Stability, Entropy and Performance in PSO

A main focus in the theory of Particle Swarm Optimization (PSO) was the convergence of the particles where various frameworks and assumptions have been adopted which lead to a variety of outcomes differing in their relevance as a predictor of the performance of the algorithm. We discuss here the interesting phenomenon that the study of the stochastic dynamics of the particles provides a limit case, while the average dynamics yields a different limit. We can specify differences between the best particle and other particles in the swarm which has an effect on the performance of the algorithm and was not considered in previous approaches. In addition to benchmark results, also the swarm entropy confirms this formulation of the stability properties of PSO. This framework enables us to describe the time scales of excursions of particles away from the best location found so far, which indicates the diversity of locations in the search space discovered so far by the particles.