Solving multimodal optimization problems by a knowledge transfer based dual niching differential evolution

Multimodal optimization problems (MMOPs) contain multiple optimal solutions in the decision space. It requires the algorithm to ensure a balance between convergence and diversity. Many existing methods utilize knowledge transfer to enhance optimization capabilities. However, these methods still suffer from the phenomenon of negative knowledge transfer. Hence, this paper proposed a knowledge transfer based dual niching differential evolution algorithm (KTDNDE) to solve MMOPs more efficiently. Its main features are: (i) past differential vectors (PDV) serve as specific knowledge to guide the evolution of the algorithm; (ii) a two-stage PDV reuse mechanism has been designed to effectively enhance the algorithm’s performance; (iii) a parameter setting based on fitness ranking is introduced to improve search efficiency. 30 nonlinear equation system (NESs) are modeled as MMOPs to verify the performance of the proposed KTDNDE. Based on the experimental results, the proposed method is superior to several state-of-the-art methods in terms of root rate and success rate. • Knowledge transfer intensity strategy is proposed to dynamic determine the timing of transfer. • Knowledge transfer mechanism determines the migration of individuals. • Parameter adaptation with niching level is introduced our approach.