@inproceedings{HillerKlugWitzig, author = {Hiller, Benjamin and Klug, Torsten and Witzig, Jakob}, title = {Reoptimization in branch-and-bound algorithms with an application to elevator control}, series = {Proceedings of the 12th International Symposium on Experimental Algorithms}, volume = {7933}, booktitle = {Proceedings of the 12th International Symposium on Experimental Algorithms}, doi = {10.1007/978-3-642-38527-8_33}, pages = {378 -- 389}, language = {en} } @incollection{Klug, author = {Klug, Torsten}, title = {Freight Train Routing}, series = {Handbook of Optimization in the Railway Industry}, volume = {268}, booktitle = {Handbook of Optimization in the Railway Industry}, publisher = {Springer International Publishing}, isbn = {978-3-319-72152-1}, doi = {10.1007/978-3-319-72153-8}, pages = {73 -- 92}, abstract = {This chapter is about strategic routing of freight trains in railway transportation networks with mixed traffic. A good utilization of a railway transportation network is important since in contrast to road and air traffic the routing through railway networks is more challenging and the extension of capacities is expensive and a long-term projects. Therefore, an optimized routing of freight trains have a great potential to exploit remaining capacity since the routing has fewer restrictions compared to passenger trains. In this chapter we describe the freight train routing problem in full detail and present a mixed-integer formulation. Wo focus on a strategic level that take into account the actual immutable passenger traffic. We conclude the chapter with a case study for the German railway network.}, language = {en} } @inproceedings{KlugJunoszaSzaniawskiKwasiborskietal., author = {Klug, Torsten and Junosza-Szaniawski, Konstanty and Kwasiborski, Slawomir and F{\"u}genschuh, Armin and Schlechte, Thomas}, title = {Fastest, Average and Quantile Schedule}, series = {SOFSEM 2015: Theory and Practice of Computer Science}, booktitle = {SOFSEM 2015: Theory and Practice of Computer Science}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/978-3-662-46078-8_17}, pages = {201 -- 216}, abstract = {We consider problems concerning the scheduling of a set of trains on a single track. For every pair of trains there is a minimum headway, which every train must wait before it enters the track after another train. The speed of each train is also given. Hence for every schedule - a sequence of trains - we may compute the time that is at least needed for all trains to travel along the track in the given order. We give the solution to three problems: the fastest schedule, the average schedule, and the problem of quantile schedules. The last problem is a question about the smallest upper bound on the time of a given fraction of all possible schedules. We show how these problems are related to the travelling salesman problem. We prove NP-completeness of the fastest schedule problem, NP-hardness of quantile of schedules problem, and polynomiality of the average schedule problem. We also describe some algorithms for all three problems. In the solution of the quantile problem we give an algorithm, based on a reverse search method, generating with polynomial delay all Eulerian multigraphs with the given degree sequence and a bound on the number of such multigraphs. A better bound is left as an open question.}, language = {en} } @inproceedings{KlugReutherSchlechte, author = {Klug, Torsten and Reuther, Markus and Schlechte, Thomas}, title = {Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling}, series = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, volume = {106}, booktitle = {22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/OASIcs.ATMOS.2022.11}, pages = {11:1 -- 11:8}, abstract = {Timetabling is a classical and complex task for public transport operators as well as for railway undertakings. The general question is: Which vehicle is taking which route through the transportation network in which order? In this paper, we consider the special setting to find optimal timetables for railway systems under a moving block regime. We directly set up on our work of [8 ], i.e., we consider the same model formulation and real-world instances of a moving block headway system. In this paper, we present a repair heuristic and a lazy-constraint approach utilizing the callback features of Gurobi, see [3]. We provide an experimental study of the different algorithmic approaches for a railway network with 100 and up to 300 train requests. The computational results show that the lazy-constraint approach together with the repair heuristic significantly improves our previous approaches.}, language = {en} } @article{SchlechteBorndoerferDenissenetal., author = {Schlechte, Thomas and Bornd{\"o}rfer, Ralf and Denißen, Jonas and Heller, Simon and Klug, Torsten and K{\"u}pper, Michael and Lindner, Niels and Reuther, Markus and S{\"o}hlke, Andreas and Steadman, William}, title = {Timetable Optimization for a Moving Block System}, series = {Journal of Rail Transport Planning \& Management}, volume = {22}, journal = {Journal of Rail Transport Planning \& Management}, issn = {2210-9706}, doi = {10.1016/j.jrtpm.2022.100315}, pages = {100315}, abstract = {We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model is able to solve reasonably sized instances with up to hundred trains to optimality.}, language = {en} }