Stasis type particle stability in a stochastic model of particle swarm optimization

Particle Swarm Optimization (PSO) is a heuristic optimization technique where particles explore optima of the fitness landscape defined in the search space. It is a practical approach but vulnerable to incorrect particle movement parameter tuning. Therefore, stochastic models of a particle and a swarm are subject to analysis. In this paper, we study the stability properties of particles controlled by a universal update equation proposed by Cleghorn and Engelbrecht. We propose a new concept of particle state, namely the stasis state when the difference between two consecutive particle location variance values is not changing much after a sufficient time. We also propose a convergence time measure, representing a minimal number of steps a particle location variance needs to reach stasis. Finally, we visualize the convergence time characteristics obtained in simulations.