Improved differential evolution algorithm based on chaotic theory and a novel Hill-Valley method for large-scale multimodal optimization problems

Multimodal optimization is one of the most challenging issues in the field of optimization, which requires to detect and locate multiple global and local optima. Differential evolution (DE) is a well-known and powerful optimization algorithm with fast convergence capability. In this paper, we proposed a method to accurately solve high dimensional multimodal problems based on DE. Parallel sub-populations that are created using roaming algorithm, are randomly assigned with several chaotically improved strategies. Furthermore, a novel Hill-Valley method is proposed for detecting whether two points are in same species or not. Finally, our proposed approach is compared with well-known state-of-the-art niching algorithms and results show that our approach outperforms all of them.