Automatic Niching Differential Evolution With Contour Prediction Approach for Multimodal Optimization Problems

Niching techniques have been widely incorporated into evolutionary algorithms (EAs) for solving multimodal optimization problems (MMOPs). However, most of the existing niching techniques are either sensitive to the niching parameters or require extra fitness evaluations (FEs) to maintain the niche detection accuracy. In this paper, we propose a new automatic niching technique based on the affinity propagation clustering (APC) and design a novel niching differential evolution (DE) algorithm, termed as automatic niching DE (ANDE), for solving MMOPs. In the proposed ANDE algorithm, APC acts as a parameter-free automatic niching method that does not need to predefine the number of clusters or the cluster size. Also, it can facilitate locating multiple peaks without extra FEs. Furthermore, the ANDE algorithm is enhanced by a contour prediction approach (CPA) and a two-level local search (TLLS) strategy. First, the CPA is a predictive search strategy. It exploits the individual distribution information in each niche to estimate the contour landscape, and then predicts the rough position of the potential peak to help accelerate the convergence speed. Second, the TLLS is a solution refine strategy to further increase the solution accuracy after the CPA roughly predicting the peaks. Compared with the other state-of-the-art DE and non-DE multimodal algorithms, even the winner of competition on multimodal optimization, the experimental results on 20 widely used benchmark functions illustrate the superiority of the proposed ANDE algorithm.