Optimization-Based Scenario Reduction for Data-Driven Two-Stage Stochastic Optimization

Dimitris Bertsimas () and Nishanth Mundru ()
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Dimitris Bertsimas: Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142
Nishanth Mundru: Benefits Science Technologies, Needham, Massachusetts 02494

Operations Research, 2023, vol. 71, issue 4, 1343-1361

Abstract: We propose a novel, optimization-based method that takes into account the objective and problem structure for reducing the number of scenarios, m , needed for solving two-stage stochastic optimization problems. We develop a corresponding convex optimization-based algorithm and show that, as the number of scenarios increase, the proposed method recovers the SAA solution. We report computational results with both synthetic and real-world data sets that show that the proposed method has significantly better performance for m = 1 − 2 % of n in relation to other state of the art methods (importance sampling, Monte Carlo sampling, and Wasserstein scenario reduction with squared Euclidean norm). Additionally, we propose variants of classical scenario reduction algorithms (which rely on the Euclidean norm) and show that these variants consistently outperform their traditional versions.

Keywords: Optimization; scenario reduction; cost function; two-stage stochastic optimization; Wasserstein distance (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:71:y:2023:i:4:p:1343-1361

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