A theoretical and empirical analysis of convergence related particle swarm optimization

Abstract

In this paper an extensive theoretical and empirical analysis of recently introduced Particle Swarm Optimization algorithm with Convergence Related parameters (CR-PSO) is presented. The convergence of the classical PSO algorithm is addressed in detail. The conditions that should be imposed on parameters of the algorithm in order for it to converge in mean-square have been derived. The practical implications of these conditions have been discussed. Based on these implications a novel, recently proposed parameterization scheme for the PSO has been introduced. The novel optimizer is tested on an extended set of benchmarks and the results are compared to the PSO with time-varying acceleration coefficients (TVAC-PSO) and the standard genetic algorithm (GA).