  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.
