Differential Evolution for Multimodal Optimization with Species by Nearest-Better Clustering

Multimodal optimization problems (MMOPs) are common in real-world applications and involve identifying multiple optimal solutions for decision makers to choose from. The core requirement for dealing with such problems is to balance the ability of exploration in the global space and exploitation in the multiple optimal areas. In this paper, based on the differential evolution (DE), we propose a novel algorithm focusing on the formulation, balance, and keypoint of species for MMOPs, called FBK-DE. First, nearest-better clustering (NBC) is used to divide the population into multiple species with minimum size limitations. Second, to avoid placing too many individuals into one species, a species balance strategy is proposed to adjust the size of each species. Third, two keypoint-based mutation operators named DE/keypoint/1 and DE/keypoint/2 are proposed to evolve each species together with traditional mutation operators. The experimental results of FBK-DE on 20 benchmark functions are compared with 15 state-of-the-art multimodal optimization algorithms. The comparisons show that the proposed FBK-DE performs competitively with these algorithms.