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

Bayesian Optimization (BO), leveraging Gaussian Process (GP) 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 (cBO), have further enhanced BO’s utility in practical scenarios by focusing the search within feasible regions defined by constraint functions. However, a significant limitation in cBO arises from the standard assumption of independence between objective and constraint functions, which may not hold in real-world applications where these functions are often correlated. To address this, we introduce a Bi-Variable Gaussian Process (BiV-GP) model within a constrained BO framework that models objective and constraint functions as correlated outputs of multiple Gaussian Processes. By capturing these dependencies directly, the BiV-GP model aims to improve optimization performance, particularly for problems characterized by complex interdependencies. Nevertheless, our experimental results indicate that BiV-GP struggles to consistently outperform simpler models like Ordinary Kriging. This underperformance can be attributed to the model’s reliance on a separable covariance matrix for representing dependencies, which may inadequately capture the relationships between functions and interactions across multiple dimensions. Additionally, the complexity of the BiV-GP model introduces challenges related to parameter estimation and computational efficiency. We show case the proposed approach with a case study on curing process optimization.