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