This paper develops an adaptive scenario partitioning approach for stochastic bilevel linear programs. The method extends the Adaptive Partitioning Method, originally designed for two-stage stochastic programs, to settings in which a leader makes a first-stage decision while anticipating scenario dependent optimal responses from a follower. The proposed approach solves a sequence of aggregated master problems … 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 develop a cutting-plane methodology that adjusts solutions to optimization problems so as to reduce features that bring about exposure to risk, such as concentration of assets or resources. The methodology is agnostic to the representation of risk but has provably good attributes. Our procedure aims to reduce the appropriate risk metric without accruing a … Read more
Variable projection is a classical technique for separable nonlinear least-squares problems, in which variables that enter linearly are eliminated exactly, yielding a reduced nonlinear problem. By expressing this framework as a particular instance of a broader class of bilevel optimization problems, we develop a constrained variable-projection framework for data-science models, where the remaining variables are … 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
Designing efficient and user-friendly multimodal transit networks is critical for modern urban mobility. We study a novel stochastic multimodal transit network design problem that integrates fixed-route services with on-demand shuttles, explicitly accounting for heterogeneous rider preferences, uncertain travel times, and passenger demand. The hierarchical decision-making process is modeled using a two-stage stochastic bilevel optimization problem, … Read more
We propose a scalable nested Benders decomposition (BD) framework for single-leader, multi-follower bilevel optimization problems. The proposed framework is applicable to bilevel optimization problems in which each follower solves a linear program and is particularly well suited for instances involving a large number of followers. By identifying the upper-level decisions as complicating variables, the method … Read more
We study linear bilevel and pricing problems in which the upper- and lower-level constraints’ right-hand sides are perturbed. In this setting, it is an important question, also for the validity of numerical solution schemes, if the solution-set mapping of the parametric bilevel problem is calm at the zero-perturbation. We provide the complete picture both for … Read more
We study optimistic robust bilevel problems with uncertainty in the follower’s problem, where the follower adopts a so-called wait-and-see approach. In this setting, the leader decides without knowledge of the specific realization of the uncertainty. Then, the uncertainty realizes in a worst-case manner, and afterward the follower makes her own decisions. For this challenging problem … Read more
We study the impact of DC power flow modeling in multi-leader single-follower market models on the AC feasibility of the market outcome. To this end, we consider strategically bidding power producers that are connected to an electricity network and a market-clearing executed by an ISO. The focus is on a pay-as-bid electricity market in which … Read more