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.

翻译：在工程和科学的许多领域,对混合、昂贵的混合、非优惠的黑箱问题优化多重、非优惠目标十分重要。这些问题的昂贵、吵闹的黑箱性质使得他们成为贝叶西亚优化(BO)的理想人选。但是,混合的和多目标的问题,由于BO的基本平稳高萨进程替代模型,是一个挑战。目前多目标的BO算法无法处理混合的可变问题。我们提出MixMOBO,这是针对这些问题的第一个混合的、可变的、多目的的贝叶西亚优化框架。我们提出一个新的获取功能,利用基因算法来抽样代理替代表面,最佳的Pareto前端用于多目标、混合的可变设计空间,在确保多种解决方案的同时,可以有效地找到它们的理想人选。这个方法足够灵活,可以纳入许多不同的内核和购置功能,包括其他作者为混合易变或多目标问题开发的那些功能。我们还提出“HedgeMoldMenderMO”,这是在多目标的购置功能中使用的组合。我们提出了一个新的获取功能。我们提出了一个新的获取功能SMC。我们表明,MixMOBBO在模拟设计上应用了一种真正的混合的模型结构,它展示了其他混合设计。