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    <publishedDate>2024-10-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Sorting Criteria for Line-based Periodic Timetabling Heuristics</title>
    <abstract language="eng">It is well-known that optimal solutions are notoriously hard to find for the Periodic Event Scheduling Problem (PESP), which is the standard mathematical formulation to optimize periodic timetables in public transport. We consider a class of incremental heuristics that have been demonstrated to be effective by Lindner and Liebchen (2023), however, for only one fixed sorting strategy of lines along which a solution is constructed. Thus, in this paper, we examine a variety of sortings based on the number, weight, weighted span, and lower bound of arcs, and test for each setting various combinations of the driving, dwelling, and transfer arcs of lines. Additionally, we assess the impact on the incremental extension of the event-activity network by minimizing resp. maximizing a connectivity measure between subsets of lines. We compare our 27 sortings on the railway instances of the benchmarking library PESPlib within the ConcurrentPESP solver framework. We are able to find five new incumbent solutions, resulting in improvements of up to 2%.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-97826</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2024-10-07</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="SourceTitle">to appear in Operations Research Proceedings 2024</enrichment>
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    <author>Patricia Ebert</author>
    <submitter>Niels Lindner</submitter>
    <author>Berenike Masing</author>
    <author>Niels Lindner</author>
    <author>Ambros Gleixner</author>
    <series>
      <title>ZIB-Report</title>
      <number>24-07</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Public Transport</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Timetabling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Periodic Event Scheduling</value>
    </subject>
    <collection role="ccs" number="J.">Computer Applications</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="institutes" number="aim">Applied Algorithmic Intelligence Methods</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="persons" number="masing">Masing, Berenike</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="Mathplus-PaA3">Mathplus-PaA3</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/9782/ZR-24-07.pdf</file>
  </doc>
  <doc>
    <id>8953</id>
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    <language>eng</language>
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    <completedDate>--</completedDate>
    <publishedDate>2023-01-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Approximating the RSRP with Predictive Maintenance</title>
    <abstract language="eng">We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for two instances derived from real world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-89531</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <author>Ralf Borndörfer</author>
    <author>Boris Grimm</author>
    <author>Alexander Tesch</author>
    <series>
      <title>ZIB-Report</title>
      <number>23-04</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Rolling Stock Rotation Planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Predictive Maintenance</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Integer Linear Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Heuristic</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Lower Bound</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="grimm">Grimm, Boris</collection>
    <collection role="persons" number="tesch">Tesch, Alexander</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="prause">Prause, Felix</collection>
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    <file>https://opus4.kobv.de/opus4-zib/files/8953/ZR-23-04.pdf</file>
  </doc>
  <doc>
    <id>9313</id>
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    <language>eng</language>
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    <publishedDate>2023-12-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Multi-Swap Heuristic for Rolling Stock Rotation Planning with Predictive Maintenance</title>
    <abstract language="eng">We present a heuristic solution approach for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). The task of this problem is to assign a sequence of trips to each of the vehicles&#13;
and to schedule their maintenance such that all trips can be operated. Here, the health states of the vehicles are considered to be random variables distributed by a family of probability distribution functions, and the maintenance services should be scheduled based on the failure probability of the vehicles. The proposed algorithm first generates a solution by solving an integer linear program and then heuristically improves this solution by applying a local search procedure. For this purpose, the trips assigned to the vehicles are split up and recombined, whereby additional deadhead trips can be inserted between the partial assignments. Subse-&#13;
quently, the maintenance is scheduled by solving a shortest path problem in a state-expanded version of a space-time graph restricted to the trips of the individual vehicles. The solution approach is tested and evaluated on a set of test instances based on real-world timetables.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-93133</identifier>
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    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>23-29</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Rolling stock rotation planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Predictive maintenance</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Heuristic</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>State-expanded graph model</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Integer linear program</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="prause">Prause, Felix</collection>
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    <file>https://opus4.kobv.de/opus4-zib/files/9313/ZR-23-29.pdf</file>
  </doc>
  <doc>
    <id>9602</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
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    <language>eng</language>
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    <title language="eng">An Iterative Refinement Approach for the Rolling Stock Rotation Problem with Predictive Maintenance</title>
    <abstract language="eng">The rolling stock rotation problem with predictive maintenance (RSRP-PdM) involves the assignment of trips to a fleet of vehicles with integrated maintenance scheduling based on the predicted failure probability of the vehicles. These probabilities are determined by the health states of the vehicles, which are considered to be random variables distributed by a parameterized family of probability distribution functions. During the operation of the trips, the corresponding parameters get updated. In this article, we present a dual solution approach for RSRP-PdM and generalize a linear programming based lower bound for this problem to families of probability distribution functions with more than one parameter. For this purpose, we define a rounding function that allows for a consistent underestimation of the parameters and model the problem by a state-expanded event-graph in which the possible states are restricted to a discrete set. This induces a flow problem that is solved by an integer linear program. We show that the iterative refinement of the underlying discretization leads to solutions that converge from below to an optimal solution of the original instance. Thus, the linear relaxation of the considered integer linear program results in a lower bound for RSRP-PdM. Finally, we report on the results of computational experiments conducted on a library of test instances.</abstract>
    <identifier type="arxiv">2404.08367</identifier>
    <enrichment key="SubmissionStatus">under review</enrichment>
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    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <author>Ralf Borndörfer</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
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  </doc>
  <doc>
    <id>9603</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
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    <language>eng</language>
    <pageFirst>58</pageFirst>
    <pageLast>63</pageLast>
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    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Multi-Swap Heuristic for Rolling Stock Rotation Planning with Predictive Maintenance</title>
    <abstract language="eng">We present a heuristic solution approach for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). The task of this problem is to assign a sequence of trips to each of the vehicles and to schedule their maintenance such that all trips can be operated. Here, the health states of the vehicles are considered to be random variables distributed by a family of probability distribution functions, and the maintenance services should be scheduled based on the failure probability of the vehicles. The proposed algorithm first generates a solution by solving an integer linear program and then heuristically improves this solution by applying a local search procedure. For this purpose, the trips assigned to the vehicles are split up and recombined, whereby additional deadhead trips can be inserted between the partial assignments. Subsequently, the maintenance is scheduled by solving a shortest path problem in a state-expanded version of a space-time graph restricted to the trips of the individual vehicles. The solution approach is tested and evaluated on a set of test instances based on real-world timetables.</abstract>
    <parentTitle language="eng">Proceedings of the 11th International Network Optimization Conference (INOC), Dublin, Ireland, March 11-23, 2024</parentTitle>
    <identifier type="doi">10.48786/inoc.2024.11</identifier>
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    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-93133</enrichment>
    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
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  <doc>
    <id>9556</id>
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    <publishedYear>2024</publishedYear>
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    <language>eng</language>
    <pageFirst>100434</pageFirst>
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    <edition/>
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    <volume>30</volume>
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    <title language="eng">Approximating rolling stock rotations with integrated predictive maintenance</title>
    <abstract language="eng">We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PdM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for six instances derived from real-world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions.</abstract>
    <parentTitle language="eng">Journal of Rail Transport Planning &amp; Management</parentTitle>
    <identifier type="doi">10.1016/j.jrtpm.2024.100434</identifier>
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    <enrichment key="AcceptedDate">2024-02-28</enrichment>
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    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <author>Ralf Borndörfer</author>
    <author>Boris Grimm</author>
    <author>Alexander Tesch</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="grimm">Grimm, Boris</collection>
    <collection role="persons" number="tesch">Tesch, Alexander</collection>
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  </doc>
  <doc>
    <id>9173</id>
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    <language>eng</language>
    <pageFirst/>
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    <edition/>
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    <completedDate>--</completedDate>
    <publishedDate>2023-07-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Construction of a Test Library for the Rolling Stock Rotation Problem with Predictive Maintenance</title>
    <abstract language="eng">We describe the development of a test library for the rolling stock rotation problem with predictive maintenance (RSRP-PdM). Our approach involves the utilization of genuine timetables from a private German railroad company. The generated instances incorporate probability distribution functions for modeling the health states of the vehicles and the considered trips possess varying degradation functions. RSRP-PdM involves assigning trips to a fleet of vehicles and scheduling their maintenance based on their individual health states. The goal is to minimize the total costs consisting of operational costs and the expected costs associated with vehicle failures. The failure probability is dependent on the health states of the vehicles, which are assumed to be random variables distributed by a family of probability distributions. Each distribution is represented by the parameters characterizing it and during the operation of the trips, these parameters get altered. Our approach incorporates non-linear degradation functions to describe the inference of the parameters but also linear ones could be applied. The resulting instances consist of the timetables of the individual lines that use the same vehicle type. Overall, we employ these assumptions and utilize open-source data to create a library of instances with varying difficulty. Our approach is vital for evaluating and comparing algorithms designed to solve the RSRP-PdM.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-91734</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <author>Ralf Borndörfer</author>
    <series>
      <title>ZIB-Report</title>
      <number>23-20</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Rolling Stock Rotation Planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Predictive Maintenance</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Test Library</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
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    <file>https://opus4.kobv.de/opus4-zib/files/9173/ZR-23-20.pdf</file>
  </doc>
  <doc>
    <id>9773</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>13:1</pageFirst>
    <pageLast>13:19</pageLast>
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    <volume>123</volume>
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    <completedDate>2024-10-07</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance</title>
    <abstract language="eng">We consider the rolling stock rotation planning problem with predictive maintenance (RSRP-PdM), where a timetable given by a set of trips must be operated by a fleet of vehicles. Here, the health states of the vehicles are assumed to be random variables, and their maintenance schedule should be planned based on their predicted failure probabilities. Utilizing the Bayesian update step of the Kalman filter, we develop a rolling horizon approach for RSRP-PdM, in which the predicted health state distributions are updated as new data become available. This approach reduces the uncertainty of the health states and thus improves the decision-making basis for maintenance planning. To solve the instances, we employ a local neighborhood search, which is a modification of a heuristic for RSRP-PdM, and demonstrate its effectiveness. Using this solution algorithm, the presented approach is compared with the results of common maintenance strategies on test instances derived from real-world timetables. The obtained results show the benefits of the rolling horizon approach.</abstract>
    <parentTitle language="eng">24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2024.13</identifier>
    <enrichment key="Series">Open Access Series in Informatics (OASIcs)</enrichment>
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    <enrichment key="SubmissionStatus">epub ahead of print</enrichment>
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    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <author>Ralf Borndörfer</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
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  </doc>
  <doc>
    <id>9785</id>
    <completedYear/>
    <publishedYear>2025</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>348</pageFirst>
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    <publisherName/>
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    <contributingCorporation/>
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    <completedDate>2025-08-12</completedDate>
    <publishedDate>--</publishedDate>
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    <title language="eng">Sorting Criteria for Line-based Periodic Timetabling Heuristics</title>
    <abstract language="eng">It is well-known that optimal solutions are notoriously hard to find for the Periodic Event Scheduling Problem (PESP), which is the standard mathematical formulation to optimize periodic timetables in public transport. We consider a class of incremental heuristics that have been demonstrated to be effective by Lindner and Liebchen (2023), however, for only one fixed sorting strategy of lines along which a solution is constructed. Thus, in this paper, we examine a variety of sortings based on the number, weight, weighted span, and lower bound of arcs, and test for each setting various combinations of the driving, dwelling, and transfer arcs of lines. Additionally, we assess the impact on the incremental extension of the event-activity network by minimizing resp. maximizing a connectivity measure between subsets of lines. We compare our 27 sortings on the railway instances of the benchmarking library PESPlib within the ConcurrentPESP solver framework. We are able to find five new incumbent solutions, resulting in improvements of up to 2%.</abstract>
    <parentTitle language="eng">Operations Research Proceedings 2024. OR 2024</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-10-07</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-97826</enrichment>
    <enrichment key="Series">Lecture Notes in Operations Research</enrichment>
    <author>Patricia Ebert</author>
    <submitter>Niels Lindner</submitter>
    <author>Berenike Masing</author>
    <author>Niels Lindner</author>
    <author>Ambros Gleixner</author>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="institutes" number="aim">Applied Algorithmic Intelligence Methods</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="persons" number="masing">Masing, Berenike</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="Mathplus-PaA3">Mathplus-PaA3</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <collection role="persons" number="Gleixner">Gleixner, Ambros</collection>
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