Robust chance-constrained optimization with discrete distributions - Bernhard, Daniela; Liers, Frauke; Stingl, Michael (2025)
Typically, probability distributions that generate uncertain parameters are uncertain themselves or even unknown. As a remedy, distributional robustness determines optimized decisions that are protected in a robust fashion against all probability distributions in some appropriately chosen ambiguity set. In this work, we consider robust joint chance-constrained optimization problems and focus on discrete probability distributions. Many methods for this kind of problems study convex or even linear constraint functions. In contrast, we introduce a practically efficient scenario-based bundle method without convexity assumptions on the constraint functions. We start by deriving an approximation problem to the original robust chance-constrained version by using smoothing and penalization techniques that build on our former work on chance-constrained optimization. Our convergence results with respect to the smoothing approximation and well-known results for penalty approximations suggest replacing the original problem with the approximation problem for large smoothing and penalty parameters. Our scenario-based bundle method starts by solving the approximation problem with a bundle method, and then uses the bundle solution to decide which scenarios to include in a scenario-expanded formulation. This formulation is a standard nonlinear optimization problem. In our numerical experiments we demonstrate the efficiency of our approach on real-world gas transport problems with uncertain demands. Comparing our results to the classical robust reformulations for ambiguity sets consisting of confidence intervals and Wasserstein balls, we observe that the scenario-based bundle method often outperforms solving the classical reformulation directly.<br
https://cris.fau.de/converis/publicweb/Publication/330005084