Bayesian Optimization for Categorical and Mixed Variables Using a Multinomial Logit Surrogate

Bayesian optimization is effective for expensive black-box problems, but standard Gaussian-process surrogates are less suitable for categorical and mixed-variable search spaces. We propose MNL-BO, a preference-based Bayesian optimization method that uses a multinomial logit surrogate trained from pairwise comparisons. The model provides interpretable utility estimates for categorical alternatives and supports continuous, discrete, and categorical variables in a unified framework. Experiments on categorical benchmarks, the Traveling Salesman Problem, and mixed-variable pressure vessel design show competitive performance against random search, local search, metaheuristics, and SMAC-inspired tree-based Bayesian optimization baselines.