Multisurrogate-Assisted Ant Colony Optimization for Expensive Optimization Problems With Continuous and Categorical Variables.

As an effective optimization tool for expensive optimization problems (EOPs), surrogate-assisted evolutionary algorithms (SAEAs) have been widely studied in recent years. However, most current SAEAs are designed for continuous/ combinatorial EOPs, which are not suitable for mixed-variable EOPs. This article focuses on one kind of mixed-variable EOP: EOPs with continuous and categorical variables (EOPCCVs). A multisurrogate-assisted ant colony optimization algorithm (MiSACO) is proposed to solve EOPCCVs. MiSACO contains two main strategies: 1) multisurrogate-assisted selection and 2) surrogate-assisted local search. In the former, the radial basis function (RBF) and least-squares boosting tree (LSBT) are employed as the surrogate models. Afterward, three selection operators (i.e., RBF-based selection, LSBT-based selection, and random selection) are devised to select three solutions from the offspring solutions generated by ACO, with the aim of coping with different types of EOPCCVs robustly and preventing the algorithm from being misled by inaccurate surrogate models. In the latter, sequence quadratic optimization, coupled with RBF, is utilized to refine the continuous variables of the best solution found so far. By combining these two strategies, MiSACO can solve EOPCCVs with limited function evaluations. Three sets of test problems and two real-world cases are used to verify the effectiveness of MiSACO. The results demonstrate that MiSACO performs well in solving EOPCCVs.