Compact uncertainty sets for robust optimization based on bootstrapped Dirichlet process mixture model

Tools

Neofytou, Andreas and Liu, Bin and Akartunali, Kerem (2025) Compact uncertainty sets for robust optimization based on bootstrapped Dirichlet process mixture model. Optimization. ISSN 0233-1934 (In Press) (https://doi.org/10.1080/02331934.2025.2451812)

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Abstract

This study utilizes unsupervised machine learning to improve the performance of robust optimization through construction of compact uncertainty sets. Robust optimization aims to find solutions that are resilient to uncertainties and variations in input parameters, allowing decision-makers to make informed decisions in the face of uncertain conditions. However, traditional optimization approaches often assume known and fixed datasets, which fails to reflect the inherent uncertainties present in real-world problems. Accurate construction of compact and reliable data-driven uncertainty sets is a critical challenge that directly impacts the effectiveness of robust optimization. To address this challenge, we propose a Dirichlet process mixture model for clustering to construct a data-driven uncertainty set suitable for robust optimization problems, allowing for more accurate uncertainty modelling. This data-driven uncertainty set is constructed by intersecting the l1 and l∞ norms for each predicted cluster and then merging these multiple basic convex uncertainty sets to create a comprehensive representation. This approach results in uncertainty sets based on clustered data that flexibly capture a compact region of uncertainty in a non-parametric manner. An innovative aspect is the introduction of statistical bootstrap to obtain a more robust clustering solution and outcome. The proposed method is applied to production planning problems and a comparative analysis with existing approaches highlights its advantages. Our method demonstrates effectiveness in improving the accuracy and robustness of solutions in robust optimization by constructing more compact uncertainty sets.

ORCID iDs

Neofytou, Andreas, Liu, Bin ORCID logoORCID: https://orcid.org/0000-0002-3946-8124 and Akartunali, Kerem ORCID logoORCID: https://orcid.org/0000-0003-0169-3833;
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