Data-Driven Distributionally Robust Chance-Constrained Optimization With Wasserstein Metric

36 Pages Posted: 14 Jul 2018 Last revised: 23 Feb 2020

See all articles by Ran Ji

Ran Ji

George Mason University

Miguel Lejeune

George Washington University

Date Written: Feb 19, 2020

Abstract

We study distributionally robust chance-constrained programming (DRCCP) optimization problems with data-driven Wasserstein ambiguity sets. The proposed algorithmic and reformulation framework applies to distributionally robust optimization problems subjected to individual as well as joint chance constraints, with random right-hand side and technology vector, and under two types of uncertainties, called uncertain probabilities and continuum of realizations. For the uncertain probabilities case, we provide new mixed-integer linear programming reformulations for DRCCP problems and derive a set of precedence optimality cuts to strengthen the formulations. For the continuum of realizations case with random right-hand side, we propose an exact mixed-integer second-order cone programming (MISOCP) reformulation and a linear programming (LP) outer approximation. For the continuum of realizations case with random technology vector, we propose two MISOCP and LP outer approximations. We show that all proposed relaxations become exact reformulations when the decision variables are binary or bounded general integers. We evaluate the scalability and tightness of the proposed MISOCP and (MI)LP formulations on a distributionally robust chance constrained knapsack problem.

Keywords: Distributionally Robust Optimization, Chance-Constrained Programming, Wasserstein Metric

Suggested Citation

Ji, Ran and Lejeune, Miguel, Data-Driven Distributionally Robust Chance-Constrained Optimization With Wasserstein Metric (Feb 19, 2020). Available at SSRN: https://ssrn.com/abstract=3201356 or http://dx.doi.org/10.2139/ssrn.3201356

Ran Ji (Contact Author)

George Mason University ( email )

Fairfax, VA
United States

Miguel Lejeune

George Washington University ( email )

Washington, DC 20052
United States

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