srMO-BO-3GP: A sequential regularized multi-objective Bayesian optimization for constrained design applications using an uncertain Pareto classifier

Journal Article · 21 October 2021 · Journal of Mechanical Design

DOI:https://doi.org/10.1115/1.4052445· OSTI ID:1820417

Tran, Anh ^[1]; Eldred, Michael ^[1]; McCann, Scott ^[2]; Wang, Yan ^[3]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2. Xilinx Inc. San Jose, CA (United States)
3. Georgia Institute of Technology, Atlanta, GA (United States)

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, and latent-variable modeling, have been proposed to address the limitations of the classical BO framework. In this work, we propose a novel multi-objective BO formalism, called srMO-BO-3GP, to solve multi-objective optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each of the GPs is assigned with a different task. The first GP is used to approximate a single-objective computed from the multi-objective definition, the second GP is used to learn the unknown constraints, and the third one is used to learn the uncertain Pareto frontier. At each iteration, a multi-objective augmented Tchebycheff function is adopted to convert multi-objective to single-objective, where the regularization with a regularized ridge term is also introduced to smooth the single-objective function. Finally, we couple the third GP along with the classical BO framework to explore the convergence and diversity of the Pareto frontier by the acquisition function for exploitation and exploration. The proposed framework is demonstrated using several numerical benchmark functions, as well as a thermomechanical finite element model for flip-chip package design optimization.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0003525
• OSTI ID: 1820417
• Report Number(s): SAND-2021-10522J; 698910
• Journal Information: Journal of Mechanical Design, Journal Name: Journal of Mechanical Design Journal Issue: 3 Vol. 144; ISSN 1050-0472
• Publisher: ASME
• Country of Publication: United States
• Language: English

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