Bayesian Optimization For Multi-Objective Mixed-Variable Problems
This work addresses a critical bottleneck in engineering and science for optimizing designs with mixed variables and multiple objectives, though it is incremental as it builds on existing Bayesian optimization methods.
The authors tackled the problem of optimizing multiple objectives for mixed-variable, expensive black-box functions, which is challenging for Bayesian optimization due to its reliance on smooth Gaussian process models. They introduced MixMOBO, the first framework for such problems, and demonstrated its effectiveness by achieving a normalized strain energy density 10^4 times greater than existing structures in a real-world architected material design.
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 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 MixMOBO, 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 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 for multi-objective problems. We present a new acquisition function, SMC. Our results 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.