Niche Center Identification Differential Evolution for Multimodal Optimization Problems

Niching techniques are commonly incorporated into evolutionary computation (EC) algorithms to address multimodal optimization problems (MMOPs). Nevertheless, identifying proper individuals as niche centers remains the main challenge in niching techniques. Generally, niche centers should possess promising fitness (fitness aspect) and should be dispersedly distributed in different search regions (distance aspect). In this study, we propose a novel niching technique known as niche center identification (NCI) and integrate it with differential evolution (DE) for tackling MMOPs, termed NCIDE. In NCI, niche centers are first identified from both the fitness and distance aspects. Individuals that are not niche centers are added to their nearest niche centers to form niches. Moreover, we develop a niche-level archival-adaptive parameter scheme (NAAPS) to adaptively adjust the parameters at the niche level and reduce their sensitivity. Meanwhile, with the help of an archive, we can preserve the identified optima and reinitialize stagnant individuals for further exploration. The experimental results on the CEC2013 multimodal benchmark test suite demonstrate that NCIDE significantly outperforms several state-of-the-art multimodal algorithms, including multiple competition winners from CEC2015 and GECCO2017-GECCO2019. Finally, NCIDE is applied to solve multimodal nonlinear equation system (NES) problems to further illustrate its practical applicability.