Particle convergence expected time in the stochastic model of PSO

Abstract

Convergence properties in the model of PSO with inertia weight are a subject of analysis. Particularly, we are interested in estimating the time necessary for a particle to obtain equilibrium state in deterministic and stochastic models. For the deterministic model, an earlier defined upper bound of particle convergence time (pctb) is revised and updated. For the stochastic model, four new measures of the expected particle convergence time are proposed: (1) the convergence of the expected location of the particle, (2) the particle location variance convergence and (3)–(4) their respective weak versions. In the experimental part of the research, graphs of recorded expected running time (ERT) values are compared to graphs of upper bound of pct from the deterministic model as well as graphs of recorded convergence times of the particle location pwcet from the stochastic model.