A Chaotic Particle Swarm Optimization Exploiting Snap-Back Repellers of a Perturbation-Based System

Abstract

The particle swarm optimization (PSO) is a population-based optimization technique, where a number of candidate solutions called particles simultaneously move toward the tentative solutions found by particles so far, which are called the personal and global bests, respectively. Since, in the PSO, the exploration ability is important to find a desirable solution, various kinds of methods have been investigated to improve it. In this paper, we propose novel PSOs exploiting a chaotic system derived from the steepest descent method with perturbations to a virtual quartic objective function having its global optima at the personal and global best. In those models, each particle’s position is updated by the proposed chaotic system or the existing update formula. Thus, the proposed PSO can search for solutions without being trapped at any local minima due to the chaoticness. Moreover, we show the sufficient condition of parameter values of the proposed system under which the system is chaotic. Through computational experiments, we confirm the performance of the proposed PSOs by applying it to some global optimization problems.