A chaotic particle swarm optimization exploiting a virtual quartic objective function based on the personal and global best solutions

The particle swarm optimization method (PSO) is one of population-based optimization techniques for global optimization, 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 a PSO with a new chaotic system derived from the steepest descent method for a virtual quartic objective function with perturbations having its global minima at the personal and global bests, 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.