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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 628357, 10 pages
http://dx.doi.org/10.1155/2014/628357
Research Article

Particle Swarm Optimization Based on Local Attractors of Ordinary Differential Equation System

1College of Science, Huazhong Agricultural University, Wuhan 430070, China
2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received 24 April 2014; Revised 8 August 2014; Accepted 15 August 2014; Published 26 August 2014

Academic Editor: Manuel De la Sen

Copyright © 2014 Wenyu Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Particle swarm optimization (PSO) is inspired by sociological behavior. In this paper, we interpret PSO as a finite difference scheme for solving a system of stochastic ordinary differential equations (SODE). In this framework, the position points of the swarm converge to an equilibrium point of the SODE and the local attractors, which are easily defined by the present position points, also converge to the global attractor. Inspired by this observation, we propose a class of modified PSO iteration methods (MPSO) based on local attractors of the SODE. The idea of MPSO is to choose the next update state near the present local attractor, rather than the present position point as in the original PSO, according to a given probability density function. In particular, the quantum-behaved particle swarm optimization method turns out to be a special case of MPSO by taking a special probability density function. The MPSO methods with six different probability density functions are tested on a few benchmark problems. These MPSO methods behave differently for different problems. Thus, our framework not only gives an interpretation for the ordinary PSO but also, more importantly, provides a warehouse of PSO-like methods to choose from for solving different practical problems.