Differential evolution based on strategy adaptation and deep reinforcement learning for multimodal optimization problems

Multimodal optimization problems (MMOPs) include multiple optima, which are common in practical fields. However, the success of solving MMOPs requires the algorithm to have both exploration and exploitation performance. How to select a reasonable search strategy is a difficult problem facing MMOPs. In this research, a differential evolution based on strategy adaptation and deep reinforcement learning, termed SA-DQNDE, is proposed to select mutation strategies reasonably and search the optima effectively, which mainly includes three aspects. First, strategy adaptation, which calculates selection probability based on the feedback of different mutation operators in previous evolution, and assigns mutation operations to each individual to provide guidance for the next stage of evolution is developed. Secondly, a new historical individual preservation method is designed to improve search efficiency. Thirdly, deep reinforcement learning is applied to select multiple local search operators to refine the accuracy of potential optimal solutions. The performance of SA-DQN-DE is tested on publicly acknowledged CEC2013 benchmark MMOP set. The experimental results demonstrate that the proposed SA-DQN-DE has competitive performance compared with some of its peer multimodal optimization algorithms.