Constrained Bayesian Optimization under Bivariate Gaussian Process with Application to Cure Process Optimization

TL;DR

This paper introduces a constrained Bayesian Optimization method using a bivariate Gaussian process to model dependence between objective and constraint functions, demonstrated on a manufacturing cure process optimization.

Contribution

It develops a novel constrained Bayesian Optimization framework based on bivariate Gaussian processes, addressing the independence assumption in prior models.

Findings

Improved optimization performance in cure process application

Effective modeling of dependence between objective and constraint

Enhanced exploration within feasible regions

Abstract

Bayesian Optimization, leveraging Gaussian process models, has proven to be a powerful tool for minimizing expensive-to-evaluate objective functions by efficiently exploring the search space. Extensions such as constrained Bayesian Optimization have further enhanced Bayesian Optimization's utility in practical scenarios by focusing the search within feasible regions defined by a black-box constraint function. However, constrained Bayesian Optimization in is developed based on the independence Gaussian processes assumption between objective and constraint functions, which may not hold in real-world applications. To address this issue, we use the bivariate Gaussian process model to characterize the dependence between the objective and constraint functions and developed the constrained expected improvement acquisition function under this model assumption. We show case the performance of the proposed approach with an application to cure process optimization in Manufacturing.