A study on two-step search based on PSO to improve convergence and diversity for Many-Objective Optimization Problems

Particle Swarm Optimization (PSO) is one of the most effective search methods in optimization problems. Multiobjective Optimization Problems (MOPs) has been focused on and PSO researches applied to MOPs have been reported. On the other hand, the problem that the search performance using conventional methods for MOPs becomes low is reported in Many-objective Optimization Problems (MaOPs) which have four or more objective functions. The authors have proposed two-step search method based on PSO for MaOPs. In the first step, it divides the population into some groups, and each group performs the single objective search for each objective function and the center of them. In the second step, the search is performed to acquire the diversity of Pareto solutions by PSO search with the goal, global-best, based on the solutions acquired in the first step. This paper defines the real coded multi-objective knapsack problem and studies the performance of the proposed method applied to this problem. The experimental results shows that the search of the first step for high convergence and that of the second step for large diversity aimed in the proposed method works well. It also shows that the proposed method is superior to other conventional methods especially in terms of the convergence in MaOPs.