Abstract

Hybrid optimization methods that combine statistical modeling with mathematical programming have become a popular solution for Bayesian optimization (BO) because they can better leverage both the efficient local search properties of the numerical method and the global search properties of the statistical model. These methods seek to create a sequential design strategy for efficiently optimizing expensive black-box functions when gradient information is not readily available. In this article, we propose a novel BO strategy that combines response surface modeling with barrier methods to efficiently solve expensive constrained optimization problems in computer modeling. At the heart of all BO algorithms is an acquisition function for effectively guiding the search. Our hybrid algorithm is guided by a novel acquisition function that tries to decrease the objective function as much as possible while simultaneously trying to ensure that the boundary of the constraint space is never crossed. Illustrations highlighting the success of our method are provided, including a real-world computer model optimization experiment from hydrology. Supplementary files for this article are available online.

摘要

将统计建模与数学规划相结合的混合优化方法已成为贝叶斯优化 (BO) 的流行解决方案，因为它们可以更好地利用数值方法的有效局部搜索属性和统计模型的全局搜索属性。这些方法寻求创建一种顺序设计策略，以在梯度信息不易获得时有效优化昂贵的黑盒函数。在本文中，我们提出了一种新颖的 BO 策略，该策略将响应面建模与障碍方法相结合，以有效解决计算机建模中昂贵的约束优化问题。所有 BO 算法的核心是用于有效指导搜索的采集功能。我们的混合算法由一种新颖的采集函数引导，该函数试图尽可能地减小目标函数，同时试图确保永远不会越过约束空间的边界。提供了强调我们方法成功的插图，包括来自水文学的真实世界计算机模型优化实验。本文的补充文件可在线获取。