Optimal Peaks Detected-Based Differential Evolution for Multimodal Optimization Problems

Multimodal optimization problems (MMOPs) have multiple global optima, hence the algorithm must preserve population diversity to locate multiple global optima and ensure the precision of the obtained solutions simultaneously. To achieve these, the niching technique is widely applied. Although the niching technique shows encouraging performance, some niches may continuously evolve even though accurate enough global optima in their regions have been found. This may cause the waste of computational resources and the inefficiency of search behavior. To maintain population diversity and accuracy, and to break through the mentioned deficiency, an optimal peaks detected-based differential evolution (OPPDE) algorithm is proposed, which has three novel components. Firstly, to maintain population diversity, OPDDE designs a parameter-insensitive OPTICS-based niching strategy to automatically partition niches. Secondly, to avoid wasting computation resources on founded global optima and enhance search efficiency, OPDDE designs an optimal peaks detection strategy that uses historical information to identify the founded global optima. Thirdly, a dynamic step local search strategy is used to refine solutions. The proposed OPDDE algorithm generally superiors some state-of-the-art algorithms regarding both the accuracy and completeness of solutions, according to experiments on widely used MMOP benchmarks.