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Computational Intelligence and Neuroscience
Volume 2013, Article ID 384125, 7 pages
Research Article

Convergence Analysis of Particle Swarm Optimizer and Its Improved Algorithm Based on Velocity Differential Evolution

School of Electrical and Information Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China

Received 22 April 2013; Revised 28 July 2013; Accepted 4 August 2013

Academic Editor: Yuanqing Li

Copyright © 2013 Hongtao Ye 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.


This paper presents an analysis of the relationship of particle velocity and convergence of the particle swarm optimization. Its premature convergence is due to the decrease of particle velocity in search space that leads to a total implosion and ultimately fitness stagnation of the swarm. An improved algorithm which introduces a velocity differential evolution (DE) strategy for the hierarchical particle swarm optimization (H-PSO) is proposed to improve its performance. The DE is employed to regulate the particle velocity rather than the traditional particle position in case that the optimal result has not improved after several iterations. The benchmark functions will be illustrated to demonstrate the effectiveness of the proposed method.