This paper presents a new type of hybrid model for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. hybridM leverages the upper confidence bound tree search (UCTS) for MCTS strategy, showcasing the tree architecture's integration into Bayesian optimization. Our innovations, including dynamic online kernel selection in the surrogate modeling phase and a unique UCTS search strategy, position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the superiority of hybrid models, highlighting their potential in Bayesian optimization.

翻译：本文提出一种新型混合模型用于贝叶斯优化，该模型擅长处理包含定量（连续型和整数型）与定性（类别型）变量的混合变量。我们提出的新型混合模型（命名为hybridM）将用于类别变量的蒙特卡洛树搜索（MCTS）结构与用于连续变量的高斯过程（GP）相结合。hybridM采用上置信界树搜索（UCTS）作为MCTS策略，展示了树形架构在贝叶斯优化中的集成。我们的创新包括在代理建模阶段引入动态在线核选择以及独特的UCTS搜索策略，这使得混合模型成为混合变量代理模型领域的一项进展。数值实验验证了混合模型的优越性，突显了其在贝叶斯优化中的应用潜力。