Soft Comput (2017) 21:5091–5102
METHODOLOGIES AND APPLICATION
Fireﬂy algorithm with adaptive control parameters
· Xinyu Zhou
· Hui Sun
· Xiang Yu
· Jia Zhao
· Laizhong Cui
Published online: 3 March 2016
© Springer-Verlag Berlin Heidelberg 2016
Abstract Fireﬂy algorithm (FA) is a new swarm intelli-
gence optimization method, which has shown good search
abilities on many optimization problems. However, the per-
formance of FA highly depends on its control parameters.
In this paper, we investigate the control parameters of FA,
and propose a modiﬁed FA called FA with adaptive con-
trol parameters (ApFA). To verify the performance of ApFA,
experiments are conducted on a set of well-known bench-
mark problems. Results show that the ApFA outperforms the
standard FA and ﬁve other recently proposed FA variants.
Communicated by V. Loia.
School of Computer and Software, Nanjing University of
Information Science and Technology, Nanjing 210044, China
School of Information Engineering, Nanchang Institute of
Technology, Nanchang 330099, China
College of Computer and Information Engineering, Jiangxi
Normal University, Nanchang 330022, China
College of Computer Science and Software Engineering,
Shenzhen University, Shenzhen 518060, China
Keywords Fireﬂy algorithm (FA) · Swarm intelligence ·
Adaptive control parameters · Self-adaptive FA · Global
Fireﬂy algorithm (FA) is a new swarm intelligence algorithm,
which simulates the behavior of the ﬂashing of ﬁreﬂies (Yang
2008). Some recent studies show that FA is competitive to
some nature-inspired algorithms in terms of the search per-
formance (Yang 2010). Like particle swarm optimization
(PSO) (Kennedy and Eberhart 1995), FA has a simple con-
cept, and it can be easily implemented in any programming
language. In the past ﬁve years, FA has been widely applied
to different optimization areas (Fister et al. 2013a).
The search of FA is determined by the attraction between
any two different ﬁreﬂies. By the attraction, a less bright
ﬁreﬂy (worse solution) can move to another brighter one
(better solution). Similar to PSO, the movement of ﬁreﬂies
is seriously affected by its corresponding control parame-
ters, such as step factor α and attractiveness coefﬁcient β
Different settings of these parameters may result in different
performance. Although some dynamic or adaptive parameter
strategies have designed to adjust α (Yu et al. 2014, 2015),
most of them lack necessary theoretical analysis.
In this paper, we investigate the effects of the control para-
meters in FA. Based on the analysis, a new FA variant called
FA with adaptive control parameters (ApFA) is proposed.
In order to verify the performance of ApFA, a set of well-
known benchmark functions are tested in the experiments.
Simulation results show that the effectiveness of the proposed
The rest of the paper is organized as follows. Section 2
presents the standard FA. Section 3 gives a brief review of