Distributionally robust joint chance-constrained programming: Wasserstein metric and second-order moment constraints

Abstract

In this paper, we propose a new approximate linear reformulation for distributionally robust joint chance programming with Wasserstein ambiguity sets and an efficient solution approach based on Benders decomposition. To provide a convex approximation to the distributionally robust chance constraint, we use the worst-case conditional value-at-risk constrained program. In addition, we derive an approach for distributionally robust joint chance programming with a hybrid ambiguity set that combines a Wasserstein ball with second-order moment constraints. This approach, which allows injecting domain knowledge into a Wasserstein ambiguity set and thus allows for less conservative solutions, has not been considered before. We propose two formulations of this problem, namely a semidefinite programming and a computationally favorable second-order cone programming formulation. The models and algorithms proposed in this paper are evaluated through computational experiments demonstrating their computational efficiency. In particular, the Benders decomposition algorithm is shown to be more than an order of magnitude faster than a standard solver allowing for the solution of large instances in a relatively short time.