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

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.

Automated summary

This article introduces a novel optimization-based method for reducing the number of scenarios needed to solve two-stage stochastic optimization problems. They develop a corresponding convex optimization algorithm and demonstrate its superiority through computational experiments.