Deep Gaussian process for enhanced Bayesian optimization and its application in additive manufacturing

• Published in: IIE transactions Vol. 57; no. 4; pp. 423 - 436
• Main Authors: Gnanasambandam, Raghav, Shen, Bo, Law, Andrew Chung Chee, Dou, Chaoran, Kong, Zhenyu (James)
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Ltd 03.04.2025
• Subjects: Additive manufacturing; Algorithms; Bayesian analysis; Black boxes; Controllability; Design engineering; Design optimization; Gaussian process; Inference; Manufacturing; Optimization; Process parameters; Regression models
• ISSN: 2472-5854; 2472-5862
• DOI: 10.1080/24725854.2024.2312905

AbstarctEngineering design problems typically require optimizing a quality measure by finding the right combination of controllable input parameters. In Additive Manufacturing (AM), the output characteristics of the process can often be non-stationary functions of the process parameters. Bayesian Optimization (BO) is a methodology to optimize such “black-box” functions, i.e., the input–output relationship is unknown and expensive to compute. Optimization tasks involving “black-box” functions widely use BO with Gaussian Process (GP) regression surrogate model. Using GPs with standard kernels is insufficient for modeling non-stationary functions, while GPs with non-stationary kernels are typically over-parameterized. On the other hand, a Deep Gaussian Process (DGP) can overcome GPs’ shortcomings by considering a composition of multiple GPs. Inference in a DGP is challenging due to its structure resulting in a non-Gaussian posterior, and using DGP as a surrogate model for BO is not straightforward. Stochastic Imputation (SI)-based inference is promising in speed and accuracy for BO. This work proposes a bootstrap aggregation-based procedure to effectively utilize the SI-based inference for BO with a DGP surrogate model. The proposed BO algorithm DGP-SI-BO is faster and empirically better than the state-of-the-art BO method in optimizing non-stationary functions. Several analytical test functions and a case study in metal AM simulation demonstrate the applicability of the proposed method.