Using BART to Perform Pareto Optimization and Quantify its Uncertainties
This work provides a new statistical method for multiobjective optimization, potentially benefiting engineers and researchers dealing with expensive data collection, offering an incremental improvement over existing methods like GPs.
This paper proposes using Bayesian Additive Regression Trees (BART) to estimate Pareto Front (PF) and Pareto Set (PS) in multiobjective optimization problems, particularly when experimental data collection is expensive. The BART-based method demonstrates convincing advantages over Gaussian Process (GP)-based methods on analytic test functions and is applied to an engineering problem.
Techniques to reduce the energy burden of an industrial ecosystem often require solving a multiobjective optimization problem. However, collecting experimental data can often be either expensive or time-consuming. In such cases, statistical methods can be helpful. This article proposes Pareto Front (PF) and Pareto Set (PS) estimation methods using Bayesian Additive Regression Trees (BART), which is a non-parametric model whose assumptions are typically less restrictive than popular alternatives, such as Gaussian Processes (GPs). These less restrictive assumptions allow BART to handle scenarios (e.g. high-dimensional input spaces, nonsmooth responses, large datasets) that GPs find difficult. The performance of our BART-based method is compared to a GP-based method using analytic test functions, demonstrating convincing advantages. Finally, our BART-based methodology is applied to a motivating engineering problem. Supplementary materials, which include a theorem proof, algorithms, and R code, for this article are available online.