Multi-objective particle swarm optimization with guided exploration for multimodal problems

Abstract

To address the multimodal and multi-objective optimization problems, various evolutionary algorithms are developed in the literature. The aim of these algorithms is to find the best feasible solution set for considered objectives. However, approaches developed in literature are unable to determine well distributed Pareto sets and Pareto front in the decision and the objective space respectively. There exists a trade-off in convergence and diversity of Pareto optimal solutions. In this paper, we propose an enhanced multi-objective particle swarm optimization (EMOPSO) method which uses Lévy flight to enhance exploration and expedite the search to obtain multiple global optima. In addition, we introduce parameter gamma that judiciously intertwines exploration and exploitation. Hence, the proposed variant EMOSPO provides diversity in the decision and objective space simultaneously. This method is also successful in maintaining multiple stable niches for multimodal solutions and forms well distributed Pareto set and Pareto front as compared to ten state-of-the-art algorithms. The EMOPSO is evaluated on 24 multimodal multi-objective problems of CEC 2020 based on four performance indicators and is analyzed on the basis of time complexity. Performance of EMOPSO and competitive algorithms is also evaluated on four real world engineering problems. The compared algorithms are ranked on basis of average ranking and Friedman test. Experimental results and analysis show the superior performance of EMOPSO in comparison to the competing state-of-the-art multi-objective algorithms.