Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including multi-objective, multi-fidelity, parallelization, latent-variable model, have been proposed to improve the limitation of the classical BO framework. In this work, we propose a novel multi-objective (MO) extension, called srMO-BO-3GP, to solve the MO optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each of the GP is assigned with a different task: the first GP is used to approximate the single-objective function, the second GP is used to learn the unknown constraints, and the third GP is used to learn the uncertain Pareto frontier. At each iteration, a MO augmented Tchebycheff function converting MO to single-objective is adopted and extended with a regularized ridge term, where the regularization is introduced to smoothen the single-objective function. Finally, we couple the third GP along with the classical BO framework to promote the richness and diversity of the Pareto frontier by the exploitation and exploration acquisition function. The proposed framework is demonstrated using several numerical benchmark functions, as well as a thermomechanical finite element model for flip-chip package design optimization.

中文翻译：

---

srMO-BO-3GP：用于设计应用的顺序正则化多目标约束贝叶斯优化

贝叶斯优化（BO）是一种高效灵活的全局优化框架，适用于非常广泛的工程应用。为了利用经典 BO 的能力，已经提出了许多扩展，包括多目标、多保真度、并行化、潜在变量模型，以改善经典 BO 框架的局限性。在这项工作中，我们提出了一种新的多目标 (MO) 扩展，称为 srMO-BO-3GP，以解决顺序设置中的 MO 优化问题。三个不同的高斯过程 (GP) 堆叠在一起，其中每个 GP 分配有不同的任务：第一个 GP 用于近似单目标函数，第二个 GP 用于学习未知约束，第三个GP 用于学习不确定的帕累托边界。在每次迭代中，采用将 MO 转换为单目标的 MO 增强 Tchebycheff 函数，并使用正则化脊项对其进行扩展，其中引入正则化以平滑单目标函数。最后，我们将第三个 GP 与经典 BO 框架结合起来，通过开发和探索获取功能促进帕累托边界的丰富性和多样性。所提出的框架使用几个数值基准函数以及用于倒装芯片封装设计优化的热机械有限元模型进行了演示。我们将第三个 GP 与经典的 BO 框架结合起来，通过开发和探索获取功能来提升帕累托边界的丰富性和多样性。所提出的框架使用几个数值基准函数以及用于倒装芯片封装设计优化的热机械有限元模型进行了演示。我们将第三个 GP 与经典的 BO 框架结合起来，通过开发和探索获取功能来提升帕累托边界的丰富性和多样性。所提出的框架使用几个数值基准函数以及用于倒装芯片封装设计优化的热机械有限元模型进行了演示。