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    <issue/>
    <volume>44</volume>
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    <completedDate>2021-11-19</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimization of Capacity Expansion in Potential-driven Networks including Multiple Looping - A comparison of modelling approaches</title>
    <abstract language="eng">In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called "potential-driven" network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones ("looping"). &#13;
The paper introduces a new mixed-integer non-linear programming (MINLP) model and a new non-linear programming (NLP) model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally.&#13;
On this basis, we give recommendations about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models.&#13;
Moreover, the paper is the first to include the practically relevant option that a particular pipeline may be looped several times.</abstract>
    <parentTitle language="eng">OR Spectrum</parentTitle>
    <identifier type="doi">https://doi.org/10.1007/s00291-021-00648-7</identifier>
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    <enrichment key="AcceptedDate">26.07.2021</enrichment>
    <author>Ralf Lenz</author>
    <submitter>Milena Petkovic</submitter>
    <author>Kai-Helge Becker</author>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
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    <collection role="projects" number="MODAL-EnergyLab">MODAL-EnergyLab</collection>
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  <doc>
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    <language>eng</language>
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    <publishedDate>2021-04-15</publishedDate>
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    <title language="eng">Pipe Merging for Transient Gas Network Problems</title>
    <abstract language="eng">In practice, transient gas transport problems frequently have to be solved for large-scale gas networks. Gas network optimization problems typically belong to the class of Mixed-Integer Nonlinear Programming Problems (MINLP). However current state-of-the-art MINLP solvers are not yet mature enough to solve large-scale real-world instances. Therefore, an established approach in practice is to solve the problems with respect to a coarser representation of the network and thereby reducing the size of the underlying model. Two well-known aggregation methods that effectively reduce the network size are parallel and serial pipe merges. However, these methods have only been studied in stationary gas transport problems so far. This paper closes this gap and presents parallel and serial pipe merging methods in the context of transient gas transport. To this end, we introduce the concept of equivalent and heuristic subnetwork replacements. For the heuristic methods, we conduct a huge empirical evaluation based on real-world data taken from one of the largest gas networks in Europe. It turns out that both, parallel and serial pipe merging can be considered as appropriate aggregation methods for real-world transient gas flow problems.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-82116</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Lenz</author>
    <submitter>Ralf Lenz</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>21-10</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pipe merging</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Network aggregation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gas network optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Transient gas flow transport</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonlinear Programming</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aim">Applied Algorithmic Intelligence Methods</collection>
    <collection role="projects" number="MODAL-EnergyLab">MODAL-EnergyLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8211/ZR_21-10.pdf</file>
  </doc>
  <doc>
    <id>7363</id>
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    <language>eng</language>
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    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2019-06-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Operation of Transient Gas Transport Networks</title>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-73639</identifier>
    <author>Kai Hoppmann</author>
    <submitter>Kai Hoppmann</submitter>
    <author>Felix Hennings</author>
    <author>Ralf Lenz</author>
    <author>Uwe Gotzes</author>
    <author>Nina Heinecke</author>
    <author>Klaus Spreckelsen</author>
    <author>Thorsten Koch</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-23</number>
    </series>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="hennig">Hoppmann, Kai</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/7363/Netmodel_Paper.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/7363/Netmodel_Paper_v2.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/7363/Netmodel_Paper_v3.pdf</file>
  </doc>
  <doc>
    <id>8519</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
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    <type>doctoralthesis</type>
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    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2021-05-06</thesisDateAccepted>
    <title language="eng">Optimization of Stationary Expansion Planning and Transient Network Control by Mixed-Integer Nonlinear Programming</title>
    <identifier type="doi">10.14279/depositonce-12765</identifier>
    <identifier type="url">http://dx.doi.org/10.14279/depositonce-12765</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Lenz</author>
    <submitter>Janina Zittel</submitter>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aim">Applied Algorithmic Intelligence Methods</collection>
    <collection role="projects" number="MODAL-EnergyLab">MODAL-EnergyLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
  </doc>
  <doc>
    <id>8008</id>
    <completedYear>2020</completedYear>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>735</pageFirst>
    <pageLast>781</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>22</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>0021-02-16</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Operation of Transient Gas Transport Networks</title>
    <abstract language="eng">In this paper, we describe an algorithmic framework for the optimal operation of transient gas transport networks consisting of a hierarchical MILP formulation together with a sequential linear programming inspired post-processing routine. Its implementation is part of the KOMPASS decision support system, which is currently used in an industrial setting.&#13;
&#13;
Real-world gas transport networks are controlled by operating complex pipeline intersection areas, which comprise multiple compressor units, regulators, and valves. In the following, we introduce the concept of network stations to model them. Thereby, we represent the technical capabilities of a station by hand-tailored artificial arcs and add them to network. Furthermore, we choose from a predefined set of flow directions for each network station and time step, which determines where the gas enters and leaves the station. Additionally, we have to select a supported simple state, which consists of two subsets of artificial arcs: Arcs that must and arcs that cannot be used. The goal is to determine a stable control of the network satisfying all supplies and demands.&#13;
&#13;
The pipeline intersections, that are represented by the network stations, were initially built centuries ago. Subsequently, due to updates, changes, and extensions, they evolved into highly complex and involved topologies. To extract their basic properties and to model them using computer-readable and optimizable descriptions took several years of effort.&#13;
&#13;
To support the dispatchers in controlling the network, we need to compute a continuously  updated list of recommended measures. Our motivation for the model presented here is to make fast decisions on important transient global control parameters, i.e., how to route the flow and where to compress the gas. Detailed continuous and discrete technical control measures realizing them, which take all hardware details into account, are determined in a subsequent step. &#13;
&#13;
In this paper, we present computational results from the KOMPASS project using detailed real-world data.</abstract>
    <parentTitle language="eng">Optimization and Engineering</parentTitle>
    <identifier type="doi">10.1007/s11081-020-09584-x</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-73639</enrichment>
    <author>Kai Hoppmann-Baum</author>
    <submitter>Kai Hoppmann-Baum</submitter>
    <author>Felix Hennings</author>
    <author>Ralf Lenz</author>
    <author>Uwe Gotzes</author>
    <author>Nina Heinecke</author>
    <author>Klaus Spreckelsen</author>
    <author>Thorsten Koch</author>
    <collection role="persons" number="hennig">Hoppmann, Kai</collection>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="Mathematical Algorithmic Intelligence">Mathematical Algorithmic Intelligence</collection>
    <collection role="institutes" number="aim">Applied Algorithmic Intelligence Methods</collection>
    <collection role="projects" number="MODAL-EnergyLab">MODAL-EnergyLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>8665</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>325</pageFirst>
    <pageLast>352</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>194</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Tight Convex Relaxations for the Expansion Planning Problem</title>
    <abstract language="eng">Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem. A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improves the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58%.</abstract>
    <parentTitle language="eng">Journal of Optimization Theory and Applications</parentTitle>
    <identifier type="doi">10.1007/s10957-022-02029-8</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">20.03.2022</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-81459</enrichment>
    <author>Ralf Lenz</author>
    <submitter>Janina Zittel</submitter>
    <author>Felipe Serrano</author>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aim">Applied Algorithmic Intelligence Methods</collection>
    <collection role="projects" number="MODAL-EnergyLab">MODAL-EnergyLab</collection>
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  </doc>
  <doc>
    <id>6972</id>
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    <language>eng</language>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-07-31</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimization of Capacity Expansion in Potential-driven Networks including Multiple Looping - A comparison of modelling approaches</title>
    <abstract language="eng">In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called "potential-driven" network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones ("looping"). &#13;
The paper introduces a new mixed-integer non-linear programming (MINLP) model and a new non-linear programming (NLP) model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally.&#13;
On this basis, we give recommendations about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models.&#13;
Moreover, the paper is the first to include the practically relevant option that a particular pipeline may be looped several times.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-69726</identifier>
    <identifier type="doi">10.1007/s00291-021-00648-7</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-69726</enrichment>
    <author>Ralf Lenz</author>
    <submitter>Ralf Lenz</submitter>
    <author>Kai-Helge Becker</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>OR in energy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Network expansion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MINLP</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="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="projects" number="ECMATH-MI10">ECMATH-MI10</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6972/ZR_18_44.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/6972/ZR_18_44_revised.pdf</file>
  </doc>
  <doc>
    <id>8145</id>
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    <language>eng</language>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-02-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Tight Convex Relaxations for the Expansion Planning Problem</title>
    <abstract language="eng">Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem.&#13;
A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improve the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58%.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-81459</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Lenz</author>
    <submitter>Ralf Lenz</submitter>
    <author>Felipe Serrano</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-05</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convex envelopes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Nonlinear Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Expansion planning of energy networks</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="Mathematical Algorithmic Intelligence">Mathematical Algorithmic Intelligence</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8145/ZR_21-05.pdf</file>
  </doc>
  <doc>
    <id>6156</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
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    <publisherName/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-12-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Looping of Pipelines in Gas Networks</title>
    <abstract language="eng">In this paper, we compare several approaches for the problem of gas network expansions using loops, that is, to build new pipelines in parallel to existing ones. We present different model formulations for the problem of continuous loop expansions as well as discrete loop expansions. We then analyze problem properties, such as the structure and convexity of the underlying feasible regions. The paper concludes with a computational study comparing the continuous and the discrete formulations.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61564</identifier>
    <author>Ralf Lenz</author>
    <submitter>Ralf Lenz</submitter>
    <author>Robert Schwarz</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-67</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed Integer Nonlinear Programming</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Gas Network Applications</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Expansion Planning</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="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6156/ZR-16-67.pdf</file>
  </doc>
  <doc>
    <id>5349</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>SIAM-MOS series on Optimization</volume>
    <type>bookpart</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Computational results for validation of nominations</title>
    <abstract language="eng">The different approaches to solve the validation of nomination problem presented in the previous chapters are evaluated computationally in this chapter. Each approach is analyzed individually, as well as the complete solvers for these problems. We demonstrate that the presented approaches can successfully solve large-scale real-world instances.</abstract>
    <parentTitle language="eng">Evaluating Gas Network Capacities</parentTitle>
    <identifier type="isbn">9781611973686</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Benjamin Hiller</author>
    <submitter>Jesco Humpola</submitter>
    <author>Jesco Humpola</author>
    <author>Thomas Lehmann</author>
    <author>Ralf Lenz</author>
    <author>Antonio Morsi</author>
    <author>Marc Pfetsch</author>
    <author>Lars Schewe</author>
    <author>Martin Schmidt</author>
    <author>Robert Schwarz</author>
    <author>Jonas Schweiger</author>
    <author>Claudia Stangl</author>
    <author>Bernhard Willert</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="lenz">Lenz, Ralf</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="ForNe">ForNe</collection>
    <collection role="projects" number="TRR154-A04">TRR154-A04</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
</export-example>
