Convergence and stochastic stability analysis of particle swarm optimization variants with generic parameter distributions

In this paper we present the convergence and stochastic stability analysis of a set of PSO variants: those that differ with the classical PSO in the statistical distribution of the three PSO tuning parameters: inertia weight, local and global acceleration. We provide an analytical expression for the upper limit of the second order stability regions (the so called USL curves) of the particle trajectories that can be applied to most of these PSO algorithms. Thus, this work generalizes to this set the result found in the literature for the classical PSO. We apply this analysis to some of these variants. Finally, numerical experiments have been performed that confirm the known fact that the best algorithm performance is provided tuning the PSO parameters close to the USL curve.