Explainability is a growing concern for optimization models used as decision-making tools. It aims to help a stakeholder understand why a model recommends a given outcome, typically by exhibiting the elements of the input that account for this outcome. We study this question for linear two-stage stochastic programs, and explain the returned decision by a … Read more
Classic linear bilevel optimization assumes that the upper-level decision impacts only the right-hand side of the lower-level constraints, which guarantees a solution under mild conditions. We study existence of solutions for linear bilevel problems with rotations (LBPR, for short), i.e., problems for which the upper-level decision modifies the left-hand side coefficients of the linear follower … Read more
Binary bilevel programs are challenging to solve due to the lack of compact single-level reformulations. Recent extended network flow-based reformulations have emerged as a promising approach, providing strong dual bounds. However, their increasing size can make them computationally prohibitive. We develop a cutting-plane framework that exploits these networks without requiring an extended-space formulation. We introduce … Read more
Interdiction for the direct current optimal power flow problem is commonly modeled in two stages, where an attacker disables components in the first stage and an operator makes remedial adjustments in the second stage. The resulting bilevel mathematical program is often solved via transformation into a single-level mixed-integer program using duality. A drawback of this … Read more
For more than 20 years, single-leader multi-follower (SLMF) problems have been treated as a more difficult class of problems in comparison to bilevel optimization. In this work we challenge this common belief, studying whether SLMF problems can be reformulated as equivalent bilevel optimization problems. We consider both optimistic and pessimistic formulations. For the optimistic case … Read more
We consider an electricity supplier for a large commercial electric vehicle (EV) fleet. The supplier uses a dynamic pricing scheme for buying and selling energy from and to the fleet, enabling the supplier to trade any deviations from the agreed day-ahead (DA) position in the intraday auction (IDA) market, while taking into account the behavior … Read more
We study stochastic optimization with a completely unobserved target distribution and samples from related source distributions. Treating the sources and the target as independent draws from a common meta-distribution, we propose Wasserstein-metric meta-distribution support learning (MDSL). The model jointly learns the center and radius of a Wasserstein ball, with an exclusion parameter controlling the fraction … Read more
Decision scenarios far from rare in practice often place data-driven decision-making in an awkward position, where the decision maker may have access to neither the target distribution itself nor any empirical samples drawn from it, especially when decisions must be made in novel or highly uncertain environments. In response, robust out-of-distribution stochastic optimization (RooDSO) has … Read more
Network design problems increasingly arise in settings where strategic infrastructure decisions and operational routing choices are made by different actors. Such interactions are naturally modeled as bilevel problems: a network operator designs or modifies a network, while users respond by selecting routes according to their own utilities. This structure captures many applications in transportation and … Read more
We study adjustable robust network design for potential-based flows with controllable elements under load uncertainty. The resulting problem combines discrete here-and-now expansion decisions with wait-and-see operational decisions governed by nonconvex flow constraints. Moreover, controllable elements introduce adjustable integer decisions, which are algorithmically challenging. We equivalently characterize robust feasibility and robust optimality of a fixed network … Read more