Data-driven distributionally robust chance-constrained optimization with Wasserstein metric

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 indi...

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Vydáno v:Journal of global optimization Ročník 79; číslo 4; s. 779 - 811
Hlavní autoři: Ji, Ran, Lejeune, Miguel A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.04.2021
Springer
Springer Nature B.V
Témata:
Computer Science
Constraints
Integer programming
Investment analysis
Knapsack problem
Linear programming
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research/Decision Theory
Optimization
Real Functions
Robustness
Series (mathematics)
Tightness
Chance-constrained programming
Mixed-integer programming
Distributionally robust optimization
Wasserstein metric
ISSN:0925-5001, 1573-2916
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Shrnutí: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-020-00966-0