Monte Carlo Analysis of Gathering and Scattering Behavior Generated by Gravitational Particle Swarm Algorithm

Abstract

In this study, we propose a novel multimodal optimization algorithm, gravitational particle swarm algorithm (GPSA), by replacing the global feedback term of a classical particle swarm optimization with a term that introduces inverse-square gravitational force between particles. We analyze the search behavior of these particles by Monte-Carlo simulation, demonstrating that the particles often gather around the global optima but seldom scatter away from them. Furthermore, our GPSA's performance is evaluated on benchmark functions, showing that it found over 95.5% and 78.2% of the global optima over the course of multiple runs for two-and three-dimensional benchmark functions, respectively. At the same time, it found all global optima at least 62% and 5% of the separate runs, whereas the existing methods almost entirely failed to do.-16 -16