Khosla et al. / J Zhejiang Univ SCIENCE A 2006 7(12):1989-1994
1989
Identification of strategy parameters for particle swarm
optimizer through Taguchi method
KHOSLA Arun
1
, KUMAR Shakti
2
, AGGARWAL K.K.
3
(
1
Department of Electronics and Communication Engineering, National Institute of Technology, Jalandhar 144011, India)
(
2
Centre for Advanced Technology, Haryana Engineering College, Jagadhari 135003, India)
(
3
Vice Chancellor, GGS Indraprastha University, Delhi 110006, India)
E-mail: khoslaak@nitj.ac.in; shakti@hec.ac.in; kka@ipu.edu
Received Nov. 23, 2005; revision accepted Feb. 26, 2006
Abstract: Particle swarm optimization (PSO), like other evolutionary algorithms is a population-based stochastic algorithm
inspired from the metaphor of social interaction in birds, insects, wasps, etc. It has been used for finding promising solutions in
complex search space through the interaction of particles in a swarm. It is a well recognized fact that the performance of evolu-
tionary algorithms to a great extent depends on the choice of appropriate strategy/operating parameters like population size,
crossover rate, mutation rate, crossover operator, etc. Generally, these parameters are selected through hit and trial process, which
is very unsystematic and requires rigorous experimentation. This paper proposes a systematic based on Taguchi method reasoning
scheme for rapidly identifying the strategy parameters for the PSO algorithm. The Taguchi method is a robust design approach
using fractional factorial design to study a large number of parameters with small number of experiments. Computer simulations
have been performed on two benchmark functions—Rosenbrock function and Griewank function—to validate the approach.
Key words: Strategy parameters, Particle swarm optimization (PSO), Taguchi method, ANOVA
doi:10.1631/jzus.2006.A1989 Document code: A CLC number: N941; TP301.6
INTRODUCTION
The particle swarm optimization (PSO) method
is a member of the broad category of swarm intelli-
gence techniques for finding optimized solutions. The
PSO algorithm is based on the social behavior of
animals such as flocking of birds and schooling of
fish, etc. PSO has its origin in simulation for visual-
izing the synchronized choreography of bird flock by
incorporating concepts such as nearest-neighbor ve-
locity matching and acceleration by distance (Par-
sopoulos and Vrahatis, 2002; Eberhart and Shi, 2001;
Kennedy and Eberhart, 1995; 2001). Later on it was
realized that the simulation could be used as an
optimizer and resulted in the first simple version of
PSO (Kennedy and Eberhart, 1995). Since then, many
variants of PSO have been suggested by different
researchers (Eberhart and Kennedy, 1995; Shi and
Eberhart, 1998; 2001; Xie et al., 2002).
In PSO, the particles have an adaptable velocity
that determines their movement in the search space.
Each particle also has a memory and can remember
the best position in the search space ever visited by it.
The position corresponding to the best fitness is
known as “pbest” and the overall best out of all the
particles in the population is called “gbest”.
Consider that the search space is d-dimensional
and that the ith particle in the swarm can be repre-
sented by X
i
=(x
i1
, x
i2
, …, x
id
) and its velocity can be
represented by another d-dimensional vector V
i
=(v
i1
,
v
i2
, …, v
id
). Let the best previously visited position of
this particle be denoted by P
i
=(p
i1
, p
i2
, …, p
id
). If the
gth particle is the best particle and the iteration
number is denoted by the superscript, then the swarm
is modified according to Eqs.(1) and (2) suggested by
Shi and Eberhart (1999).
1
11 2 2
()(),
nnnn nnn
n
id id id id id
id
wvcrpx crpx
v
+
=+ −+ − (1)
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