@misc{GamrathFischerGallyetal.2016, author = {Gamrath, Gerald and Fischer, Tobias and Gally, Tristan and Gleixner, Ambros and Hendel, Gregor and Koch, Thorsten and Maher, Stephen J. and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schenker, Sebastian and Schwarz, Robert and Serrano, Felipe and Shinano, Yuji and Vigerske, Stefan and Weninger, Dieter and Winkler, Michael and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 3.2}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57675}, year = {2016}, abstract = {The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers. This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.}, language = {en} } @inproceedings{FischerSchlechte2017, author = {Fischer, Frank and Schlechte, Thomas}, title = {Strong Relaxations for the Train Timetabling Problem using Connected Configurations}, volume = {59}, booktitle = {17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)}, editor = {D'Angelo, Gianlorenzo and Dollevoet, Twan}, isbn = {978-3-95977-042-2}, doi = {10.4230/OASIcs.ATMOS.2017.11}, year = {2017}, abstract = {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.}, language = {en} } @inproceedings{FischerGrimmKlugetal.2017, author = {Fischer, Frank and Grimm, Boris and Klug, Torsten and Schlechte, Thomas}, title = {A Re-optimization Approach for Train Dispatching}, booktitle = {Operations Research Proceedings 2016}, doi = {10.1007/978-3-319-55702-1_85}, pages = {645 -- 651}, year = {2017}, abstract = {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.}, language = {en} } @misc{FischerSchlechte2017, author = {Fischer, Frank and Schlechte, Thomas}, title = {Strong Relaxations for the Train Timetabling Problem using Connected Configurations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64743}, year = {2017}, abstract = {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.}, language = {en} } @misc{FischerGrimmKlugetal.2016, author = {Fischer, Frank and Grimm, Boris and Klug, Torsten and Schlechte, Thomas}, title = {A Re-optimization Approach for Train Dispatching}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60493}, year = {2016}, abstract = {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.}, language = {en} } @misc{FischerSchlechte2015, author = {Fischer, Frank and Schlechte, Thomas}, title = {Comparing two dual relaxations of large scale train timetabling problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56068}, year = {2015}, abstract = {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.}, language = {en} } @incollection{CaimiFischerSchlechte2018, author = {Caimi, Gabrio and Fischer, Frank and Schlechte, Thomas}, title = {Railway Track Allocation}, volume = {268}, booktitle = {Handbook of Optimization in the Railway Industry}, publisher = {Springer International Publishing}, isbn = {978-3-319-72152-1}, doi = {https://doi.org/10.1007/978-3-319-72153-8}, pages = {141 -- 160}, year = {2018}, abstract = {This chapter addresses the classical task to decide which train runs on which track in a railway network. In this context a track allocation defines the precise routing of trains through a railway network, which usually has only a limited capacity. Moreover, the departure and arrival times at the visited stations of each train must simultaneously meet several operational and safety requirements. The problem to find the 'best possible' allocation for all trains is called the track allocation problem (TTP). Railway systems can be modeled on a very detailed scale covering the behavior of individual trains and the safety system to a large extent. However, those microscopic models are too big and not scalable to large networks, which make them inappropriate for mathematical optimization on a network wide level. Hence, most network optimization approaches consider simplified, so called macroscopic, models. In the first part we take a look at the challenge to construct a reliable and condensed macroscopic model for the associated microscopic model and to facilitate the transition between both models of different scale. In the main part we focus on the optimization problem for macroscopic models of the railway system. Based on classical graph-theoretical tools the track allocation problem is formulated to determine conflict-free paths in corresponding time-expanded graphs. We present standard integer programming model formulations for the track allocation problem that model resource or block conflicts in terms of packing constraints. In addition, we discuss the role of maximal clique inequalities and the concept of configuration networks. We will also present classical decomposition approaches like Lagrangian relaxation and bundle methods. Furthermore, we will discuss recently developed techniques, e.g., dynamic graph generation. Finally, we will discuss the status quo and show a vision of mathematical optimization to support real world track allocation, i.e. integrated train routing and scheduling, in a data-dominated and digitized railway future.}, language = {en} } @inproceedings{FischerSchlechte2015, author = {Fischer, Frank and Schlechte, Thomas}, title = {Comparing two dual relaxations of large scale train timetabling problems}, booktitle = {Proceedings of Conference on Advanced Systems in Public Transport 2015}, year = {2015}, abstract = {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.}, language = {en} }