Customized Evolutionary Expensive Optimization: Efficient Search and Surrogate Strategies for Continuous and Categorical Variables

Surrogate-assisted evolutionary algorithms for addressing expensive optimization problems with both continuous and categorical variables (EOPCCVs) are still in the early stages of development. This study makes significant advancements by leveraging the mixed-variable nature of EOPCCVs in two crucial ways. First, it introduces a novel hybrid approach combining differential evolution and upper confidence bound sampling (DEUCB), designed to explore the mixed search space effectively. Second, a specialized value distance metric (VDM) is proposed, integrating continuous and categorical variables, to enhance the accuracy of the radial basis function (RBF) model approximation. Finally, we present a customized evolutionary expensive optimization algorithm (CEEO), which seamlessly incorporates DEUCB and RBF-VDM into the widely utilized global and local surrogate-assisted evolutionary optimization framework. Experimental results, compared against state-of-the-art counterparts on three distinct sets of benchmark problems and a convolutional neural network hyperparameter optimization task, consistently affirm the efficacy of the proposed CEEO in addressing EOPCCVs. The source code for the proposed CEEO algorithm is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/CIAM-Group/EvolutionaryAlgorithm_Codes/tree/main/CEEO_Code</uri>.