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Robust Stochastic Optimization Made Easy with RSOME

Zhi Chen (), Melvyn Sim () and Peng Xiong ()
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Zhi Chen: Department of Management Sciences, College of Business, City University of Hong Kong, Kowloon Tong, Hong Kong
Melvyn Sim: Department of Analytics and Operations, NUS Business School, National University of Singapore, Singapore 119077
Peng Xiong: Department of Analytics and Operations, NUS Business School, National University of Singapore, Singapore 119077

Management Science, 2020, vol. 66, issue 8, 3329-3339

Abstract: We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree-based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, Robust Stochastic Optimization Made Easy (RSOME), to facilitate the implementation of RSO models. The model of uncertainty incorporates both discrete and continuous random variables, typically assumed in scenario-tree-based stochastic linear optimization and distributionally robust optimization, respectively. To address the nonanticipativity of recourse decisions, we introduce the event-wise recourse adaptations, which integrate the scenario-tree adaptation originating from stochastic linear optimization and the affine adaptation popularized in distributionally robust optimization. Our proposed event-wise ambiguity set is rich enough to capture traditional statistic-based ambiguity sets with convex generalized moments, mixture distribution, φ-divergence, Wasserstein (Kantorovich-Rubinstein) metric, and also inspire machine-learning-based ones using techniques such as K-means clustering and classification and regression trees. Several interesting RSO models, including optimizing over the Hurwicz criterion and two-stage problems over Wasserstein ambiguity sets, are provided.

Keywords: stochastic linear optimization; distributionally robust optimization; machine learning (search for similar items in EconPapers)
Date: 2020
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