Scenario Reduction for Distributionally Robust Optimization
Aigner KM, Denzler S, Liers F, Pokutta S, Sharma K (2025)
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2025
URI: https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/573
DOI: 10.48550/arXiv.2503.11484
Abstract
Stochastic and (distributionally) robust optimization problems often become computationally challenging as the number of scenarios increases. Scenario reduction is therefore a key technique for improving tractability. We introduce a general scenario reduction method for distributionally robust optimization (DRO), which includes stochastic and robust optimization as special cases. Our approach constructs the reduced DRO problem by projecting the original ambiguity set onto a reduced set of scenarios. Under mild conditions, we establish bounds on the relative quality of the reduction. The methodology is applicable to random variables following either discrete or continuous probability distributions, with representative scenarios appropriately selected in both cases. Given the relevance of optimization problems with linear and quadratic objectives, we further refine our approach for these settings. Finally, we demonstrate its effectiveness through numerical experiments on mixed-integer benchmark instances from MIPLIB and portfolio optimization problems. Our results show that the proposed approximation significantly reduces solution time while maintaining high solution quality with only minor errors.
Authors with CRIS profile
Kevin-Martin Aigner
Professur für Optimization under Uncertainty & Data Analysis
Sebastian Denzler
Professur für Optimization under Uncertainty & Data Analysis
Frauke Liers-Bergmann
Professur für Optimization under Uncertainty & Data Analysis
Related research project(s)
Management CRC TRR 154 (SFB/TRR 154 Z03)
TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154)
July 1, 2022 - June 30, 2026
Robust optimization of gas networks (B06) (SFB/TRR 154 B06)
TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154)
July 1, 2022 - June 30, 2026
Involved external institutions
Germany (DE)How to cite
APA:
Aigner, K.-M., Denzler, S., Liers, F., Pokutta, S., & Sharma, K. (2025). Scenario Reduction for Distributionally Robust Optimization. (Unpublished, Submitted).
MLA:
Aigner, Kevin-Martin, et al. Scenario Reduction for Distributionally Robust Optimization. Unpublished, Submitted. 2025.
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