EURO 2025 Leeds
Abstract Submission

208. Decomposition Algorithms, and Convex approximations for Distributionally Robust optimization with Wasserstein Metric

Invited abstract in session TB-31: Robust and Distributionally Robust Optimization - Theory and Applications, stream Stochastic and Robust optimization.

Tuesday, 10:30-12:00
Room: Maurice Keyworth 1.06

Authors (first author is the speaker)

1. Alban Kryeziu
Operations Research, University of Groningen

Abstract

When dealing with problems where both the model parameters are uncertain and their distribution is unknown, Distributionally Robust Optimization (DRO) is the popular modeling framework to solve such problems. In this paper, we focus on the DRO for the two-stage totally unimodular integer recourse models, where we propose novel approaches for solving such problems. The first two approaches are based on a modified column generation scheme where we iteratively add variables and only optimality cuts to the master problem. The first one is a standard algorithm, whereas the second one is derived from a result we prove here, and it requires less information about the second-stage value function. The third approach is a regularization scheme where we prove that in many cases the first two methods take a long time to converge, whereas with regularization, we can ensure faster convergence. In addition, we propose a novel pragmatic approach that capitalizes on convex approximations, and we call this a pragmatic approach. We assess the performance of the solutions for these approximations. To this end, we solve a problem of a stochastic activity network and a gas network problem. As an ambiguity set, we consider distributions that lie within a chosen Wasserstein distance from the reference distribution. Our numerical experiments show that the novel pragmatic approach, when compared to the Sample Average Approximation (SAA) and the standard Wasserstein DRO for solving two-stage DRO models

Keywords

Status: accepted

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