A network community-based differential evolution for multimodal optimization problems

Multimodal optimization problems (MMOPs) aim to locate multiple global optima simultaneously, which requires a high diversity of solutions. As a diversity preservation strategy customized for evolutionary algorithms (EAs), niching has been extensively incorporated into many algorithms to deal with MMOPs. However, many existing niching techniques require pre-defined parameters to control the size or number of niches, making the algorithm sensitive to parameters. Taking individuals as nodes, the inverse distance of two individuals as edges, and the historical information of recent generations as node attributes, we can construct a population as a network, whose purpose is to divide niches through community detection without relying on sensitive parameters. Inspired by this idea, this paper proposes a network community-based differential evolution for multimodal optimization problems (NetCDEMMOPs). In NetCDEMMOPs, three strategies are proposed and work together. Firstly, the community detection-based niching (CDN) strategy constructs the population as an attribute network and automatically divides it into multiple niches without sensitive parameters. Secondly, the community elites-based updating (CEU) strategy allocates more evolutionary resources to elite individuals of communities, then predicts and updates these elites based on historical information. Finally, the poor individual remolding (PIR) strategy remolds the last-ranking individuals and guides them toward promising positions. After extensive experimentation with the widely adopted CEC'2013 test suit, the experimental results reveal the superiority of NetCDEMMOPs over many successful or recent algorithms for MMOPs.