Hybrid Uniform Distribution of Particle Swarm Optimizer

Junqi ZHANG  Ying TAN  Lina NI  Chen XIE  Zheng TANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A    No.10    pp.1782-1791
Publication Date: 2010/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.1782
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: VLSI Design Technology and CAD
particle swarm optimizer,  hybrid uniform distribution,  exploitation,  exploration,  search strategy,  

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Particle swarm optimizer (PSO) is a stochastic global optimization technique based on a social interaction metaphor. Because of the complexity, dynamics and randomness involved in PSO, it is hard to theoretically analyze the mechanism on which PSO depends. Statistical results have shown that the probability distribution of PSO is a truncated triangle, with uniform probability across the middle that decreases on the sides. The "truncated triangle" is also called the "Maya pyramid" by Kennedy. However, very little is known regarding the sampling distribution of PSO in itself. In this paper, we theoretically analyze the "Maya pyramid" without any assumption and derive its computational formula, which is actually a hybrid uniform distribution that looks like a trapezoid and conforms with the statistical results. Based on the derived density function of the hybrid uniform distribution, the search strategy of PSO is defined and quantified to characterize the mechanism of the search strategy in PSO. In order to show the significance of these definitions based on the derived hybrid uniform distribution, the comparison between the defined search strategies of the classical linear decreasing weight based PSO and the canonical constricted PSO suggested by Clerc is illustrated and elaborated.