Analysis of particle interaction in particle swarm optimization

In this paper, we analyze the behavior of particle swarm optimization (PSO) on the facet of particle interaction. We firstly propose a statistical interpretation of particle swarm optimization in order to capture the stochastic behavior of the entire swarm. Based on the statistical interpretation, we investigate the effect of particle interaction by focusing on the social-only model and derive the upper and lower bounds of the expected particle norm. Accordingly, the lower and upper bounds of the expected progress rate on the sphere function are also obtained. Furthermore, the sufficient and necessary condition for the swarm to converge is derived to demonstrate the PSO convergence caused by the effect of particle interaction.