TY - CHAP A1 - Fischer, Frank A1 - Schlechte, Thomas ED - D'Angelo, Gianlorenzo ED - Dollevoet, Twan T1 - Strong Relaxations for the Train Timetabling Problem using Connected Configurations T2 - 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017) N2 - The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral. Y1 - 2017 SN - 978-3-95977-042-2 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2017.11 VL - 59 ER - TY - CHAP A1 - Fischer, Frank A1 - Grimm, Boris A1 - Klug, Torsten A1 - Schlechte, Thomas T1 - A Re-optimization Approach for Train Dispatching T2 - Operations Research Proceedings 2016 N2 - The Train Dispatching Problem (TDP) is to schedule trains through a network in a cost optimal way. Due to disturbances during operation existing track allocations often have to be re-scheduled and integrated into the timetable. This has to be done in seconds and with minimal timetable changes to guarantee smooth and conflict free operation. We present an integrated modeling approach for the re-optimization task using Mixed Integer Programming. Finally, we provide computational results for scenarios provided by the INFORMS RAS Problem Soling Competition 2012. Y1 - 2017 U6 - https://doi.org/10.1007/978-3-319-55702-1_85 SP - 645 EP - 651 ER - TY - CHAP A1 - Fischer, Frank A1 - Schlechte, Thomas T1 - Comparing two dual relaxations of large scale train timetabling problems T2 - Proceedings of Conference on Advanced Systems in Public Transport 2015 N2 - Railway transportation and in particular train timetabling is one of the basic and source application areas of combinatorial optimization and integer programming. We will discuss two well established modeling techniques for the train timetabling problem. In this paper we focus on one major ingredient - the bounding by dual relaxations. We compare two classical dual relaxations of large scale time expanded train timetabling problems - the Lagrangean Dual and Lagrangean Decomposition. We discuss the convergence behavior and show limitations of the Lagrangean Decomposition approach for a configuration based model. We introduce a third dualization approach to overcome those limitations. Finally, we present promising preliminary computational experiments that show that our new approach indeed has superior convergence properties. Y1 - 2015 ER -