Vol.1, No.2, 151-155 (2009) Natural Science
http://dx.doi.org/10.4236/ns.2009.12019
Copyright © 2009 SciRes. OPEN ACCESS
A Modified Particle Swarm Optimization Algorithm
Ai-Qin Mu1,2, De-Xin Cao1, Xiao-Hua Wang2
1College of Science, China University of Mining & Technology, XuZhou, China; muaqin@126.com, caodx@cumt.edu.cn
2Foundation Departments, Xuzhou Air Force Academy, XuZhou, China
Received 17 August 2009; revised 28 August 2009; accepted 30 August 2009.
ABSTRACT
Particle Swarm Optimization (PSO) is a new
optimization algorithm, which is applied in
many fields widely. But the original PSO is
likely to cause the local optimization with
premature convergence phenomenon. By
using the idea of simulated annealing algo-
rithm, we propose a modified algorithm
which makes the most optimal particle of
every time of iteration evolving continu-
ously, and assign the worst particle with a
new value to increase its disturbance. By
the testing of three classic testing functions,
we conclude the modified PSO algorithm
has the better performance of convergence
and global searching than the original PSO.
Keywords: PSO; Simulated Annealing Algorithm;
Global Searching
1. INTRODUCTION
PSO algorithm is a new intelligent optimization algo-
rithm intimating the bird swarm behaviors, which was
proposed by psychologist Kennedy and Dr. Eberhart in
1995 [1]. Compared with other optimization algorithms,
the PSO is more objective and easily to perform well, it
is applied in many fields such as the function optimiza-
tion, the neural network training, the fuzzy system con-
trol, etc.
In PSO algorithm, each individual is called “particle”,
which represents a potential solution. The algorithm
achieves the best solution by the variability of some par-
ticles in the tracing space. The particles search in the
solution space following the best particle by changing
their positions and the fitness frequently, the flying di-
rection and velocity are determined by the objective
function.
For improving the convergence performance of PSO,
the inertia factorwis used by Shi and Eberhart [2] to
control the impact on current particle by former parti-
cle’s velocity. PSO algorithm has preferred global
searching ability whenwis relatively large. On the con-
trary, its local searching ability becomes better when
wis smaller. Now the PSO algorithm with inertia
weight factor was called standard PSO.
However, in PSO algorithm, particles would lost the
ability to explore new domains when they are searching
in solution space, that is to say it will entrap in local op-
timization and causes the premature phenomenon.
Therefore, it is very import for PSO algorithm to be
guaranteed to converge to the global optimal solution,
and many modify PSO algorithms were researched in
recent ten years. For example, linearly decreasing inertia
weight technique was studied in [3].
In order to solve the premature phenomenon, many
modified algorithms based on Simulated Annealing Al-
gorithm are proposed. For example, the new location of
all particles is selected according to the probability [4, 5];
the PSO and simulated annealing algorithm are iterated
alternatively [6,7]; Gao Ying and Xie Shengli [8] add
hybridization and Gaussian mutation to alternative itera-
tions; in [9] particles are divided into two groups, PSO
and simulated annealing algorithm are iterated to them
respectively and then mixed two algorithms. This paper
proposed a new modify PSO algorithm. The arrange-
ment of this paper is as follows. In section 2, the princi-
ple of standard PSO is introduced. In section 3, the
modified PSO algorithm is described. In section 4, three
benchmark functions are used to evaluate the perform-
ance of algorithm, and the conclusions are given in sec-
tion 5.
2. STANDARD PSO ALGORITHM
Assuming 12
(, ,,)
iii iD
xx x
is the position of i-th
particle in D-dimension, 12
(,, ,)
iii iD
Vvv v is its ve-
locity which represents its direction of searching. In it-
eration process, each particle keeps the best position
pbest found by itself, besides, it also knows the best po-
sition gbest searched by the group particles, and changes
its velocity according two best positions. The standard