Orateur
Description
The distributionally robust optimization (DRO) framework has emerged as a powerful approach for dealing with uncertainty. In the context of unit commitment, where demand uncertainty affects the right-hand side of constraints, we investigate a DRO approach based on the Wasserstein distance with the $L^2 $-norm. This approach can be addressed using Benders' decomposition as in the risk-neutral approach. However, the key difference lies in the oracle problem that generates valid cuts for the master problem. While the risk-neutral approach requires solving a linear oracle problem at each iteration and for each scenario, the DRO formulation leads to a quadratic convex maximization oracle problem, which has been proven to be NP-hard. Thus, directly solving it with a commercial solver like Gurobi may be inefficient, significantly slowing down Benders' decomposition.
In this talk, we present an efficient solution method for the DRO unit commitment problem, grounded in two key contributions. First, we propose a novel Benders’ reformulation of the stochastic unit commitment that enables faster convergence. Second, we use the Frank-Wolfe algorithm to address the NP-hard oracle subproblem. Finally, numerical experiments assess the efficiency of our approach.
