Particle Swarm Optimization with Ring Topology for Multi-modal Multi-objective Problems

Abstract

Multi-modal multi-objective optimization problems (MMOPs) are ubiquitous in real-world applications, in which multiple objective functions are conflicting and need to be optimized simultaneously. Furthermore, multiple Pareto optimal solutions of MMOPs are mapped to the same point on the Pareto front. Canonical multi-objective optimization algorithms show poor performance for MMOPs due to the lack of diversity maintenance in the decision space. In this paper, a particle swarm optimization with ring topology, denoted as PSO-RT, is proposed for solving MMOPs. The population is firstly divided into several sub-populations based on a dynamic radius to form a ring topology. Then, each solution will update its position by learning from one of its personal best positions and the best position of its neighbors. The personal best position to be learned is selected based on the special crowding distance to improve the exploration capability, and the best position of its neighbors is selected according to the weighted indicator to speed up convergence. The performance of PSO-RT is evaluated on 22 test problems. Experimental results show that our proposed PSO-RT can obtain competitive or better results than some state-of-the-art algorithms proposed for MMOPs in terms of Pareto sets proximity (PSP) and inverted generational distance (IGDX) matrics.