Solving Expensive Multimodal Optimization Problem by a Decomposition Differential Evolution Algorithm

• Published in: IEEE transactions on cybernetics Vol. 53; no. 4; pp. 2236 - 2246
• Main Authors: Gao, Weifeng, Wei, Zhifang, Gong, Maoguo, Yen, Gary G.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.04.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Clustering; Costs; Decomposition; Differential evolution (DE); Evolutionary algorithms; Evolutionary computation; expensive multimodal optimization problems (EMMOPs); Global optimization; Linear programming; Mathematical models; Optimization; Radial basis function; radial basis function (RBF); Search engines; Search problems; Sociology; Statistics
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2021.3113575

An expensive multimodal optimization problem (EMMOP) is that the computation of the objective function is time consuming and it has multiple global optima. This article proposes a decomposition differential evolution (DE) based on the radial basis function (RBF) for EMMOPs, called D/REM. It mainly consists of two phases: the promising subregions detection (PSD) and the local search phase (LSP). In PSD, a population update strategy is designed and the mean-shift clustering is employed to predict the promising subregions of EMMOP. In LSP, a local RBF surrogate model is constructed for each promising subregion and each local RBF surrogate model tracks a global optimum of EMMOP. In this way, an EMMOP is decomposed into many expensive global optimization subproblems. To handle these subproblems, a popular DE variant, JADE, acts as the search engine to deal with these subproblems. A large number of numerical experiments unambiguously validate that D/REM can solve EMMOPs effectively and efficiently.