Chaotic particle swarm optimization with an intensive search around the personal and global bests

The particle swarm optimization method (PSO) is a population-based optimization technique. 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 a PSO with a new chaotic system derived from the steepest descent method for a virtual quartic objective function with perturbations having global minima at the personal and global bests obtained by particles so far, where elements of each particle´s position are updated by the proposed chaotic system or the standard update formula. Thus, the proposed PSO can search for solutions around the personal and global bests intensively without being trapped at any local minimum due to the chaoticness. Moreover, we show approximately the sufficient condition of parameter values of the proposed system under which the system is chaotic. Through computational experiments, we verify the performance of the proposed PSO by applying it to some global optimization problems.