We present MESMOC+, an improved version of Max-value Entropy search for Multi-Objective Bayesian optimization with Constraints (MESMOC). MESMOC+ can be used to solve constrained multi-objective problems when the objectives and the constraints are expensive to evaluate. MESMOC+ works by minimizing the entropy of the solution of the optimization problem in function space, i.e., the Pareto frontier, to guide the search for the optimum. The cost of MESMOC+ is linear in the number of objectives and constraints. Furthermore, it is often significantly smaller than the cost of alternative methods based on minimizing the entropy of the Pareto set. The reason for this is that it is easier to approximate the required computations in MESMOC+. Moreover, MESMOC+'s acquisition function is expressed as the sum of one acquisition per each black-box (objective or constraint). Thus, it can be used in a decoupled evaluation setting in which one chooses not only the next input location to evaluate, but also which black-box to evaluate there. We compare MESMOC+ with related methods in synthetic and real optimization problems. These experiments show that the entropy estimation provided by MESMOC+ is more accurate than that of previous methods. This leads to better optimization results. MESMOC+ is also competitive with other information-based methods for constrained multi-objective Bayesian optimization, but it is significantly faster.

翻译：我们展示了MESMOOC+,这是对多目标贝叶斯优化的改进版最大值搜索(MESOMOC ) 。 MESMOOC+ 可以在目标和限制评估费用昂贵时用于解决受限制的多目标问题。 MESMOOC+通过最大限度地减少功能空间(即帕雷托边疆界)优化问题解决方案的灵敏度来指导最佳搜索。 MESMOC+ 的成本在目标和限制数量上是线性的。 此外,它往往比基于尽量减少帕雷托设置的酶的替代方法的成本要低得多。 其原因是,在MESMOOC+ 上,要比较容易接近所需的多目标计算。 此外,MESMOOC+ 的购置功能表现为每个黑盒(即Paretob)的购买量总和。 因此,可以在一个分解的评估环境中使用它不仅选择下一个输入地点,而且选择一个黑箱来评估。 我们将MESOC+ 与IMOC 的正统性测试结果比MIS+ 之前的更精确的精确性方法更能展示。 这些是以前的最精确的、最优化方法。 通过以前的最精确的、更精确的模拟的模拟方法,这些是以前的最精确地展示的。