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    <title language="eng">Handbook of Optimization in the Railway Industry</title>
    <abstract language="eng">This book promotes the use of mathematical optimization and operations research methods in rail transportation.  The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art.&#13;
&#13;
There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational.  These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning.  Individual chapters cover:&#13;
&#13;
Simulation&#13;
&#13;
Capacity Assessment&#13;
&#13;
Network Design&#13;
&#13;
Train Routing&#13;
&#13;
Robust Timetabling&#13;
&#13;
Event Scheduling&#13;
&#13;
Track Allocation&#13;
&#13;
Blocking&#13;
&#13;
Shunting&#13;
&#13;
Rolling Stock&#13;
&#13;
Crew Scheduling&#13;
&#13;
Dispatching&#13;
&#13;
Delay Propagation</abstract>
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    <author>Erwin Abbink</author>
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    <editor>Torsten Klug</editor>
    <author>Nikola Bešinovic</author>
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    <editor>Carlo Mannino</editor>
    <author>Markus Bohlin</author>
    <editor>Markus Reuther</editor>
    <author>Valentina Cacchiani</author>
    <author>Gabrio Caimi</author>
    <editor>Thomas Schlechte</editor>
    <author>Stefano de Fabris</author>
    <author>Twan Dollevoet</author>
    <author>Frank Fischer</author>
    <author>Armin Fügenschuh</author>
    <author>Laura Galli</author>
    <author>Rob M.P. Goverde</author>
    <author>Ronny Hansmann</author>
    <author>Henning Homfeld</author>
    <author>Dennis Huisman</author>
    <author>Marc Johann</author>
    <author>Torsten Klug</author>
    <author>Johanna Törnquist Krasemann</author>
    <author>Leo Kroon</author>
    <author>Leonardo Lamorgese</author>
    <author>Frauke Liers</author>
    <author>Carlo Mannino</author>
    <author>Giorgio Medeossi</author>
    <author>Dario Pacciarelli</author>
    <author>Markus Reuther</author>
    <author>Thomas Schlechte</author>
    <author>Marie Schmidt</author>
    <author>Anita Schöbel</author>
    <author>Hanno Schülldorf</author>
    <author>Anke Stieber</author>
    <author>Sebastian Stiller</author>
    <author>Paolo Toth</author>
    <author>Uwe Zimmermann</author>
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    <title language="eng">Strong Relaxations for the Train Timetabling Problem using Connected Configurations</title>
    <abstract language="eng">The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral.</abstract>
    <parentTitle language="deu">17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)</parentTitle>
    <identifier type="isbn">978-3-95977-042-2</identifier>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2017.11</identifier>
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    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <editor>Gianlorenzo D'Angelo</editor>
    <submitter>Thomas Schlechte</submitter>
    <author>Frank Fischer</author>
    <editor>Twan Dollevoet</editor>
    <author>Thomas Schlechte</author>
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    <pageFirst>645</pageFirst>
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    <title language="eng">A Re-optimization Approach for Train Dispatching</title>
    <abstract language="eng">The Train Dispatching Problem (TDP) is to schedule trains through a network in a cost optimal way. Due to disturbances during operation existing track allocations often have to be re-scheduled and integrated into the timetable. This has to be done in seconds and with minimal timetable changes to guarantee smooth and conflict free operation. We present an integrated modeling approach for the re-optimization task using Mixed Integer Programming. Finally, we provide computational results for scenarios provided by the INFORMS RAS Problem Soling Competition 2012.</abstract>
    <parentTitle language="eng">Operations Research Proceedings 2016</parentTitle>
    <identifier type="doi">10.1007/978-3-319-55702-1_85</identifier>
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    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-60493</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <submitter>Thomas Schlechte</submitter>
    <author>Frank Fischer</author>
    <author>Boris Grimm</author>
    <author>Torsten Klug</author>
    <author>Thomas Schlechte</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="grimm">Grimm, Boris</collection>
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    <title language="eng">Strong Relaxations for the Train Timetabling Problem using Connected Configurations</title>
    <abstract language="eng">The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-64743</identifier>
    <enrichment key="SourceTitle">Appeared in: 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)</enrichment>
    <author>Frank Fischer</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Thomas Schlechte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-46</number>
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    <title language="eng">A Re-optimization Approach for Train Dispatching</title>
    <abstract language="eng">The Train Dispatching Problem (TDP) is to schedule trains through a network in a cost optimal way. Due to disturbances during operation existing track allocations often have to be re-scheduled and integrated into the timetable. This has to be done in seconds and with minimal timetable changes to guarantee smooth and conflict free operation. &#13;
We present an integrated modeling approach for the re-optimization task using Mixed Integer Programming. Finally, we provide computational results for scenarios provided by the INFORMS RAS Problem Soling Competition 2012.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60493</identifier>
    <author>Frank Fischer</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Boris Grimm</author>
    <author>Torsten Klug</author>
    <author>Thomas Schlechte</author>
    <series>
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      <number>16-49</number>
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    <title language="eng">Comparing two dual relaxations of large scale train timetabling problems</title>
    <abstract language="eng">Railway transportation and in particular train timetabling is one of the basic and source application areas of combinatorial optimization and integer programming. We will discuss two well established modeling techniques for the train timetabling problem. In this paper we focus on one major ingredient - the bounding by dual relaxations. We compare two classical dual relaxations of large scale time expanded train timetabling problems - the Lagrangean Dual and Lagrangean Decomposition. We discuss the convergence behavior and show limitations of the Lagrangean Decomposition approach for a configuration based model. We introduce a third dualization approach to overcome those limitations. Finally, we present promising preliminary computational experiments that show that our new approach indeed has superior convergence properties.</abstract>
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    <identifier type="urn">urn:nbn:de:0297-zib-56068</identifier>
    <author>Frank Fischer</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Thomas Schlechte</author>
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      <number>15-43</number>
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    <title language="eng">Railway Track Allocation</title>
    <abstract language="eng">This chapter addresses the classical task to decide which train runs on which track in a railway network. In this context a track allocation defines the precise routing of trains through a railway network, which usually has only a limited capacity.&#13;
Moreover, the departure and arrival times at the visited stations of each train must simultaneously meet several operational and safety requirements.&#13;
The problem to find the 'best possible' allocation for all trains&#13;
is called the track allocation problem (TTP).&#13;
Railway systems can be modeled on a very detailed scale covering the behavior of individual trains and the safety system to a large extent. However, those microscopic models are too big and not scalable to large networks, which make them inappropriate for mathematical optimization on a network wide level. Hence, most network optimization approaches consider simplified, so called macroscopic, models. In the first part we take a look at the challenge to construct a reliable and condensed macroscopic model for the associated microscopic model and to facilitate the transition between both models of different scale.&#13;
In the main part we focus on the optimization problem for macroscopic models of the railway system. Based on classical graph-theoretical tools the track allocation problem is formulated to determine conflict-free paths in corresponding time-expanded graphs. We present standard integer programming model formulations for the track allocation problem that model resource or block conflicts in terms of packing constraints. In addition, we discuss the role of maximal clique inequalities and the concept of configuration networks. We will also present classical decomposition approaches like Lagrangian relaxation and bundle methods. Furthermore, we will discuss recently developed techniques, e.g., dynamic graph generation.&#13;
Finally, we will discuss the status quo and show a vision of mathematical optimization to support real world track allocation, i.e. integrated train routing and scheduling, in a data-dominated&#13;
and digitized railway future.</abstract>
    <parentTitle language="eng">Handbook of Optimization in the Railway Industry</parentTitle>
    <identifier type="isbn">978-3-319-72152-1</identifier>
    <identifier type="doi">https://doi.org/10.1007/978-3-319-72153-8</identifier>
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    <author>Gabrio Caimi</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Frank Fischer</author>
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    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
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    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
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    <completedDate>2015-07-23</completedDate>
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    <title language="eng">Comparing two dual relaxations of large scale train timetabling problems</title>
    <abstract language="eng">Railway transportation and in particular train timetabling is one of the basic and source application areas of combinatorial optimization and integer programming. We will discuss two well established modeling techniques for the train timetabling problem. In this paper we focus on one major ingredient - the bounding by dual relaxations. We compare two classical dual relaxations of large scale time expanded train timetabling problems - the Lagrangean Dual and Lagrangean Decomposition. We discuss the convergence behavior and show limitations of the Lagrangean Decomposition approach for a configuration based model. We introduce a third dualization approach to overcome those limitations. Finally, we present promising preliminary computational experiments that show that our new approach indeed has superior convergence properties.</abstract>
    <parentTitle language="eng">Proceedings of Conference on Advanced Systems in Public Transport 2015</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-56068</enrichment>
    <author>Frank Fischer</author>
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    <author>Thomas Schlechte</author>
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    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
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