@inproceedings{LindnerLiebchenMasing2021, author = {Lindner, Niels and Liebchen, Christian and Masing, Berenike}, title = {Forward Cycle Bases and Periodic Timetabling}, series = {21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)}, booktitle = {21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:526-opus4-15408}, pages = {2:1 -- 2:14}, year = {2021}, abstract = {Periodic timetable optimization problems in public transport can be modeled as mixed-integer linear programs by means of the Periodic Event Scheduling Problem (PESP). In order to keep the branch-and-bound tree small, minimum integral cycle bases have been proven successful. We examine forward cycle bases, where no cycle is allowed to contain a backward arc. After reviewing the theory of these bases, we describe the construction of an integral forward cycle basis on a line-based event-activity network. Adding turnarounds to the instance R1L1 of the benchmark library PESPlib, we computationally evaluate three types of forward cycle bases in the Pareto sense, and come up with significant improvements concerning dual bounds.}, language = {en} } @article{LindnerLiebchen2022, author = {Lindner, Niels and Liebchen, Christian}, title = {Timetable merging for the Periodic Event Scheduling Problem}, series = {EURO Journal on Transportation and Logistics}, volume = {11}, journal = {EURO Journal on Transportation and Logistics}, publisher = {Elsevier}, issn = {2192-4376}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:526-opus4-16054}, year = {2022}, abstract = {We propose a new mixed integer programming based heuristic for computing new benchmark primal solutions for instances of the PESPlib. The PESPlib is a collection of instances for the Periodic Event Scheduling Problem (PESP), comprising periodic timetabling problems inspired by real-world railway timetabling settings, and attracting several international research teams during the last years. We describe two strategies to merge a set of good periodic timetables. These make use of the instance structure and minimum weight cycle bases, finally leading to restricted mixed integer programming formulations with tighter variable bounds. Implementing this timetable merging approach in a concurrent solver, we improve the objective values of the best known solutions for the smallest and largest PESPlib instances by 1.7 and 4.3 percent, respectively.}, language = {en} } @incollection{BorndoerferKarbsteinLiebchenetal.2018, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika and Liebchen, Christian and Lindner, Niels}, title = {A Simple Way to Compute the Number of Vehicles That Are Required to Operate a Periodic Timetable}, series = {18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)}, booktitle = {18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)}, editor = {Bornd{\"o}rfer, Ralf and Storandt, Sabine}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik GmbH}, address = {Wadern}, isbn = {978-3-95977-096-5}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:526-opus4-10549}, publisher = {Technische Hochschule Wildau}, pages = {16:1 -- 16:15}, year = {2018}, abstract = {We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it? In [Julius Paetzold et al., 2017], for this sequential approach, it is proposed to first expand the periodic timetable over time, and then answer the above question by solving a flow-based aperiodic optimization problem. In this contribution we propose to keep the compact periodic representation of the timetable and simply solve a particular perfect matching problem. For practical networks, it is very much likely that the matching problem decomposes into several connected components. Our key observation is that there is no need to change any turnaround decision for the vehicles of a line during the day, as long as the timetable stays exactly the same.}, language = {en} } @inproceedings{MasingLindnerLiebchen2023, author = {Masing, Berenike and Lindner, Niels and Liebchen, Christian}, title = {Integrating Line Planning for Construction Sites into Periodic Timetabling via Track Choice}, series = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, isbn = {978-3-95977-302-7}, issn = {2190-6807}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:526-opus4-17916}, pages = {5:1 -- 5:15}, year = {2023}, abstract = {We consider maintenance sites for urban rail systems, where unavailable tracks typically require changes to the regular timetable, and often even to the line plan. In this paper, we present an integrated mixed-integer linear optimization model to compute an optimal line plan that makes best use of the available tracks, together with a periodic timetable, including its detailed routing on the tracks within the stations. The key component is a flexible, turn-sensitive event-activity network that allows to integrate line planning and train routing using a track choice extension of the Periodic Event Scheduling Problem (PESP). Major goals are to maintain as much of the regular service as possible, and to keep the necessary changes rather local. Moreover, we present computational results on real construction site scenarios on the S-Bahn Berlin network. We demonstrate that this integrated problem is indeed solvable on practically relevant instances.}, language = {en} } @inproceedings{LindnerLiebchen2020, author = {Lindner, Niels and Liebchen, Christian}, title = {Determining All Integer Vertices of the PESP Polytope by Flipping Arcs}, series = {20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)}, booktitle = {20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)}, editor = {Huisman, Dennis and Zaroliagis, Christos D.}, publisher = {Schloss Dagstuhl, Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, isbn = {978-3-95977-170-2}, issn = {2190-6807}, doi = {10.4230/OASIcs.ATMOS.2020.5}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:526-opus4-13650}, year = {2020}, abstract = {We investigate polyhedral aspects of the Periodic Event Scheduling Problem (PESP), the mathematical basis for periodic timetabling problems in public transport. Flipping the orientation of arcs, we obtain a new class of valid inequalities, the flip inequalities, comprising both the known cycle and change-cycle inequalities. For a point of the LP relaxation, a violated flip inequality can be found in pseudo-polynomial time, and even in linear time for a spanning tree solution. Our main result is that the integer vertices of the polytope described by the flip inequalities are exactly the vertices of the PESP polytope, i.e., the convex hull of all feasible periodic slacks with corresponding modulo parameters. Moreover, we show that this flip polytope equals the PESP polytope in some special cases. On the computational side, we devise several heuristic approaches concerning the separation of cutting planes from flip inequalities. We finally present better dual bounds for the smallest and largest instance of the benchmarking library PESPlib.}, language = {en} }