\(\) In the minimum spanning tree (MST) interdiction problem, we are given a graph \(G=(V,E)\) with edge weights, and want to find some \(X\subseteq E\) satisfying a knapsack constraint such that the MST weight in \((V,E\setminus X)\) is maximized. Since MSTs of \(G\) are the minimum weight bases in the graphic matroid of \(G\), this … Read more
\(\) We analyze the inverse of integer programs (IPs) using the Gomory corner relaxation (GCR). We prove the inverse GCR is equivalent to the inverse of a shortest path problem, yielding a polyhedral representation of the GCR inverse-feasible region. We propose a linear program formulation for the inverse GCR under \(L_1\) and \(L_\infty\) norms.The inverse … Read more
\(\) We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender’s objective of maximizing a k-submodular function. We allow uncertainties arising … Read more
We present a feedback scheme for non-cooperative dynamic games and investigate its stabilizing properties. The dynamic games are modeled as generalized Nash equilibrium problems (GNEP), in which the shared constraint consists of linear time-discrete dynamic equations (e.g., sampled from a partial or ordinary differential equation), which are jointly controlled by the players’ actions. Further, the … Read more
This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the $l$-type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms … Read more
Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of … Read more
We propose a criterion space search algorithm for bi-objective mixed integer linear programming problems. The Pareto frontier of these problems can have a complex structure, as it can include isolated points, open, half-open and closed line segments. Therefore, its exact detection is an achievable though hard computational task. Our algorithm works by alternating the resolution … Read more
Security agencies throughout the world use bodyguards to protect government officials and public figures. In this paper, we consider a two-person zero-sum game between a defender who allocates such bodyguards to protect several targets and an attacker who chooses one target to attack. Because the number of feasible bodyguard allocations grows quickly as either the … Read more
Reducing inefficient truck movements, this research investigates the potential of freight consolidation through carrier collaboration. Considering the financial benefits of consolidation and the additional cost arising from collaboration, we propose a cooperative game to explore under which circumstances carriers can collaborate. We show that stable cost allocations are not always possible, affecting stability and thus … Read more
A key factor towards a low-carbon society is energy efficient heating of private houses. The choice of heating technology as well as the decision for certain energy-efficient house renovations are made mainly by individual homeowners. In contrast, municipal energy network planning heavily depends on and strongly affects these decisions. Further, there are different conflicting objectives … Read more