A Novel Method for Analysing the Population Dynamic Behavior of Particle Swarm Optimization

Most of the existing population behavior studies are about the analysis of the population dynamic behavior of genetic algorithm, while there is little analysis of the population dynamic behavior of particle swarm optimization (PSO). Therefore, there is an urgent need for a new method to characterize the population dynamic behavior of PSO in the search process. In this paper, we propose some metrics based on relative entropy, principal component analysis and correlation coefficient, to characterize the population dynamic behavior of PSO, named KL measure (KLM) and principal correlation coefficient (PCC). KLM and PCC are used to describe the divergence and correlation between the differences of objective functions and particle positions. Using these proposed metrics KLM and PCC, we can effectively divide the search process of the population into three stages: random search stage, fine search stage and convergence stage. Experimental results, with classical optimization problems and different running parameters, show that the proposed metrics KLM and PCC can capture the dynamic alteration of population behavior even when the population is in a relatively convergent state, hence, which can characterize the whole search process of the population in much fine granularity.