Machine Learning for K-Adaptability in Two-Stage Robust Optimization

Abstract

Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets and optimizes decisions corresponding to each of these subsets. In a general case, it is solved using the K-adaptability branch-and-bound algorithm, which requires exploration of exponentially growing solution trees. To accelerate finding high-quality solutions in such trees, we propose a machine learning-based node selection strategy. In particular, we construct a feature engineering scheme based on general two-stage robust optimization insights, which allows us to train our machine learning tool on a database of resolved branch-and-bound trees and to apply it as is to problems of different sizes and/or types. We experimentally show that using our learned node selection strategy outperforms a vanilla, random node selection strategy when tested on problems of the same type as the training problems as well as in cases when the K-value or the problem size differs from the training ones. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grants OCENW.GROOT.2019.015 and VI.Veni.191E.035]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0314 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0314 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .