09 1.9656E+07 Fun . Item . ADNOLACO . MOFOA . CDLOBA . HGWO . OBLGWO . CGSCA . DECLS . m_SCA . ASCA . RDWOA . F1 AVG 7.4890E+03 2.6659E+11 1.1860E+08 9.8644E+10 1.6259E+09 1.8038E+11 4.3208E+04 1.1659E+11 1.7395E+11 1.6257E+09 STD 1.1500E+04 2.9163E+09 4.3436E+08 6.4337E+09 4.7170E+08 1.0208E+10 1.5420E+05 1.1924E+10 1.0889E+10 8.2562E+08 F2 AVG 2.2103E+124 1.4337E+170 5.2749E+108 2.0825E+141 2.0695E+111 2.1183E+154 9.3571E+140 1.9885E+142 8.2332E+152 3.8852E+121 STD 1.2063E+125 6.5535E+04 2.8892E+109 1.1140E+142 1.0918E+112 6.5535E+04 2.2765E+141 1.0891E+143 6.5535E+04 1.8975E+122 F3 AVG 4.8496E+05 3.3878E+05 3.5897E+05 3.4290E+05 2.7117E+05 3.0652E+05 3.6165E+05 2.3533E+05 3.0891E+05 2.4121E+05 STD 1.0611E+05 4.1893E+03 6.0769E+04 1.2289E+04 3.2659E+04 1.3205E+04 7.1351E+03 2.5490E+04 1.6684E+04 2.4056E+04 F4 AVG 7.1619E+02 9.8993E+04 1.0384E+03 1.1506E+04 1.1254E+03 3.5416E+04 6.2981E+02 1.2525E+04 3.5853E+04 1.3476E+03 STD 5.3753E+01 3.1894E+03 1.9438E+02 9.5145E+02 1.1907E+02 3.5697E+03 1.2163E+01 2.8724E+03 6.5714E+03 3.6521E+02 F5 AVG 1.0356E+03 2.1482E+03 2.0537E+03 1.7147E+03 1.4600E+03 1.9671E+03 1.4361E+03 1.4752E+03 1.9676E+03 1.5300E+03 STD 7.6523E+01 3.4233E+01 1.1649E+02 3.0433E+01 5.9878E+01 3.5841E+01 3.3791E+01 8.3796E+01 6.4216E+01 1.3757E+02 F6 AVG 6.2653E+02 7.1986E+02 6.8471E+02 6.7635E+02 6.6759E+02 6.9561E+02 6.0000E+02 6.6402E+02 6.9933E+02 6.6472E+02 STD 7.8185E+00 6.6900E-01 6.5137E+00 2.1515E+00 6.5744E+00 3.2808E+00 3.2333E-05 4.4856E+00 6.7811E+00 4.3655E+00 F7 AVG 1.8849E+03 4.0484E+03 1.0612E+04 2.7756E+03 2.0844E+03 3.4986E+03 1.7719E+03 2.9515E+03 3.4701E+03 3.0214E+03 STD 1.9674E+02 2.3049E+01 8.0636E+02 8.1691E+01 2.4210E+02 1.1878E+02 3.0608E+01 1.4885E+02 1.3148E+02 2.8194E+02 F8 AVG 1.3286E+03 2.6218E+03 2.5074E+03 2.0444E+03 1.8056E+03 2.3277E+03 1.7368E+03 1.8160E+03 2.3086E+03 1.9451E+03 STD 5.8418E+01 1.8829E+01 1.4357E+02 3.2868E+01 9.4937E+01 5.8800E+01 2.9505E+01 7.7212E+01 7.6281E+01 1.5553E+02 F9 AVG 2.4228E+04 8.4986E+04 4.6525E+04 5.4408E+04 6.3836E+04 7.4059E+04 5.5498E+03 3.9587E+04 7.5185E+04 3.7592E+04 STD 5.3088E+03 2.3539E+03 4.9506E+03 3.4835E+03 1.3177E+04 4.8473E+03 1.4774E+03 6.0003E+03 6.8227E+03 1.5683E+04 F10 AVG 1.7812E+04 3.1984E+04 1.7072E+04 2.6586E+04 1.9220E+04 3.1485E+04 3.0082E+04 1.9264E+04 3.2007E+04 2.0292E+04 STD 1.1221E+03 3.6082E+02 1.4829E+03 7.7946E+02 2.3324E+03 5.2698E+02 6.5169E+02 1.9629E+03 5.1006E+02 2.7397E+03 F11 AVG 9.9379E+03 2.0789E+05 6.7031E+03 1.6414E+05 1.0833E+04 1.0033E+05 3.1352E+04 5.1992E+04 1.0218E+05 1.7517E+04 STD 9.6729E+03 1.3716E+04 4.0965E+03 1.4250E+04 2.1040E+03 1.3367E+04 6.6190E+03 1.2490E+04 1.2713E+04 6.6262E+03 F12 AVG 7.5757E+06 2.1606E+11 4.6144E+07 3.1645E+10 7.1116E+08 7.1415E+10 4.4184E+08 2.8958E+10 6.9386E+10 6.8604E+08 STD 6.9837E+06 4.5345E+09 5.5919E+07 5.3914E+09 2.1203E+08 7.8574E+09 8.6258E+07 8.7858E+09 9.9846E+09 5.5244E+08 F13 AVG 2.0868E+04 5.2849E+10 1.0932E+05 5.9270E+09 6.9671E+06 1.2061E+10 1.3416E+04 3.5353E+09 1.1967E+10 5.3983E+06 STD 7.5373E+04 1.0352E+09 4.0055E+04 8.8136E+08 4.9318E+06 1.6166E+09 1.8069E+04 1.9116E+09 2.0502E+09 1.1036E+07 F14 AVG 1.5078E+06 1.3468E+08 1.2958E+05 1.7172E+07 3.9045E+06 1.9849E+07 1.5786E+07 6.8683E+06 2.8036E+07 1.1514E+06 STD 1.4766E+06 6.1067E+07 7.6183E+04 4.7886E+06 1.7908E+06 6.7191E+06 5.0504E+06 3.8909E+06 9.4003E+06 6.4054E+05 F15 AVG 1.6609E+04 3.0262E+10 8.4933E+04 1.4272E+09 1.9564E+06 3.5057E+09 9.0010E+04 5.7371E+08 3.3284E+09 2.1981E+05 STD 5.0583E+04 2.7362E+09 4.0391E+04 4.3787E+08 1.3876E+06 9.3572E+08 8.8746E+04 3.6495E+08 1.1273E+09 5.3550E+05 F16 AVG 6.6434E+03 2.3738E+04 8.1300E+03 1.0698E+04 7.6664E+03 1.3572E+04 9.6383E+03 7.7936E+03 1.3235E+04 8.2393E+03 STD 8.2906E+02 1.0712E+03 1.1508E+03 5.9296E+02 1.0001E+03 6.8627E+02 2.2584E+02 8.5707E+02 8.3110E+02 1.1059E+03 F17 AVG 5.6437E+03 1.7703E+07 6.5886E+03 9.1020E+03 6.0496E+03 1.5756E+04 6.0690E+03 5.9054E+03 1.4448E+04 6.2959E+03 STD 6.6753E+02 4.5571E+06 7.2372E+02 1.4102E+03 8.2625E+02 3.8147E+03 3.4936E+02 8.9765E+02 4.0679E+03 5.3886E+02 F18 AVG 5.1288E+06 3.2505E+08 3.2446E+05 2.5429E+07 5.6945E+06 3.9108E+07 2.6368E+07 7.2592E+06 5.3191E+07 2.8888E+06 STD 4.3169E+06 5.3263E+07 1.3206E+05 1.1496E+07 3.5660E+06 1.5264E+07 6.8522E+06 3.6073E+06 1.8344E+07 1.2115E+06 F19 AVG 7.8708E+03 2.9956E+10 5.3708E+05 1.5195E+09 1.2747E+07 3.1403E+09 1.2685E+05 6.3269E+08 2.9811E+09 3.5842E+05 STD 6.1693E+03 6.6276E+08 9.0180E+04 3.7044E+08 6.0691E+06 6.8995E+08 2.0389E+05 7.2790E+08 6.6316E+08 6.1825E+05 F20 AVG 6.0145E+03 8.0829E+03 6.0718E+03 6.5880E+03 5.5299E+03 7.3165E+03 6.0509E+03 5.3837E+03 7.4329E+03 5.6141E+03 STD 4.8292E+02 3.0670E+02 6.5325E+02 4.2348E+02 4.0669E+02 2.5988E+02 2.1118E+02 5.6446E+02 2.9667E+02 5.1892E+02 F21 AVG 2.8678E+03 5.3143E+03 4.2484E+03 3.5719E+03 3.2756E+03 4.0029E+03 3.2659E+03 3.3638E+03 4.0062E+03 3.7683E+03 STD 7.4927E+01 1.7921E+02 1.8973E+02 3.8397E+01 1.5595E+02 8.5515E+01 2.6046E+01 8.1485E+01 8.1329E+01 1.9551E+02 F22 AVG 1.9178E+04 3.6258E+04 1.8699E+04 1.8341E+04 2.2891E+04 3.4000E+04 3.2386E+04 2.1204E+04 3.4343E+04 2.2283E+04 STD 1.2135E+03 4.4456E+02 1.5259E+03 5.0158E+03 2.8055E+03 4.3433E+02 5.8276E+02 1.2782E+03 7.1415E+02 2.5397E+03 F23 AVG 3.3905E+03 6.8306E+03 5.3128E+03 4.3012E+03 3.7851E+03 4.7881E+03 3.5892E+03 3.9822E+03 5.0081E+03 4.0537E+03 STD 1.1848E+02 2.1284E+02 3.7581E+02 5.3491E+01 1.2112E+02 9.9330E+01 2.5562E+01 1.2181E+02 1.1627E+02 2.6177E+02 F24 AVG 3.9036E+03 1.1023E+04 7.3185E+03 5.1827E+03 4.4646E+03 6.2179E+03 4.1370E+03 4.9662E+03 6.8352E+03 4.8846E+03 STD 1.3174E+02 1.4735E+03 6.5895E+02 1.0053E+02 3.6010E+02 2.1362E+02 3.3035E+01 2.0142E+02 2.7484E+02 2.7643E+02 F25 AVG 3.4044E+03 2.6792E+04 3.7641E+03 9.4723E+03 4.0717E+03 1.6039E+04 3.3438E+03 9.8121E+03 1.6448E+04 4.0102E+03 STD 7.7846E+01 9.1658E+02 1.7697E+02 7.5318E+02 1.5222E+02 1.3168E+03 6.1314E+01 1.2513E+03 1.1414E+03 1.6916E+02 F26 AVG 1.1704E+04 5.6637E+04 4.1868E+04 2.3796E+04 1.6545E+04 3.4587E+04 1.5008E+04 2.1750E+04 3.5339E+04 2.4339E+04 STD 8.7131E+02 9.9892E+02 4.9154E+03 7.4399E+02 3.0656E+03 2.0526E+03 3.5337E+02 1.5039E+03 2.0231E+03 2.7210E+03 F27 AVG 3.5066E+03 1.7305E+04 5.4698E+03 5.4541E+03 3.8290E+03 7.1120E+03 3.6373E+03 4.6760E+03 7.3378E+03 4.2874E+03 STD 8.7869E+01 1.6806E+03 9.3749E+02 1.6707E+02 1.2738E+02 3.9532E+02 5.4933E+01 2.7216E+02 5.1179E+02 3.0870E+02 F28 AVG 4.8905E+03 3.3439E+04 5.4069E+03 1.1382E+04 4.1143E+03 2.1339E+04 3.4571E+03 1.3468E+04 2.2535E+04 4.1814E+03 STD 3.6786E+03 2.8981E+02 1.1020E+03 1.0866E+03 1.4600E+02 1.8837E+03 2.2407E+02 1.5674E+03 2.1318E+03 2.6248E+02 F29 AVG 7.0211E+03 9.7288E+05 1.3322E+04 1.5038E+04 9.2552E+03 1.9849E+04 7.9335E+03 1.0174E+04 1.9038E+04 1.0239E+04 STD 1.0329E+03 2.6234E+05 1.8358E+03 7.2458E+02 8.7445E+02 3.2160E+03 2.8961E+02 7.6378E+02 3.5497E+03 7.4440E+02 F30 AVG 1.1931E+04 4.8597E+10 6.1114E+06 4.6826E+09 1.0639E+08 7.7550E+09 6.1740E+04 1.9431E+09 8.0201E+09 4.1378E+07 STD 5.3950E+03 3.8432E+09 4.8568E+06 7.5131E+08 3.3195E+07 1.2305E+09 2.0132E+04 1.1183E+09 1.5980E+09 1.9656E+07 Open in new tab Appendix B: An Overview of ACOR In ACOR, it is fundamental to design algorithms that convert discrete probability distributions into continuous probability density functions. For that reason, ACOR adopted the Gaussian kernel function as the probability density function, which is a weighted sum of several 1D Gaussian functions, as in equation (B.1). $$\begin{equation*} {G^i}\left( x \right) = \mathop \sum \limits_{l = 1}^k {w_l}g_l^i\left( x \right) = \mathop \sum \limits_{l = 1}^k {w_l}\frac{1}{{\sigma _l^i\sqrt {2\pi } }}{e^{ - \frac{{{{\left( {x - \mu _l^i} \right)}^2}}}{{2\sigma {{_l^i}^2}}}}}, \end{equation*} $$(B.1) where k denotes the number of single-dimensional Gaussian functions (SCF) composing the Gaussian kernel function, |$w = \{ {{w_1},\ \ldots ,\ {w_k}} \}$| is the weight vector associated with SCF, |${\mu ^i} = \{ {\mu _1^i,\ \ldots ,\ \mu _k^i} \}$| is the mean vector associated with SCF, |${\sigma ^i} = \{ {\sigma _1^i,\ \ldots ,\ \sigma _k^i} \}$| is a single-dimensional vector of standard deviations associated with SCF. The solution of ACOR consists of storing a certain amount of solutions in a solution archive. For a n-dimensional problem, one solution can be denoted as |${s_l} = \{ {s_l^1,\ \ldots ,\ s_l^n} \}$| in the archive. The solution archive stores each solution and the corresponding objective function value, and the structure of the solution archive is shown in Fig. B1. The ordering of the solutions in the archive is determined by the quality of the corresponding objective function values, and the higher quality solutions are ordered with a smaller ordinal number. Moreover, each solution |${s_l}$| has a weight value |${w_l}$| corresponding to it, which corresponds to the Gaussian function whose mean and standard deviation are l and |$qk$|⁠. Therefore, if the function value corresponding to each solution satisfies |$f( {{x_1}} ) \le \ldots f( {{x_l}} ) \le \ldots f( {{x_k}} )$|⁠, then the weight corresponding to each solution satisfies |${w_1} \ge \ldots {w_l} \ge \ldots {w_k}$|⁠. The ant selects the guide solution according to the ratio corresponding to the size of the weights and |${w_l}$| can be obtained with equation (B.2). $$\begin{equation*} {w_l} = \frac{1}{{qk\sqrt {2\pi } }}{e^{ - \frac{{{{\left( {l - 1} \right)}^2}}}{{2{q^2}{k^2}}}}}, \end{equation*} $$(B.2) where q is a parameter in the algorithm, which is used to reconcile the local optimum with the global optimum. The weight of the optimal solution is inversely proportional to the value of q, and proportional to the probability of the most available solution being selected. Conversely, the more uniform the solution weights are, the more equal the selection chance. Figure B1: Open in new tabDownload slide A brief description of the archive in ACOR. In practice, the implementation of the sampling process can be mainly divided into three steps. The size |${w_l}$| is calculated in the first step according to equation (B.2). The second step selects a Gaussian kernel function |$g_l^i( x )$| from the Gaussian kernel function |${G^i}( x )$| according to the probability |${p_l}$| and determines the chosen guiding solution |${s_l}$|⁠, where |${p_l}$| is calculated according to equation (B.3). The third step samples each of the n solution components around the guiding solution |${s_l}$| by a Gaussian function |$g_l^i( x )$|⁠. The |$\mu _l^i$| of this Gaussian function can be obtained according to equation (B.4) and |$\sigma _l^i$| can be calculated according to equation (B.5). $$\begin{equation*} {p_l} = \frac{{{w_l}}}{{\mathop \sum \nolimits_{r = 1}^k {w_r}}} \end{equation*} $$(B.3) $$\begin{equation*} {\mu ^i} = \left\{ {\mu _1^i, \ldots ,\mu _k^i} \right\} = \left\{ {s_1^i, \ldots ,s_k^i} \right\} \end{equation*} $$(B.4) $$\begin{equation*} \sigma _l^i = \xi \mathop \sum \limits_{e\ = \ 1}^k \frac{{\left| {s_e^i - s_l^i} \right|}}{{k - 1}}, \end{equation*} $$(B.5) where |$\xi > 0$| is a parameter that acts the same way as the pheromone volatilization rate in ACO, where the larger the value of |$\xi $| is, the slower the convergence rate is. The update of pheromones in ACOR is achieved by updating solutions in the archive. The update of the solutions in the archive is mainly done by merging the m new solutions constructed by the ant with the k old solutions in the archive, selecting the k better solutions from these |$k + m$| solutions and sorting them into the solution archive, and discarding the remaining m worse solutions. The flowchart of ACOR is given in Fig. B2. Figure B2: Open in new tabDownload slide The flowchart of ACOR. © The Author(s) 2022. Published by Oxford University Press on behalf of the Society for Computational Design and Engineering. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. © The Author(s) 2022. Published by Oxford University Press on behalf of the Society for Computational Design and Engineering.
TI - Opposition-based ant colony optimization with all-dimension neighborhood search for engineering design
JF - Journal of Computational Design and Engineering
DO - 10.1093/jcde/qwac038
DA - 2022-06-27
UR - https://www.deepdyve.com/lp/oxford-university-press/opposition-based-ant-colony-optimization-with-all-dimension-TtGG2osFSK
SP - 1007
EP - 1044
VL - 9
IS - 3
DP - DeepDyve
ER -