Particle Swarm Convergence: Standardized Analysis and Topological Influence

Abstract

This paper has two primary aims. Firstly, to empirically verify the use of a specially designed objective function for particle swarm optimization (PSO) convergence analysis. Secondly, to investigate the impact of PSO's social topology on the parameter region needed to ensure convergent particle behavior. At present there exists a large number of theoretical PSO studies, however, all stochastic PSO models contain the stagnation assumption, which implicitly removes the social topology from the model, making this empirical study necessary. It was found that using a specially designed objective function for convergence analysis is both a simple and valid method for convergence analysis. It was also found that the derived region needed to ensure convergent particle behavior remains valid regardless of the selected social topology.