Using polarity, we give an outer polyhedral approximation for the epigraph of set functions. For a submodular function, we prove that the corresponding polar relaxation is exact; hence, it is equivalent to the Lov\’asz extension. The polar approach provides an alternative proof for the convex hull description of the epigraph of a submodular function. Computational … Read more
Large logistics service providers often need to containerize and route thousands or millions of items per year. In practice, companies specify business rules of how to pack and transport items from their origin to destination. Handling and respecting those business rules manually is a complex and time-consuming task. We propose a variant of the variable … Read more
While many heuristics have been proposed for the problem of patient-to-room assignment (PRA) with a large variety of different practical constraints, a thorough investigation of the problem’s structure itself has been neglected so far. Therefore, in this paper, we present insights about the basic, underlying combinatorial problem of PRA. At first we consider the problem … Read more
We introduce the (directed) multi-stop station location problem. The goal is to install stations such that ordered (multi-)sets of stops can be traversed with respect to range restrictions that are reset whenever a station is visited. Applications arise in telecommunications and transportation, e.g., charging station placement problems. The problem generalizes several network optimization problems such … Read more
We consider stochastic problems in which both the objective function and the feasible set are affected by uncertainty. We address these problems using a K-adaptability approach, in which K solutions for the underlying problem are computed before the uncertainty dissolves and afterwards the best of them can be chosen for the realised scenario. This paradigm … Read more
Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic Unit Cell (PUC) and the efficacy of non-uniform designs in multi-scale material optimization. Here, we introduce a novel strategy for concurrent minimum-compliance design of … Read more
We consider the least squares regression problem, penalized with a combination of the L0 and L2 norms (a.k.a. L0 L2 regularization). Recent work presents strong evidence that the resulting L0-based estimators can outperform popular sparse learning methods, under many important high-dimensional settings. However, exact computation of L0-based estimators remains a major challenge. Indeed, state-of-the-art mixed … Read more
In critical node problems, the task is identify a small subset of so-called critical nodes whose deletion maximally degrades a network’s “connectivity” (however that is measured). Problems of this type have been widely studied, e.g., for limiting the spread of infectious diseases. However, existing approaches for solving them have typically been limited to networks having … Read more
The prize-collecting Steiner tree problem (PCSTP) is a well-known generalization of the classic Steiner tree problem in graphs, with a large number of practical applications. It attracted particular interest during the 11th DIMACS Challenge in 2014, and since then, several PCSTP solvers have been introduced in the literature. Although these new solvers further, and often … 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