A Multi-Angle Hierarchical Differential Evolution Approach for Multimodal Optimization Problems

Zhao Hong,Dong Liu,Zhi-Hui Zhan,Zong-Gan Chen,Jun Zhang

doi:10.1109/access.2020.3027559

Abstract

Multimodal optimization problem (MMOP) is one of the most common problems in engineering practices that requires multiple optimal solutions to be located simultaneously. An efficient algorithm for solving MMOPs should balance the diversity and convergence of the population, so that the global optimal solutions can be located as many as possible. However, most of existing algorithms are easy to be trapped into local peaks and cannot provide high-quality solutions. To better deal with MMOPs, considerations on the solution quality angle and the evolution stage angle are both taken into account in this paper and a multi-angle hierarchical differential evolution (MaHDE) algorithm is proposed. Firstly, a fitness hierarchical mutation (FHM) strategy is designed to balance the exploration and exploitation ability of different individuals. In the FHM strategy, the individuals are divided into two levels (i.e., low/high-level) according to their solution quality in the current niche. Then, the low/high-level individuals are applied to different guiding strategies. Secondly, a directed global search (DGS) strategy is introduced for the low-level individuals in the late evolution stage, which can improve the population diversity and provide these low-level individuals with the opportunity to re-search the global peaks. Thirdly, an elite local search (ELS) strategy is designed for the high-level individuals in the late evolution stage to refine their solution accuracy. Extensive experiments are developed to verify the performance of MaHDE on the widely used MMOPs test functions i.e., CEC’2013. Experimental results show that MaHDE generally outperforms the compared state-of-the-art multimodal algorithms.

Highlights

Multimodal optimization problems (MMOPs), as one kind of challenging and interesting optimization problems, have attracted increasing attentions in recent years [1]–[4]
From the evolution stage perspective, the directed global search (DGS) strategy is designed for the low-level individuals in the late evolution stage, which can improve the population diversity and provide the new opportunity for exploring more global peaks
The elite local search (ELS) strategy is designed for the high-level individuals, which borrows a narrow sampling space of Gaussian distribution to refine the accuracy of solutions in the late evolution stage

Summary

INTRODUCTION

Multimodal optimization problems (MMOPs), as one kind of challenging and interesting optimization problems, have attracted increasing attentions in recent years [1]–[4]. This paper proposes a new algorithm based on DE, which designs different strategies to accommodate individuals of different fitness levels and search requirement in different evolution stages for efficiently solving MMOPs. III. From the above three situations, we can find that when f (A) is lower than the mean fitness (f ) of the current niche, using the better individuals (i.e., the larger vertical distance) to guide A can help to locate the global peaks quickly and avoid local peaks. The DE/rand strategy decreases the convergence speed due to the random searching directions, and the DE/best strategy is easy to trap into local peaks for the homogeneous guidance direction To avoid this situation, the FHM strategy can provide adaptive guide individual evolution, which divides the individuals of a niche into two levels (i.e., low/high level) according to their fitness quality.

DGS STRATEGY

ELS STRATEGY

EXPERIMENTAL STUDIES

26: End If

Findings

CONCLUSION