Differential evolution with nearest density clustering for multimodal optimization problems

Multimodal optimization problems (MMOPs) refer to problems with multiple optimal solutions in a given search region. Evolutionary algorithms (EAs) are widely used to search for optimal solutions. To address the multimodal problem, we propose differential evolution with nearest density clustering (NDC-DE), which combines a density clustering-based technique and a differential evolutionary algorithm. NDC-DE includes three mechanisms. First, we use nearest density clustering (NDC) to divide the initial population into multiple subpopulations and identify the best individuals in each ecological niche. Combining niche techniques with evolutionary algorithms significantly improve their ability to solve MMOPs. Clustering algorithms are useful niche techniques divide the population into subpopulations based on different characteristics. Second, we propose two new mutation operators based on nbest. Last, an adaptive species redistribution mechanism based on the opposition-based learning (OBL) mechanism is proposed during the evolutionary iteration of NDC-DE to enhance the diversity of niches. We compare NDC-DE with 15 other algorithms on the CEC2013 benchmark function and show that it outperforms these algorithms in handling MMOPs.