The literature on pessimistic bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling constraints. In this note, we show that this is not the case. To this end, given a pessimistic problem with coupling constraints, we derive … Read more
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor exploited computationally. Based on the recent results by Goerigk et al. (2025), this paper is the first one that reformulates a given strictly robust optimization … Read more
We study a bilevel hub location problem where on the upper level, a shipment service provider –the leader–builds a transportation network and sets the prices of shipments on each possible transportation relation. Here, the leader has to take into account the customers’ reaction — the follower — who will only purchase transport services depending on … Read more
Integer bilevel programs are notoriously difficult to solve due to the absence of strong and efficiently computable relaxations. In this work, we introduce a novel single-level reformulation of these programs by leveraging a network flow-based representation of the follower’s value function, utilizing decision diagrams and linear programming duality. This approach enables the development of scalable … Read more
In this paper, we study the two-stage distributionally robust optimization (DRO) problem from the primal perspective. Unlike existing approaches, this perspective allows us to build a deeper and more intuitive understanding on DRO, to leverage classical and well established solution methods and to develop a general and fast decomposition algorithm (and its variants), and to … Read more
We study multi-follower bilevel optimization problems with binary linking variables where the second level consists of many independent integer-constrained subproblems. This problem class not only generalizes many classical interdiction problems but also arises naturally in many network design problems where the second-level subproblems involve complex routing decisions of the actors involved. We propose a novel … Read more
Explainable artificial intelligence is one of the most important trends in modern machine-learning research. The idea is to explain the outcome of a model by presenting a certain change in the input of the model so that the outcome changes significantly. In this paper, we study this question for linear optimization problems as an automated … Read more
We study bilevel problems with a convex quadratic mixed-integer upper-level, integer linking variables, and a nonconvex quadratic, purely continuous lower-level problem. We prove $\Sigma_p^2$-hardness of this class of problems, derive an iterative lower- and upper-bounding scheme, and show its finiteness and correctness in the sense that it computes globally optimal points or proves infeasibility of … Read more
Supply chains and logistics can be well represented with hub networks. Operations of these hubs can be disrupted due to unanticipated occurrences or attacks. This study includes Closest assignment Constraints related to hub disruption problems, which can be used in single-level reformulation of the bilevel model. In this study, We propose new sets of constraints … Read more
This study addresses discrete network design problems under traffic equilibrium conditions or DNDPs. Given a network and a budget, DNDPs aim to model all-or-nothing decisions such as link addition to minimize network congestion effects. Congestion is measured using traffic equilibrium theory where link travel times are modeled as convex flow-dependent functions and where users make … Read more