Paper Info
Title
Data-Driven Distributionally Robust Chance-Constrained Optimization With Wasserstein Metric
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 all types of distributionally robust chance-constrained 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 (UP) case, we provide new mixed-integer linear programming reformulations for DRCCP problems. 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 (CR) 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. For DRCCP with individual chance constraint and random right-hand side under both the UP and CR cases, we also propose linear programming reformulations which need the ex-ante derivation of the worst-case value-at-risk via the solution of a finite series of linear programs determined via a bisection-type procedure. We evaluate the scalability and tightness of the proposed MISOCP and (MI)LP formulations on a distributionally robust chance-constrained knapsack problem.
Year
DOI
Venue
2021
10.1007/s10898-020-00966-0
JOURNAL OF GLOBAL OPTIMIZATION
Keywords
DocType
Volume
Distributionally robust optimization, Chance-constrained programming, Wasserstein metric, Mixed-integer programming
Journal
79
Issue
ISSN
Citations 
4
0925-5001
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Ran Ji120.71
Miguel A. Lejeune225321.95