@misc{BorndoerferWeismantel1997, author = {Bornd{\"o}rfer, Ralf and Weismantel, Robert}, title = {Set Packing Relaxations of Some Integer Programs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2998}, number = {SC-97-30}, year = {1997}, abstract = {This paper is about {\em set packing relaxations\/} of combinatorial optimization problems associated with acyclic digraphs and linear orderings, cuts and multicuts, and vertex packings themselves. Families of inequalities that are valid for such a relaxation as well as the associated separation routines carry over to the problems under investigation.}, language = {en} } @misc{BorndoerferWeismantel1997, author = {Bornd{\"o}rfer, Ralf and Weismantel, Robert}, title = {Discrete Relaxations of Combinatorial Programs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3230}, number = {SC-97-54}, year = {1997}, abstract = {This paper investigates {\em relations\/} among combinatorial optimization problems. To establish such relations we introduce a transformation technique \mbox{---{\em aggregation}---} that allows to relax an integer program by means of another integer program. We prove that various families of prominent inequalities for the acyclic subdigraph problem, the multiple knapsack problem, the max cut, graph, and the clique partitioning problem, the set covering problem, and the set packing problem can be derived and separated in polynomial time in this way. Our technique is algorithmic. It has been implemented and used in a set partitioning code.}, language = {en} } @misc{BorndoerferGroetschelKlostermeieretal.1997, author = {Bornd{\"o}rfer, Ralf and Gr{\"o}tschel, Martin and Klostermeier, Fridolin and K{\"u}ttner, Christian}, title = {Optimierung des Berliner Behindertenfahrdienstes}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2799}, number = {SC-97-10}, year = {1997}, abstract = {In diesem Artikel geben wir einen {\"U}berblick {\"u}ber das Telebus-Projekt am Konrad-Zuse-Zentrum, Berlin, durch das der Behindertenfahrdienst in Berlin reorganisiert und optimiert wurde. Wir berichten kurz {\"u}ber die mathematischen Probleme und, etwas ausf{\"u}hrlicher, {\"u}ber die nicht-mathematischen Schwierigkeiten, die bei der Durchf{\"u}hrung dieses Projektes auftraten.}, language = {de} } @inproceedings{PrauseBorndoerfer2024, author = {Prause, Felix and Bornd{\"o}rfer, Ralf}, title = {A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance}, volume = {123}, booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)}, doi = {10.4230/OASIcs.ATMOS.2024.13}, pages = {13:1 -- 13:19}, year = {2024}, abstract = {We consider the rolling stock rotation planning problem with predictive maintenance (RSRP-PdM), where a timetable given by a set of trips must be operated by a fleet of vehicles. Here, the health states of the vehicles are assumed to be random variables, and their maintenance schedule should be planned based on their predicted failure probabilities. Utilizing the Bayesian update step of the Kalman filter, we develop a rolling horizon approach for RSRP-PdM, in which the predicted health state distributions are updated as new data become available. This approach reduces the uncertainty of the health states and thus improves the decision-making basis for maintenance planning. To solve the instances, we employ a local neighborhood search, which is a modification of a heuristic for RSRP-PdM, and demonstrate its effectiveness. Using this solution algorithm, the presented approach is compared with the results of common maintenance strategies on test instances derived from real-world timetables. The obtained results show the benefits of the rolling horizon approach.}, language = {en} } @inproceedings{BorndoerferJocasWeiser2026, author = {Bornd{\"o}rfer, Ralf and Jocas, Arturas and Weiser, Martin}, title = {An Eikonal Approach for Globally Optimal Free Flight Trajectories}, arxiv = {http://arxiv.org/abs/2603.11830}, year = {2026}, abstract = {We present an eikonal-based approach that is capable of finding a continuous globally optimal trajectory for an aircraft in a stationary wind field. This minimizes emissions and fuel consumption. If the destination is close to a cut locus of the associated Hamilton-Jacobi-Bellman equation, small numerical discretization errors can lead to selecting a merely locally optimal trajectory and missing the globally optimal one. Based on finite element error estimates, we construct a trust region around the cut loci in order to guarantee uniqueness of trajectories for destinations sufficiently far from cut loci.}, language = {en} }