Andreas Bärmann In the present work, we consider Zuckerberg’s method for geometric convex-hull proofs introduced in [Geometric proofs for convex hull defining formulations, Operations Research Letters 44(5), 625–629 (2016)]. It has only been scarcely adopted in the literature so far, despite the great flexibility in designing algorithmic proofs for the completeness of polyhedral descriptions that it offers. … Read more
For the problem to find an m-clique in an m-partite graph, staircase compatibility has recently been introduced as a polynomial-time solvable special case. It is a property of a graph together with an m-partition of the vertex set and total orders on each subset of the partition. In optimization problems involving m-cliques in m-partite graphs … Read more
We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph. In this work, we study the case where there is a partition on one of the two bipartite node sets such … 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
Timetabling of railway traffic and other modes of transport is among the most prominent applications of discrete optimization in practice. However, it has only been recently that the connection between timetabling and energy consumption has been studied more extensively. In our joint project VAG Verkehrs-Aktiengesellschaft, the transit authority and operator of underground transport in the … Read more
Globalized robust optimization has been proposed as a generalization of the standard robust optimization framework in order to allow for a controlled decrease in protection depending on the distance of the realized scenario from the predefined uncertainty set. In this work, we specialize the notion of globalized robustness to Gamma-uncertainty in order to extend its … Read more
In this paper, we demonstrate how to learn the objective function of a decision-maker while only observing the problem input data and the decision-maker’s corresponding decisions over multiple rounds. Our approach is based on online learning and works for linear objectives over arbitrary feasible sets for which we have a linear optimization oracle. As such, … Read more
We consider the clique problem with multiple-choice constraints (CPMC) and characterize a case where it is possible to give an efficient description of the convex hull of its feasible solutions. This new special case, which we call staircase compatibility, generalizes common properties in several applications and allows for a linear description of the integer feasible … Read more
The clique problem with multiple-choice constraints (CPMC) represents a very common substructure in many real-world applications, for example scheduling problems with precedence constraints. It consists in finding a clique in a graph whose nodes are partitioned into subsets, such that exactly one node from each subset is chosen. Even though we can show that (CPMC) … Read more
Robust optimization is an important technique to immunize optimization problems against data uncertainty. In the case of a linear program and an ellipsoidal uncertainty set, the robust counterpart turns into a second-order cone program. In this work, we investigate the efficiency of linearizing the second-order cone constraints of the latter. This is done using the … Read more