Using BART to Perform Pareto Optimization and Quantify its Uncertainties

Akira Horiguchi*, Thomas J. Santner, Ying Sun, Matthew T. Pratola

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 nonparametric 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.

Original languageEnglish (US)
Pages (from-to)564-574
Number of pages11
Issue number4
StatePublished - 2022


  • Band depth
  • Bayesian methods
  • Computer experiments
  • Pareto Set
  • Random Sets

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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