A multiple optimal solutions search method by using a Particle Swarm Optimization algorithm utilizing the distribution of personal bests

We propose a basic method for finding multiple optimal solutions by using a modified Particle Swarm Optimization (PSO) algorithm which utilizes the distribution of personal bests (pbests). The proposed method has the following features: (a) global search for multiple optimal solutions sequentially by using a modified PSO algorithm, called “main-PSO,” in which the global best (gbest) is replaced by the personal best (pbest) of another particle in order to gather pbests in a self-organizing manner; (b) prediction of the attracting region of optimal solutions by analyzing the distribution of pbests in terms of the distance in the search space and the objective space; (c) local search for an accurate optimal solution in the predicted region intensively by using a standard PSO algorithm, called “sub-PSO”; and, (d) exclusion of locally searched regions from the original search domain in order to improve the efficiency of global search. By numerical experiments, we study its ability to find global and local optimal solutions.