Multiple Optimal Solutions Search by Using Swarm Division Particle Swarm Optimization Algorithm which Utilizes the Distribution of Personal Best Solutions

We propose a new Particle Swarm Optimization (PSO) algorithm which utilizes the information about the distribution of personal bests (pbests). Basically, it applies the standard PSO; however, when the global best (gbest) approaches an optimal solution, its attracting region is estimated by using the distribution information. If particles gather around the gbest, the swarm is divided into two sub-swarms: (a) the local search sub-swarm, which keeps searching for the local solution by using the standard PSO; and, (b) the other solutions search sub-swarm, which moves particles to different solutions by using a modified PSO. When the local search is completed, the standard PSO is appled to all the particles again to trigger the estimation of the attracting region of another optimal solution. Additional resetting of particles in several situations is also applied to keep the diversity of global search. We show the usefulness of the proposed method by numerical experiments.