Using BART to Perform Pareto Optimization and Quantify its Uncertainties

TL;DR

This paper introduces a BART-based approach for Pareto optimization and uncertainty quantification, outperforming Gaussian Processes in complex, high-dimensional, and large data scenarios, with applications to engineering problems.

Contribution

It presents a novel BART-based method for Pareto front and set estimation, addressing limitations of GPs in challenging optimization scenarios.

Findings

BART-based method outperforms GP-based methods on test functions.

The approach handles high-dimensional and nonsmooth responses effectively.

Application to engineering problems demonstrates practical utility.

Abstract

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.