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.

中文翻译：

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用分解差分进化算法解决昂贵的多模态优化问题

昂贵的多模态优化问题（EMMOP）是目标函数的计算耗时且具有多个全局最优值。本文提出了一种基于径向基函数 (RBF) 的 EMMOP 分解差分进化 (DE)，称为 D/REM。它主要由两个阶段组成：有希望的子区域检测（PSD）和局部搜索阶段（LSP）。在 PSD 中，设计了种群更新策略，并采用均值漂移聚类来预测 EMMOP 的有希望的子区域。在 LSP 中，为每个有希望的子区域构建局部 RBF 代理模型，每个局部 RBF 代理模型跟踪 EMMOP 的全局最优值。这样，一个 EMMOP 被分解成许多昂贵的全局优化子问题。为了处理这些子问题，一种流行的 DE 变体 JADE，作为搜索引擎来处理这些子问题。大量的数值实验明确地验证了 D/REM 可以有效且高效地求解 EMMOPs。