8 Search Results for "Reuther, Markus"

Document
DOI: 10.4230/LIPIcs.GD.2025.39
Optimizing Wiggle in Storylines

Authors: Alexander Dobler, Tim Hegemann, Martin Nöllenburg, and Alexander Wolff

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
A storyline visualization shows interactions between characters over time. Each character is represented by an x-monotone curve. Time is mapped to the x-axis, and groups of characters that interact at a particular point t in time must be ordered consecutively in the y-dimension at x = t. The predominant objective in storyline optimization so far has been the minimization of crossings between (blocks of) characters. Building on this work, we investigate another important, but less studied quality criterion, namely the minimization of wiggle, i.e., the amount of vertical movement of the characters over time. Given a storyline instance together with an ordering of the characters at any point in time, we show that wiggle count minimization is NP-complete. In contrast, we provide algorithms based on mathematical programming to solve linear wiggle height minimization and quadratic wiggle height minimization efficiently. Finally, we introduce a new method for routing character curves that focuses on keeping distances between neighboring curves constant as long as they run in parallel. We have implemented our algorithms, and we conduct a case study that explores the differences between the three optimization objectives. We use existing benchmark data, but we also present a new use case for storylines, namely the visualization of rolling stock schedules in railway operation.
Cite as

Alexander Dobler, Tim Hegemann, Martin Nöllenburg, and Alexander Wolff. Optimizing Wiggle in Storylines. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dobler_et_al:LIPIcs.GD.2025.39,
  author =	{Dobler, Alexander and Hegemann, Tim and N\"{o}llenburg, Martin and Wolff, Alexander},
  title =	{{Optimizing Wiggle in Storylines}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.39},
  URN =		{urn:nbn:de:0030-drops-250252},
  doi =		{10.4230/LIPIcs.GD.2025.39},
  annote =	{Keywords: Storyline visualization, wiggle minimization, NP-complete, linear programming, quadratic programming, experimental analysis}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2025.14
Using A* for Optimal Train Routing on Moving Block Systems

Authors: Stefan Engels and Robert Wille

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
Modern control systems based on Moving Block allow for shorter headways and higher capacity on existing railway infrastructure. At the same time, few algorithms for optimal routing on networks equipped with such modern control systems exist. Previous methods rely on Mixed Integer Linear Programming (MILP) and face a trade-off between model size and accuracy, especially considering comparably complex and nonlinear headway constraints as well as train dynamics. With this work, we propose a complementary approach based on A*. Under a reasonable and easy assumption on train driver behavior, we propose a solution encoding and state space that is flexible concerning the choice of search algorithm and the modeling detail. The applicability is showcased on a small benchmark set. The implementation is available open-source as part of the Munich Train Control Toolkit (MTCT) on GitHub at https://github.com/cda-tum/mtct.
Cite as

Stefan Engels and Robert Wille. Using A* for Optimal Train Routing on Moving Block Systems. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{engels_et_al:OASIcs.ATMOS.2025.14,
  author =	{Engels, Stefan and Wille, Robert},
  title =	{{Using A* for Optimal Train Routing on Moving Block Systems}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{14:1--14:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.14},
  URN =		{urn:nbn:de:0030-drops-247701},
  doi =		{10.4230/OASIcs.ATMOS.2025.14},
  annote =	{Keywords: ETCS, Train Routing, Moving Block, A*, Munich Train Control Toolkit}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2022.11
Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling

Authors: Torsten Klug, Markus Reuther, and Thomas Schlechte

Published in: OASIcs, Volume 106, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)

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 [T. Schlechte et al., 2022], 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 [Gurobi Optimization, 2022]. 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.
Cite as

Torsten Klug, Markus Reuther, and Thomas Schlechte. Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 11:1-11:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{klug_et_al:OASIcs.ATMOS.2022.11,
  author =	{Klug, Torsten and Reuther, Markus and Schlechte, Thomas},
  title =	{{Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling}},
  booktitle =	{22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)},
  pages =	{11:1--11:8},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-259-4},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{106},
  editor =	{D'Emidio, Mattia and Lindner, Niels},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2022.11},
  URN =		{urn:nbn:de:0030-drops-171159},
  doi =		{10.4230/OASIcs.ATMOS.2022.11},
  annote =	{Keywords: Moving Block, Railway Track Allocation, Timetabling, Train Routing}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2019.1
A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance

Authors: Boris Grimm, Ralf Borndörfer, Markus Reuther, and Thomas Schlechte

Published in: OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)

Abstract
For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see [Maróti and Kroon, 2005; Gábor Maróti and Leo G. Kroon, 2007], or [Cordeau et al., 2001] for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in [Ralf Borndörfer et al., 2015]. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of [Reuther, 2017] that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values.
Cite as

Boris Grimm, Ralf Borndörfer, Markus Reuther, and Thomas Schlechte. A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 1:1-1:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{grimm_et_al:OASIcs.ATMOS.2019.1,
  author =	{Grimm, Boris and Bornd\"{o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas},
  title =	{{A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{1:1--1:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-128-3},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{75},
  editor =	{Cacchiani, Valentina and Marchetti-Spaccamela, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.1},
  URN =		{urn:nbn:de:0030-drops-114136},
  doi =		{10.4230/OASIcs.ATMOS.2019.1},
  annote =	{Keywords: Railway Operations Research, Integer Programming, Infeasible Path Cuts, Cut Separation, Rolling Stock Rotation Problem}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.111
Regional Search for the Resource Constrained Assignment Problem

Authors: Ralf Borndörfer and Markus Reuther

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
The resource constrained assignment problem (RCAP) is to find a minimal cost partition of the nodes of a directed graph into cycles such that a resource constraint is fulfilled. The RCAP has its roots in rolling stock rotation optimization where a railway timetable has to be covered by rotations, i.e., cycles. In that context, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes variants of the vehicle routing problem (VRP). The paper contributes an exact branch and bound algorithm for the RCAP and, primarily, a straightforward algorithmic concept that we call regional search (RS). As a symbiosis of a local and a global search algorithm, the result of an RS is a local optimum for a combinatorial optimization problem. In addition, the local optimum must be globally optimal as well if an instance of a problem relaxation is computed. In order to present the idea for a standardized setup we introduce an RS for binary programs. But the proper contribution of the paper is an RS that turns the Hungarian method into a powerful heuristic for the resource constrained assignment problem by utilizing the exact branch and bound. We present computational results for RCAP instances from an industrial cooperation with Deutsche Bahn Fernverkehr AG as well as for VRP instances from the literature. The results show that our RS provides a solution quality of 1.4 % average gap w.r.t. the best known solutions of a large test set. In addition, our branch and bound algorithm can solve many RCAP instances to proven optimality, e.g., almost all asymmetric traveling salesman and capacitated vehicle routing problems that we consider.
Cite as

Ralf Borndörfer and Markus Reuther. Regional Search for the Resource Constrained Assignment Problem. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 111-129, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2015.111,
  author =	{Bornd\"{o}rfer, Ralf and Reuther, Markus},
  title =	{{Regional Search for the Resource Constrained Assignment Problem}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{111--129},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.111},
  URN =		{urn:nbn:de:0030-drops-54536},
  doi =		{10.4230/OASIcs.ATMOS.2015.111},
  annote =	{Keywords: assignment problem, local search, branch and bound, rolling stock rota- tion problem, vehicle routing problem}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2014.62
Local Search for the Resource Constrained Assignment Problem

Authors: Markus Reuther

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
The resource constrained assignment problem (RCAP) is to find a minimal cost cycle partition in a directed graph such that a resource constraint is fulfilled. The RCAP has its roots in an application that deals with the covering of a railway timetable by rolling stock vehicles. Here, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes several variants of vehicle routing problems. We contribute a local search algorithm for this problem that is derived from an exact algorithm which is similar to the Hungarian method for the standard assignment problem. Our algorithm can be summarized as a k-OPT heuristic, exchanging k arcs of an alternating cycle of the incumbent solution in each improvement step. The alternating cycles are found by dual arguments from linear programming. We present computational results for instances from our railway application at Deutsche Bahn Fernverkehr AG as well as for instances of the vehicle routing problem from the literature.
Cite as

Markus Reuther. Local Search for the Resource Constrained Assignment Problem. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. 62-78, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{reuther:OASIcs.ATMOS.2014.62,
  author =	{Reuther, Markus},
  title =	{{Local Search for the Resource Constrained Assignment Problem}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{62--78},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.62},
  URN =		{urn:nbn:de:0030-drops-47538},
  doi =		{10.4230/OASIcs.ATMOS.2014.62},
  annote =	{Keywords: Assignment Problem, Local Search, Rolling Stock Rotation Problem, Vehicle Routing Problem}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2014.79
A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem

Authors: Ralf Borndörfer, Markus Reuther, and Thomas Schlechte

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems.
Cite as

Ralf Borndörfer, Markus Reuther, and Thomas Schlechte. A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. 79-91, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2014.79,
  author =	{Bornd\"{o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas},
  title =	{{A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation  Problem}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{79--91},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.79},
  URN =		{urn:nbn:de:0030-drops-47549},
  doi =		{10.4230/OASIcs.ATMOS.2014.79},
  annote =	{Keywords: Coarse-To-Fine Linear Programming, Rolling Stock Rotation Problem}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2011.146
A Hypergraph Model for Railway Vehicle Rotation Planning

Authors: Ralf Borndörfer, Markus Reuther, Thomas Schlechte, and Steffen Weider

Published in: OASIcs, Volume 20, 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2011)

Abstract
We propose a model for the integrated optimization of vehicle rotations and vehicle compositions in long distance railway passenger transport. The main contribution of the paper is a hypergraph model that is able to handle the challenging technical requirements as well as very general stipulations with respect to the "regularity" of a schedule. The hypergraph model directly generalizes network flow models, replacing arcs with hyperarcs. Although NP-hard in general, the model is computationally well-behaved in practice. High quality solutions can be produced in reasonable time using high performance Integer Programming techniques, in particular, column generation and rapid branching. We show that, in this way, large-scale real world instances of our cooperation partner DB Fernverkehr can be solved.
Cite as

Ralf Borndörfer, Markus Reuther, Thomas Schlechte, and Steffen Weider. A Hypergraph Model for Railway Vehicle Rotation Planning. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 20, pp. 146-155, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2011.146,
  author =	{Bornd\"{o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas and Weider, Steffen},
  title =	{{A Hypergraph Model for Railway Vehicle Rotation Planning}},
  booktitle =	{11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{146--155},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-33-0},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{20},
  editor =	{Caprara, Alberto and Kontogiannis, Spyros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2011.146},
  URN =		{urn:nbn:de:0030-drops-32746},
  doi =		{10.4230/OASIcs.ATMOS.2011.146},
  annote =	{Keywords: Rolling Stock Planning, Hypergraph Modeling, Integer Programming, Column Generation, Rapid Branching}
}
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