This study addresses the bilevel discrete network design problem (DNDP) with congestion, with special emphasis on fairness. The upper-level decision-maker (the network designer) selects a set of arcs to add to an existing transportation network, while the lower-level decision-makers (drivers) respond by choosing routes that minimize their individual travel times, resulting in user equilibrium. Most … Read more
We consider several hierarchical optimization programs: (generalized) semi-infinite and existence-constrained semi-infinite programs, minmax, and bilevel programs. Multiple adaptive discretization-based algorithms have been published for these program classes in recent decades. However, rigorous numerical performance comparisons between these algorithms are lacking. Indeed, if numerical comparisons are provided at all, they usually compare a small selection of … Read more
In this paper, we study a network interdiction problem on a multiple allocation, uncapacitated hub network. The problem is formulated as a bilevel Stackelberg game between an attacker and a defender, where the attacker identifies r out of p hubs to interdict so as to maximize the worst-case post-interdiction performance of the system with the … Read more
This paper considers an extension of the shortest path network interdiction problem that incorporates robustness to account for parameter uncertainty. The shortest path interdiction problem is a game of two players with conflicting agendas and capabilities: an evader, who traverses the arcs of a network from a source node to a sink node using the … Read more
It is well known that the classical Markowitz model for portfolio optimization is extremely sensitive to estimation errors on the expected asset returns. Robust optimization mitigates this issue. We focus on ellipsoidal uncertainty sets around the point estimates of the expected asset returns. We investigate the performance of diagonal estimation-error matrices in the description of … Read more