Consider an undirected network with traversal times on its edges and a set of commodities with connection requests from sources to destinations and release dates. The non-stop disjoint trajectories problem is to find trajectories that fulfill all requests, such that the commodities never meet. In this extension to the \NP-complete disjoint paths problem, trajectories must … Read more
The vehicle routing problem with time windows (VRPTW) is one of the most studied variants of routing problems. We consider the Split Delivery VRPTW (SDVRPTW), an extension in which customers can be visited multiple times, if advantageous. While this additional flexibility can result in significant cost reductions, it also results in additional modeling and computational … Read more
Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to … Read more
Given a graph G and an interdiction budget k, the Edge Interdiction Clique Problem (EICP) asks to find a subset of at most k edges to remove from G so that the size of the maximum clique, in the interdicted graph, is minimized. The EICP belongs to the family of interdiction problems with the aim … Read more
We utilize association schemes to analyze the quality of semidefinite programming (SDP) based convex relaxations of integral packing and covering polyhedra determined by matchings in hypergraphs. As a by-product of our approach, we obtain bounds on the clique and stability numbers of some regular graphs reminiscent of classical bounds by Delsarte and Hoffman. We determine … Read more
Submodularity, a discrete analog of convexity, is a key property in discrete optimization that features in the construction of valid inequalities and analysis of the greedy algorithm. In this paper, we broaden the approximate submodularity literature, which so far has largely focused on variants of greedy algorithms and iterative approaches. We define metrics that quantify … Read more
Rank aggregation is widely used in group decision-making and many other applications where it is of interest to consolidate heterogeneous ordered lists. Oftentimes, these rankings may involve a large number of alternatives, contain ties, and/or be incomplete, all of which complicate the use of robust aggregation methods. In particular, these characteristics have limited the applicability … Read more
Connectivity is a central concept in combinatorial optimization, graph theory, and operations research. In many applications, one is interested in finding an optimal subset of vertices with the essential requirement that the vertices are connected, but not how they are connected. I.e., it is not relevant, which edges are selected to obtain connectivity. Two natural … Read more
In this paper, we consider the (additive integrality) gap of the cutting stock problem (CSP) and the skiving stock problem (SSP). Formally, the gap is defined as the difference between the optimal values of the ILP and its LP relaxation. For both, the CSP and the SSP, this gap is known to be bounded by … Read more
A natural and important generalization of submodularity—$k$-submodularity—applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In this paper, we study maximization problems with $k$-submodular objective functions. We propose valid linear inequalities, namely the $k$-submodular inequalities, for the hypograph of any $k$-submodular … Read more