Bayesian Optimization For Multi-Objective Mixed-Variable Problems

Optimizing multiple, non-preferential objectives for mixed-variable, expensive black-box problems is important in many areas of engineering and science. The expensive, noisy black-box nature of these problems makes them ideal candidates for Bayesian optimization (BO). Mixed-variable and multi-objective problems, however, are a challenge due to the BO's underlying smooth Gaussian process surrogate model. Current multi-objective BO algorithms cannot deal with mixed-variable problems. We present MixMOBO, the first mixed variable multi-objective Bayesian optimization framework for such problems. Using a genetic algorithm to sample the surrogate surface, optimal Pareto-fronts for multi-objective, mixed-variable design spaces can be found efficiently while ensuring diverse solutions. The method is sufficiently flexible to incorporate many different kernels and acquisition functions, including those that were developed for mixed-variable or multi-objective problems by other authors. We also present HedgeMO, a modified Hedge strategy that uses a portfolio of acquisition functions in multi-objective problems. We present a new acquisition function SMC. We show that MixMOBO performs well against other mixed-variable algorithms on synthetic problems. We apply MixMOBO to the real-world design of an architected material and show that our optimal design, which was experimentally fabricated and validated, has a normalized strain energy density $10^4$ times greater than existing structures.