@misc{LoebelLindnerBorndoerfer2019, author = {L{\"o}bel, Fabian and Lindner, Niels and Bornd{\"o}rfer, Ralf}, title = {The Restricted Modulo Network Simplex Method for Integrated Periodic Timetabling and Passenger Routing}, issn = {1438-0064}, doi = {https://doi.org/https://doi.org/10.1007/978-3-030-48439-2_92}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73868}, year = {2019}, abstract = {The Periodic Event Scheduling Problem is a well-studied NP-hard problem with applications in public transportation to find good periodic timetables. Among the most powerful heuristics to solve the periodic timetabling problem is the modulo network simplex method. In this paper, we consider the more difficult version with integrated passenger routing and propose a refined integrated variant to solve this problem on real-world-based instances.}, language = {en} } @inproceedings{LoebelLindner2025, author = {L{\"o}bel, Fabian and Lindner, Niels}, title = {A Geometric Approach to Integrated Periodic Timetabling and Passenger Routing}, volume = {137}, booktitle = {25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)}, editor = {Sauer, Jonas and Schmidt, Marie}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, isbn = {978-3-95977-404-8}, issn = {2190-6807}, doi = {10.4230/OASIcs.ATMOS.2025.2}, url = {http://nbn-resolving.de/urn:nbn:de:0030-drops-247580}, pages = {2:1 -- 2:19}, year = {2025}, abstract = {We offer a geometric perspective on the problem of integrated periodic timetabling and passenger routing in public transport. Inside the space of periodic tensions, we single out those regions, where the same set of paths provides shortest passenger routes. This results in a polyhedral subdivision, which we combine with the known decomposition by polytropes. On each maximal region of the common refinement, the integrated problem is solvable in polynomial time. We transform these insights into a new geometry-driven primal heuristic, integrated tropical neighborhood search (ITNS). Computationally, we compare implementations of ITNS and the integrated (restricted) modulo network simplex algorithm on the TimPassLib benchmark set, and contribute better solutions in terms of total travel time for all but one of the twenty-five instances for which a proven optimal solution is not yet known.}, language = {en} } @inproceedings{LoebelLindnerBorndoerfer2020, author = {L{\"o}bel, Fabian and Lindner, Niels and Bornd{\"o}rfer, Ralf}, title = {The Restricted Modulo Network Simplex Method for Integrated Periodic Timetabling and Passenger Routing}, booktitle = {Operations Research Proceedings 2019}, editor = {Neufeld, Janis S. and Buscher, Udo and Lasch, Rainer and M{\"o}st, Dominik and Sch{\"o}nberger, J{\"o}rn}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-48438-5}, doi = {https://doi.org/10.1007/978-3-030-48439-2_92}, pages = {757 -- 763}, year = {2020}, abstract = {The Periodic Event Scheduling Problem is a well-studied NP-hard problem with applications in public transportation to find good periodic timetables. Among the most powerful heuristics to solve the periodic timetabling problem is the modulo network simplex method. In this paper, we consider the more difficult version with integrated passenger routing and propose a refined integrated variant to solve this problem on real-world-based instances.}, language = {en} }