Outlier aware differential evolution for multimodal optimization problems

Abstract

Multimodal optimization problems (MMOPs) target to locate multiple global optima simultaneously, which mainly face two challenges: how to maximize the number of global peaks and how to enhance the accuracy of the found solutions. To deal with these two challenges, an outlier aware differential evolution (OADE) algorithm is proposed in this paper, which includes three novel mechanisms. Firstly, a dimension and guidance-balanced mutation (DGM) strategy is proposed to improve the accuracy of solutions by balancing the information of individuals, niching, and population. Secondly, an outlier-based selection (OBS) strategy is designed to increase the population diversity and further to locate as many peaks as possible, which combines the fitness information and the distribution information of individuals. Thirdly, an inactive outlier-based re-initialization (IOR) strategy is proposed to enable the inactive outliers to jump out of local optima when dealing with high-dimensional MMOPs. The performance of OADE is tested on 20 widely used multimodal benchmarks. The experimental results show that the proposed OADE generally has better or competitive performance compared with some well-performing and state-of-the-art multimodal optimization algorithms.