@article{RiedmuellerLindner2025, author = {Riedm{\"u}ller, Stephanie and Lindner, Niels}, title = {Column Generation for Periodic Timetabling}, arxiv = {http://arxiv.org/abs/2510.12466}, year = {2025}, abstract = {Periodic timetabling for public transportation networks is typically modelled as a Periodic Event Scheduling Problem (PESP). Solving instances of the benchmark library PESPlib to optimality continues to pose a challenge. As a further approach towards this goal, we remodel the problem by a time discretization of the underlying graph and consider arc-based as well as path-based integer programming formulations. For the path-based case, we use cycles on the graph expansion of the operational lines as variables and, therefore, include more of the problem inherent structure into the model. A consequence is the validity of several known inequalities and a lower bound on the LP-relaxation, that is the best known to date. As an extension we integrate passenger routing into the new model. The proposed models have an advantage in the linear programming relaxation, on the one hand, but have an increased problem size, on the other hand. We define the corresponding pricing problems for the use of column generation to handle the size. Both models are practically tested on different problem 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} } @article{vanLieshoutLindner2025, author = {van Lieshout, Rolf and Lindner, Niels}, title = {A Compact Cycle Formulation for the Multiperiodic Event Scheduling Problem}, arxiv = {http://arxiv.org/abs/2507.17566}, year = {2025}, abstract = {The Periodic Event Scheduling Problem (PESP) is a fundamental model in periodic timetabling for public transport systems, assuming a common period across all events. However, real-world networks often feature heterogeneous service frequencies. This paper studies the Multiperiodic Event Scheduling Problem (MPESP), a generalization of PESP that allows each event to recur at its own individual period. While more expressive, MPESP presents new modeling challenges due to the loss of a global period. We present a cycle-based formulation for MPESP that extends the strongest known formulation for PESP and, in contrast to existing approaches, is valid for any MPESP instance. Crucially, the formulation requires a cycle basis derived from a spanning tree satisfying specific structural properties, which we formalize and algorithmically construct, extending the concept of sharp spanning trees to rooted instances. We further prove a multiperiodic analogue of the cycle periodicity property. Our new formulation solves nearly all tested instances, including several large-scale real-world public transport networks, to optimality or with small optimality gaps, dramatically outperforming existing arc-based models. The results demonstrate the practical potential of MPESP in capturing heterogeneous frequencies without resorting to artificial event duplication.}, language = {en} } @misc{TeschBorndoerfer2025, author = {Tesch, Alexander and Bornd{\"o}rfer, Ralf}, title = {Mathematische Optimierung in der OP-Planung}, volume = {5}, journal = {OP-Management up2date}, number = {1}, publisher = {Thieme}, doi = {10.1055/a-2322-2124}, pages = {21 -- 34}, year = {2025}, abstract = {Deutsche Krankenh{\"a}user sehen sich derzeit mit enormen Schwierigkeiten konfrontiert. Ungef{\"a}hr jede 2. Klinik muss drastische Sparmaßnahmen ergreifen, was auch die Allgemeinversorgung beeintr{\"a}chtigt. Die Gr{\"u}nde daf{\"u}r sind vielschichtig: stark gestiegene Sach- und Personalkosten bei gleicher Finanzierung, teilweiser Patientenr{\"u}ckgang, starke regionale Unterschiede in der Versorgung, Fachkr{\"a}ftemangel und fehlende Investitionen in Kern- und Zukunftsbereiche, insbesondere der Digitalisierung. Das belastet die Haushalte der Kliniken. Insbesondere die Digitalisierung und die Anwendung von Methoden der k{\"u}nstlichen Intelligenz und der mathematischen Optimierung k{\"o}nnten eine Schl{\"u}sselrolle spielen, um die komplexen Krankenhausprozesse mit Kennzahlen qualitativ zu bewerten und zu verbessern. In diesem Artikel stellen wir vier Praxisprobleme aus der OP-Planung vor und benennen welche Entscheidungen, Nebenbedingungen und Zielkriterien mit mathematischen Entscheidungsmodellen dargestellt und optimiert werden k{\"o}nnen. Hierzu erl{\"a}utern wir das erweiterte Potenzial einer umfassenden Anwendung von mathematischer Optimierung im OP-Bereich.}, language = {de} } @article{MaristanydelasCasasSedenoNodaBorndoerfer2025, author = {Maristany de las Casas, Pedro and Sede{\~n}o-Noda, Antonio and Bornd{\"o}rfer, Ralf}, title = {New Dynamic Programming Algorithm for the Multiobjective Minimum Spanning Tree Problem}, volume = {173}, journal = {Computers \& Operations Research}, arxiv = {http://arxiv.org/abs/2306.16203}, doi = {10.1016/j.cor.2024.106852}, pages = {106852}, year = {2025}, abstract = {The Multiobjective Minimum Spanning Tree (MO-MST) problem is a variant of the Minimum Spanning Tree problem, in which the costs associated with every edge of the input graph are vectors. In this paper, we design a new dynamic programming MO-MST algorithm. Dynamic programming for a MO-MST instance leads to the definition of an instance of the One-to-One Multiobjective Shortest Path (MOSP) problem and both instances have equivalent solution sets. The arising MOSP instance is defined on a so called transition graph. We study the original size of this graph in detail and reduce its size using cost dependent arc pruning criteria. To solve the MOSP instance on the reduced transition graph, we design the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting recent improvements on MOSP algorithms from the literature. All in all, the new IG-MDA outperforms the current state of the art on a big set of instances from the literature. Our code and results are publicly available.}, language = {en} } @article{MasingLindnerBortoletto2025, author = {Masing, Berenike and Lindner, Niels and Bortoletto, Enrico}, title = {Computing All Shortest Passenger Routes with a Tropical Dijkstra Algorithm}, volume = {14}, journal = {EURO Journal on Transportation and Logistics}, arxiv = {http://arxiv.org/abs/2412.14654}, doi = {10.1016/j.ejtl.2025.100163}, year = {2025}, abstract = {Given a public transportation network, which and how many passenger routes can potentially be shortest paths, when all possible timetables are taken into account? This question leads to shortest path problems on graphs with interval costs on their arcs and is closely linked to multi-objective optimization. We introduce a Dijkstra algorithm based on polynomials over the tropical semiring that computes complete or minimal sets of efficient paths. We demonstrate that this approach is computationally feasible by employing it on the public transport network of the city of Wuppertal and instances of the benchmarking set TimPassLib, and we evaluate the resulting sets of passenger routes.}, language = {en} } @article{GrimmHoogervorstBorndoerfer2025, author = {Grimm, Boris and Hoogervorst, Rowan and Bornd{\"o}rfer, Ralf}, title = {A Comparison of Two Models for Rolling Stock Scheduling}, volume = {59}, journal = {Transportation Science}, number = {5}, arxiv = {http://arxiv.org/abs/2312.09697}, doi = {10.1287/trsc.2024.0505}, year = {2025}, abstract = {A major step in the planning process of passenger railway operators is the assignment of rolling stock, that is, train units, to the trips of the timetable. A wide variety of mathematical optimization models have been proposed to support this task, which we discuss and argue to be justified in order to deal with operational differences between railway operators, and hence different planning requirements, in the best possible way. Our investigation focuses on two commonly used models, the composition model and the hypergraph model, that were developed for Netherlands Railways (NS) and DB Fernverkehr AG (DB), respectively. We compare these models in two distinct problem settings, an NS setting and DB-light setting and consider different model variants to tune the models to these settings. We prove that in both of these settings, the linear programming bounds of the two models are equally strong as long as a number of reasonable assumptions are met. However, through a numerical evaluation on NS and DB-light instances, we show that the numerical performance of the models strongly depends on the instances. Although the composition model is the most compact and fastest model for the NS instances, an adjusted version of this model grows quickly for the DB-light instances and is then outperformed by the considered hypergraph model variants. Moreover, we show that a depot-extended version of the hypergraph model is able to combine strengths of both models and show good performance on both the NS and DB-light instances.}, language = {en} } @article{BortolettoLindnerMasing2025, author = {Bortoletto, Enrico and Lindner, Niels and Masing, Berenike}, title = {The Tropical and Zonotopal Geometry of Periodic Timetables}, volume = {73}, journal = {Discrete \& Computational Geometry}, doi = {10.1007/s00454-024-00686-2}, pages = {719 -- 763}, year = {2025}, abstract = {The Periodic Event Scheduling Problem (PESP) is the standard mathematical tool for optimizing periodic timetables in public transport. A solution to a PESP instance consists of three parts: a periodic timetable, a periodic tension, and integer offset values. While the space of periodic tensions has received much attention in the past, we explore geometric properties of the other two components. The general aim of this paper is to establish novel connections between periodic timetabling and discrete geometry. Firstly, we study the space of feasible periodic timetables as a disjoint union of polytropes. These are polytopes that are convex both classically and in the sense of tropical geometry. We then study this decomposition and use it to outline a new heuristic for PESP, based on neighbourhood relations of the polytropes. Secondly, we recognize that the space of fractional cycle offsets is in fact a zonotope, and then study its zonotopal tilings. These are related to the hyperrectangle of fractional periodic tensions, as well as the polytropes of the periodic timetable space, and we detail their interplay. To conclude, we also use this new understanding to give tight lower bounds on the minimum width of an integral cycle basis.}, language = {en} } @inproceedings{LindnerLiebchen2025, author = {Lindner, Niels and Liebchen, Christian}, title = {Incremental Heuristics for Periodic Timetabling}, booktitle = {Operations Research Proceedings 2023}, editor = {Voigt, Guido and Fliedner, Malte and Haase, Knut and Br{\"u}ggemann, Wolfgang and Hoberg, Kai and Meissner, J{\"o}rn}, publisher = {Springer Nature Switzerland}, address = {Cham}, doi = {10.1007/978-3-031-58405-3_59}, pages = {461 -- 467}, year = {2025}, abstract = {We present incremental heuristics for the Periodic Event Scheduling Problem (PESP), the standard mathematical tool to optimize periodic timetables in public transport. The core of our method is to solve successively larger subinstances making use of previously found solutions. Introducing the technical notion of free stratifications, we formulate a general scheme for incremental heuristics for PESP. More practically, we use line and station information to create heuristics that add lines or stations one by one, and we evaluate these heuristics on instances of the benchmarking library PESPlib. This approach is indeed viable, and leads to new incumbent solutions for six PESPlib instances.}, language = {en} } @article{MaristanydelasCasasSedenoNodaBorndoerferetal.2025, author = {Maristany de las Casas, Pedro and Sede{\~n}o-Noda, Antonio and Bornd{\"o}rfer, Ralf and Huneshagen, Max}, title = {K-Shortest Simple Paths Using Biobjective Path Search}, volume = {17}, journal = {Mathematical Programming Computation}, arxiv = {http://arxiv.org/abs/2309.10377}, doi = {10.1007/s12532-025-00276-0}, pages = {349 -- 384}, year = {2025}, abstract = {In this paper we introduce a new algorithm for the k-Shortest Simple Paths (K-SSP) problem with an asymptotic running time matching the state of the art from the literature. It is based on a black-box algorithm due to Roditty and Zwick (2012) that solves at most 2k instances of the Second Shortest Simple Path (2-SSP) problem without specifying how this is done. We fill this gap using a novel approach: we turn the scalar 2-SSP into instances of the Biobjective Shortest Path problem. Our experiments on grid graphs and on road networks show that the new algorithm is very efficient in practice.}, language = {en} } @misc{Bushe2021, type = {Master Thesis}, author = {Bushe, Julian}, title = {Rolling Stock Rotation Optimization with Maintenance Paths}, year = {2021}, abstract = {Die Planung vom Zuguml{\"a}ufen ist eine der wichtigsten Aufgaben f{\"u}r Eisenbahnun- ternehmen. Dabei spielt auch die Einhaltung von vorgegebenen Wartungsintervallen eine zentrale Rolle f{\"u}r die Sicherheit und Zuverl{\"a}ssigkeit der Schienenfahrzeuge. Wir zeigen, wie man dieses Umlaufplanungsproblem unter Beachtung von Wartungsbe- dingungen mathematisch formuliert, modelliert und l{\"o}st — sowohl in der Theorie als auch im Anwendungsfall mit Szenarien der DB Fernverkehr AG, einer Konzern- tochter der Deutschen Bahn f{\"u}r den Schienenpersonenfernverkehr. Markus Reuther hat sich in seiner Dissertation [11] mit diesem Problem besch{\"a}ftigt und es mit Hilfe eines passenden Hypergraphen als gemischt-ganzzahliges Programm modelliert. Neben der Modellierung pr{\"a}sentiert Reuther in seiner Arbeit neuartige algorithmische Ideen, darunter den sogenannten Coarse-to-Fine -Ansatz, bei dem zun{\"a}chst Teile des Problems auf einer weniger detaillierten ( coarse ) Ebene gel{\"o}st werden und diese L{\"o}sung dann verwendet wird, um auf effiziente Art und Weise eine L{\"o}sung f{\"u}r das urspr{\"u}ngliche Problem zu finden. Zur Wartungsplanung nutzt Reuther einen Fluss im Hypergraphen, der den Ressourcenverbrauch der Fahrzeuge modelliert. In der linearen Relaxierung des Modells f{\"u}hrt dies dazu, dass die Zahl der notwendigen Wartungen systematisch untersch{\"a}tzt wird. Dadurch bleibt in vielen F{\"a}llen eine große L{\"u}cke zwischen dem Zielfunktionswert einer optimalen L{\"o}sung des ganzzahligen Problems und der untere Schranke, die uns die lineare Relaxierung liefert. Wir nehmen uns in dieser Arbeit dieses Problems an. Wir entwickeln ein auf Pfaden basierendes ganzzahliges Modell f{\"u}r das Umlaufplanungsproblem und zeigen, dass die untere Schranke mindestens so scharf oder sch{\"a}rfer ist als die untere Schranke, die das Modell von Reuther liefert. Um das Modell zu l{\"o}sen, entwickeln wir einen Algorithmus, der Spaltengenerierung mit dem Coarse-to-Fine-Ansatz von Reuther verbindet. Weiterhin entwickeln wir eine Spaltenauswahlregel zur Beschleunigung des Algorithmus. Das Modell und alle in der Arbeit vorgestellten Algorithmen wur- den im Rahmen der Arbeit implementiert und mit Anwendungsszenarien der DB Fernverkehr AG getestet. Unsere Tests zeigen, dass unser Modell f{\"u}r fast alle Szena- rien deutlich sch{\"a}rfere untere Schranken liefert als das Modell von Reuther. In den getesteten Instanzen konnten wir durch die Verbesserung der unteren Schranke bis zu 99\% der Optimalit{\"a}tsl{\"u}cke schließen. In einem Drittel der F{\"a}lle konnten wir durch unseren Ansatz auch f{\"u}r das ganzzahlige Programm verbesserte Zielfunktionswerte erreichen}, language = {en} } @article{LindnerMasing2025, author = {Lindner, Niels and Masing, Berenike}, title = {On the split closure of the periodic timetabling polytope}, journal = {Mathematical Programming}, publisher = {Springer Science and Business Media LLC}, issn = {0025-5610}, doi = {10.1007/s10107-025-02220-5}, year = {2025}, abstract = {The Periodic Event Scheduling Problem (PESP) is the central mathematical tool for periodic timetable optimization in public transport. PESP can be formulated in several ways as a mixed-integer linear program with typically general integer variables. We investigate the split closure of these formulations and show that split inequalities are identical with the recently introduced flip inequalities. While split inequalities are a general mixed-integer programming technique, flip inequalities are defined in purely combinatorial terms, namely cycles and arc sets of the digraph underlying the PESP instance. It is known that flip inequalities can be separated in pseudo-polynomial time. We prove that this is best possible unless P = NP, but also observe that the complexity becomes linear-time if the cycle defining the flip inequality is fixed. Moreover, introducing mixed-integer-compatible maps, we compare the split closures of different formulations, and show that reformulation or binarization by subdivision do not lead to stronger split closures. Finally, we estimate computationally how much of the optimality gap of the instances of the benchmark library PESPlib can be closed exclusively by split cuts, and provide better dual bounds for five instances.}, language = {en} } @inproceedings{LoebelBorndoerferWeider2025, author = {L{\"o}bel, Fabian and Bornd{\"o}rfer, Ralf and Weider, Steffen}, title = {Non-linear Battery Behavior in Electric Vehicle Scheduling Problems}, booktitle = {Operations Research Proceedings 2023. OR 2023.}, editor = {Voigt, Guido and Fliedner, Malte and Haase, Knut and Br{\"u}ggermann, Wolfgang and Hoberg, Kai and Meissner, Joern}, publisher = {Springer Nature Switzerland}, address = {Cham}, isbn = {9783031584046}, issn = {2731-040X}, doi = {10.1007/978-3-031-58405-3_53}, pages = {415 -- 421}, year = {2025}, abstract = {The currently most popular approach to handle non-linear battery behavior for electric vehicle scheduling is to use a linear spline interpolation of the charge curve. We show that this can lead to approximate models that underestimate the charge duration and overestimate the state of charge, which is not desirable. While the error is of second order with respect to the interpolation step size, the associated mixed-integer linear programs do not scale well with the number of spline segments. It is therefore recommendable to use coarse interpolation grids adapted to the curvature of the charge curve, and to include sufficient safety margins to ensure solutions of approximate models remain feasible subjected to the exact charge curve.}, language = {en} } @inproceedings{LindnerMehlBartoszuketal.2025, author = {Lindner, Niels and Mehl, Lukas and Bartoszuk, Karolina and Berendes, Sarah and Zittel, Janina}, title = {Demand Uncertainty in Energy Systems: Scenario Catalogs vs. Integrated Robust Optimization}, booktitle = {Proceedings of the 38th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems}, year = {2025}, abstract = {Designing efficient energy systems is indispensable for shaping a more sustainable society. This involves making infrastructure investment decisions that must be valid for a long-term time horizon. While energy system optimization models constitute a powerful technique to support planning decisions, they need to cope with inherent uncertainty. For example, predicting future demand on a scale of decades is not only an intricate challenge in itself, but small fluctuations in such a forecast might also largely impact the layout of a complex energy system. In this paper, we compare two methodologies of capturing demand uncertainty for linear-programming based energy system optimization models. On one hand, we generate and analyze catalogs of varying demand scenarios, where each individual scenario is considered independently, so that the optimization produces scenario-specific investment pathways. On the other hand, we make use of robust linear programming to meet the demand of all scenarios at once. Since including a multitude of scenarios increases the size and complexity of the optimization model, we will show how to use warm-starting approaches to accelerate the computation process, by exploiting the similar structure of the linear program across different demand inputs. This allows to integrate a meaningful number of demand scenarios with fully-fledged energy system models. We demonstrate the practical use of our methods in a case study of the Berlin-Brandenburg area in Germany, a region that contains both a metropolitan area and its rural surroundings. As a backbone, we use the open-source framework oemof to create a sector-coupled optimization model for planning an energy system with up to 100\% reduction of greenhouse gas emissions. This model features a fine-grained temporal resolution of one hour for the full year 2050. We consider uncertainty in demand for electricity, hydrogen, natural gas, central, and decentral heat. Based on our computations, we analyze the trade-offs in terms of quality and computation time for scenario catalogs and the robust optimization approach. We further demonstrate that our procedure provides a valuable strategy for decision makers to gain insight on the robustness and sensitivity of solutions regarding demand variability.}, language = {en} } @inproceedings{LindnerLiebchen2020, author = {Lindner, Niels and Liebchen, Christian}, title = {Determining all integer vertices of the PESP polytope by flipping arcs}, volume = {85}, 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 fuer Informatik}, address = {Dagstuhl, Germany}, doi = {10.4230/OASIcs.ATMOS.2020.5}, pages = {5:1 -- 5:18}, 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} } @inproceedings{LindnerMasingLiebchen2024, author = {Lindner, Niels and Masing, Berenike and Liebchen, Christian}, title = {Integrierte Baufahrplanoptimierung auf dem Netz der S-Bahn Berlin}, volume = {002/140}, booktitle = {HEUREKA'24 - Optimierung in Verkehr und Transport}, year = {2024}, abstract = {Zur Instandhaltung von Eisenbahnnetzen sind regelm{\"a}ßig Baumaßnahmen erforderlich. Diese erfordern stets Anpassungen der Fahrpl{\"a}ne. Um den Fahrg{\"a}sten trotz der Baumaßnahme weiterhin einen m{\"o}glichst großen Teil des Regelangebotes bieten zu k{\"o}nnen, bewegen sich die resultierenden Baufahrpl{\"a}ne insbesondere in Schnellbahnnetzen mit ihren dichten Zugfolgen h{\"a}ufig nahe der Kapazit{\"a}tsgrenze der Infrastruktur. Etablierte Verfahren zur Taktfahrplanoptimierung k{\"o}nnen diesen Anforderungen nicht gen{\"u}gen, da in der Praxis Anpassungen von Laufwegen der Linien, sowie der Gleisbelegungen h{\"a}ufig Teil der realisierten L{\"o}sungen sind. F{\"u}r diese Aufgabe haben die Autoren zuletzt ein Optimierungsmodell vorgestellt, welches diese M{\"o}glichkeiten aussch{\"o}pft. In dem vorliegenden Beitrag wird erstmalig dessen Anwendung auf ein unmittelbar der Praxis der Baufahrplanung entnommenes Beispiel aus dem Netz der Berliner S-Bahn im Detail beschrieben.}, language = {de} } @inproceedings{LindnerMasing2024, author = {Lindner, Niels and Masing, Berenike}, title = {SAT-Generated Initial Solutions for Integrated Line Planning and Turn-Sensitive Periodic Timetabling with Track Choice}, booktitle = {hEART 2024: 12th Symposium of the European Association for Research in Transportation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-98066}, year = {2024}, abstract = {Periodic timetabling is a challenging planning task in public transport. As safety requirements are crucial, track allocation is indispensable for validating the practical feasibility of a railway timetable. For busy stations with limited capacities, this requires a detailed planning of turn-arounds. It is therefore desirable to integrate timetabling not only with track allocation, but also with vehicle scheduling and line planning. This is captured by the Integrated Line Planning and Turn-Sensitive Periodic Timetabling Problem with Track Choice, whose MIP formulation has been demonstrated to be effective for construction site railway rescheduling, as long as a good quality initial solution is available. In this paper, we discuss how to generate such a solution by extending the SAT formulation of the Periodic Event Scheduling Problem with track choice, track occupation, and minimum service frequency components. The SAT approach is superior to pure MIP on real-world instances of the S-Bahn Berlin network.}, language = {de} } @inproceedings{LindnerLiebchenMasing2021, author = {Lindner, Niels and Liebchen, Christian and Masing, Berenike}, title = {Forward Cycle Bases and Periodic Timetabling}, volume = {96}, booktitle = {21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)}, doi = {10.4230/OASIcs.ATMOS.2021.2}, 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} } @inproceedings{LindnerMaristanydelasCasasSchiewe2021, author = {Lindner, Niels and Maristany de las Casas, Pedro and Schiewe, Philine}, title = {Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data}, volume = {96}, booktitle = {21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)}, doi = {10.4230/OASIcs.ATMOS.2021.7}, pages = {7:1 -- 7:15}, year = {2021}, abstract = {We investigate preprocessing for single-source shortest path queries in digraphs, where arc costs are only known to lie in an interval. More precisely, we want to decide for each arc whether it is part of some shortest path tree for some realization of costs. We show that this problem is solvable in polynomial time by giving a combinatorial algorithm, using optimal structures that we call forks. Our algorithm turns out to be very efficient in practice, and is sometimes even superior in quality to a heuristic developed for the one-to-one shortest path problem in the context of passenger routing in public transport.}, language = {en} } @inproceedings{BortolettovanLieshoutMasingetal.2024, author = {Bortoletto, Enrico and van Lieshout, Rolf Nelson and Masing, Berenike and Lindner, Niels}, title = {Periodic Event Scheduling with Flexible Infrastructure Assignment}, volume = {123}, booktitle = {24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)}, doi = {10.4230/OASIcs.ATMOS.2024.4}, pages = {4:1 -- 4:18}, year = {2024}, abstract = {We present novel extensions of the Periodic Event Scheduling Problem (PESP) that integrate the assignment of activities to infrastructure elements. An application of this is railway timetabling, as station and platform capacities are limited and need to be taken into account. We show that an assignment of activities to platforms can always be made periodic, and that it can be beneficial to allow larger periods for the assignment than for the timetable. We present mixed-integer programming formulations for the general problem, as well as for the practically relevant case when multiple platforms can be considered equivalent, for which we present a bipartite matching approach. We finally test and compare these models on real-world instances.}, language = {en} }