Adaptive Estimation Distribution Distributed Differential Evolution for Multimodal Optimization Problems

Multimodal optimization problems (MMOPs) require algorithms to locate multiple optima simultaneously. When using evolutionary algorithms (EAs) to deal with MMOPs, an intuitive idea is to divide the population into several small “niches,” where different niches focus on locating different optima. These population partition strategies are called “niching” techniques, which have been frequently used for MMOPs. The algorithms for simultaneously locating multiple optima of MMOPs are called multimodal algorithms. However, many multimodal algorithms still face the difficulty of population partition since most of the niching techniques involve the sensitive niching parameters. Considering this issue, in this article, we propose a parameter-free niching method based on adaptive estimation distribution (AED) and develop a distributed differential evolution (DDE) algorithm, which is called AED-DDE, for solving MMOPs. In AED-DDE, each individual finds its own appropriate niche size to form a niche and acts as an independent unit to find a global optimum. Therefore, we can avoid the difficulty of population partition and the sensitivity of niching parameters. Different niches are co-evolved by using the master–slave multiniche distributed model. The multiniche co-evolution mechanism can improve the population diversity for fully exploring the search space and finding more global optima. Moreover, the AED-DDE algorithm is further enhanced by a probabilistic local search (PLS) to refine the solution accuracy. Compared with other multimodal algorithms, even the winner of CEC2015 multimodal competition, the comparison results fully demonstrate the superiority of AED-DDE.