Particle swarm variants: standardized convergence analysis

This paper presents an objective function specially designed for the convergence analysis of a number of particle swarm optimization (PSO) variants. It was found that using a specially designed objective function for convergence analysis is both a simple and valid method for performing assumption free convergence analysis. It was also found that the canonical particle swarm's topology did not have an impact on the parameter region needed to ensure convergence. The parameter region needed to ensure convergent particle behavior was empirically obtained for the fully informed PSO, the bare bones PSO, and the standard PSO 2011 algorithm. In the case of the bare bones PSO and the standard PSO 2011, the region needed to ensure convergent particle behavior differs from previous theoretical work. The difference in the obtained regions in the bare bones PSO is a direct result of the previous theoretical work relying on simplifying assumptions, specifically the stagnation assumption. A number of possible causes for the discrepancy in the obtained convergent region for the standard PSO 2011 are given.