Particle Swarm Optimization with Minimum Spanning Tree Topology for Multimodal Optimzation

Abstract

Multimodal optimization amounts to finding multiple optima of a problem. In recent years, particle swarm optimization (PSO) algorithms have been widely used by the evolutionary computation community to tackle multimodal problems. However, the capability of using a suitable PSO communication topology to induce stable niching behavior has not been well explored. In this paper, we propose a minimum spanning tree (MST) topology for PSO to solve multimodal problems. In each iteration, a minimum spanning tree is built based on the configuration of particles. The neighbors of each particle are determined according to the MST. The MST topology is able to capture the distribution of particles using a small number of edges. Moreover, a number of max weighted edges in the MST are cut to avoid the genetic drift phenomenon and to enhance the niching performance. The proposed topology is integrated with a canonical PSO and a locally informed particle optimizer (LIPS) to tackle multimodal problems. Experiments have been conducted on the CEC2013 benchmark functions to test the performance the integrated algorithms. Experimental results show that PSOs with MST topology are very effective in solving multimodal problems.