@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} }