srMO-BO-3GP: A sequential regularized multi-objective constrained Bayesian optimization for design applications

TL;DR

This paper introduces srMO-BO-3GP, a novel sequential multi-objective Bayesian optimization method that uses three Gaussian processes to efficiently explore and approximate Pareto frontiers in complex engineering design problems.

Contribution

The paper proposes a new multi-objective Bayesian optimization framework with three stacked Gaussian processes and a regularized Tchebycheff approach, enhancing exploration and Pareto frontier approximation.

Findings

Effective in benchmark tests for multi-objective optimization.

Successfully applied to thermomechanical finite element model.

Improves diversity and convergence of Pareto solutions.

Abstract

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.