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 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 language | English (US) |
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Pages (from-to) | 564-574 |
Number of pages | 11 |
Journal | Technometrics |
Volume | 64 |
Issue number | 4 |
DOIs | |
State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022 American Statistical Association and the American Society for Quality.
Keywords
- Band depth
- Bayesian methods
- Computer experiments
- Pareto Set
- Random Sets
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics