Dynamic Neighborhood-Based Particle Swarm Optimization for Multimodal Problems

Xu-Tao Zhang,Xin-Fang Ji,Biao Xu,Wei Zhang,Jun Zhang,Bo Yang

doi:10.1155/2020/6675996

Abstract

Various black-box optimization problems in real world can be classified as multimodal optimization problems. Neighborhood information plays an important role in improving the performance of an evolutionary algorithm when dealing with such problems. In view of this, we propose a particle swarm optimization algorithm based on dynamic neighborhood to solve the multimodal optimization problem. In this paper, a dynamic ε-neighborhood selection mechanism is first defined to balance the exploration and exploitation of the algorithm. Then, based on the information provided by the neighborhoods, four different particle position updating strategies are designed to further support the algorithm’s exploration and exploitation of the search space. Finally, the proposed algorithm is compared with 7 state-of-the-art multimodal algorithms on 8 benchmark instances. The experimental results reveal that the proposed algorithm is superior to the compared ones and is an effective method to tackle multimodal optimization problems.

Highlights

Various black-box problems to be tackled difficultly in the real world have the characteristic of multimodal problem [1]
Eight widely used benchmark problems are selected to test the performance of the algorithm. ese benchmark problems are derived from the IEEE CEC 2013 special section on multimodal optimization [37]. e characteristics of these instances are shown in Table 1, where the “Peak height” refers to the value of the global optimal solution
(2) For F4 and F7(5D), except EMO-MMO and VNCDE, Peak ratio (PR) obtained by the remaining five algorithms are significantly inferior to dynamic neighborhood-based multimodal PSO algorithm (DNPSO). (3) For F5, there is no significant difference between DNPSO and EMO-MMO, but the PRs obtained by DNPSO are significantly better than those of the other six compared ones

Summary

Introduction

Various black-box problems to be tackled difficultly in the real world have the characteristic of multimodal problem [1]. Qu et al [26] proposed a distancebased locally informed PSO (LIPS), where the global best position is replaced by multiple local best positions to guide the update of particles for converging to different optimal subspaces. Based on the locality sensitive hashing, Zhang et al proposed a fast niching technique to find the neighborhood set of particles, which can keep a balance between the exploration and exploitation of the algorithm while reducing the computational complexity of EAs [27]. In order to handle the above problems, a dynamic neighborhood-based multimodal PSO algorithm (DNPSO) is proposed in this paper. E proposed DNPSO is presented, including the dynamic ε-neighborhood selection mechanism, four different position updating strategies, and the framework of the proposed algorithm.

Particle Swarm Optimization Algorithm

Dynamic Neighborhood-Based PSO for Multimodal Problems

Experiments and Analysis

Findings

Conclusions