A surrogate-assisted evolutionary algorithm with knowledge transfer for expensive multimodal optimization problems

As a kind of common problems in practical applications, expensive multimodal optimization problems (EMMOPs) require to locate as many global optima as possible with a few costly or/and time-consuming fitness evaluations. This poses a great challenge since even capturing a single optimum is not so easy. To address this issue, this study proposes a surrogate-assisted multimodal evolutionary algorithm with knowledge transfer (SAKT-MMEA), where a modality prediction method based on global surrogate-assisted sampling (GSSMP) and a joint surrogate-assisted local search method (JSLS) are designed for efficient modality exploration and exploitation, respectively. By pre-constructing a global surrogate model, GSSMP samples and approximately evaluates adequate solutions such that the fitness landscape of an EMMOP can be well depicted and the modalities are expected to be fully detected. For each identified modality, JSLS adaptively takes a local surrogate model or a global one as the objective function to exploit the optimum while preventing it from getting trapped in a local optimum. To further enhance the exploitation efficiency, a knowledge transfer-based optimizer is developed for JSLS to collaboratively perform multiple local search on different modalities. Extensive experimental results on EMMOPs with different features demonstrate that SAKT-MMEA gains competitive edges over six state-of-the-art algorithms.