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<export-example>
  <doc>
    <id>453</id>
    <completedYear>2019</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-11-15</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modeling Hydrogen Networks for Future Energy Systems: A Comparison of Linear and Nonlinear Approaches</title>
    <abstract language="eng">Common energy system models that integrate hydrogen transport in pipelines typically simplify fluid flow models and reduce the network size in order to achieve solutions quickly. This contribution analyzes two different types of pipeline network topologies (namely, star and tree networks) and two different fluid flow models (linear and nonlinear) for a given hydrogen capacity scenario of electrical reconversion in Germany to analyze the impact of these simplifications. For each network topology, robust demand and supply scenarios are generated. The results show that a simplified topology, as well as the consideration of detailed fluid flow, could heavily influence the total pipeline investment costs. For the given capacity scenario, an overall cost reduction of the pipeline costs of 37% is observed for the star network with linear cost compared to the tree network with nonlinear fluid flow. The impact of these improvements regarding the total electricity reconversion costs has led to a cost reduction of 1.4%, which is fairly small. Therefore, the integration of nonlinearities into energy system optimization models is not recommended due to their high computational burden. However, the applied method for generating robust demand and supply scenarios improved the credibility and robustness of the network topology, while the simplified fluid flow consideration can lead to infeasibilities. Thus, we suggest the utilization of the nonlinear model for post- processing to prove the feasibility of the results and strengthen their credibility, while retaining the computational performance of linear modeling.</abstract>
    <parentTitle language="deu">International Journal of Hydrogen Energy</parentTitle>
    <identifier type="doi">10.1016/j.ijhydene.2019.10.080</identifier>
    <enrichment key="SubmissionStatus">Published</enrichment>
    <licence>Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International</licence>
    <author>Markus Reuß</author>
    <author>Lara Welder</author>
    <author>Johannes Thürauf</author>
    <author>Jochen Linßen</author>
    <author>Thomas Grube</author>
    <author>Lars Schewe</author>
    <author>Martin Schmidt</author>
    <author>Detlef Stolten</author>
    <author>Martin Robinius</author>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">B07</collection>
    <collection role="subprojects" number="">B08</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/453/Modeling_Hydrogen_Networks_for_Energy_Systems.pdf</file>
  </doc>
  <doc>
    <id>550</id>
    <completedYear>2024</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2024-04-06</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adjustable Robust Nonlinear Network Design under Demand Uncertainties</title>
    <abstract language="eng">We study network design problems for nonlinear and nonconvex flow models under demand uncertainties. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many, demand scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear optimization problem, we show that a given network design is robust feasible, i.e., it admits a feasible transport for all demand uncertainties, if and only if a finite number of worst-case demand scenarios can be routed through the network. We compute these worst-case scenarios by solving polynomially many nonlinear optimization problems. Embedding this result for robust feasibility in an adversarial approach leads to an exact algorithm that computes an optimal robust network design in a finite number of iterations. Since all of the results are valid for general potential-based flows, the approach can be applied to different utility networks such as gas, hydrogen, or water networks. We finally demonstrate the applicability of the method by computing robust gas networks that are protected from future demand fluctuations.</abstract>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Johannes Thürauf</author>
    <author>Julia Grübel</author>
    <author>Martin Schmidt</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Robust Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonlinear Flows</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Potential-based Networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Demand Uncertainties</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-integer Nonlinear Optimization</value>
    </subject>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <collection role="institutes" number="">Technische Universität Nürnberg</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/550/adjustable-robust-nonlinear-network-design.pdf</file>
  </doc>
  <doc>
    <id>484</id>
    <completedYear>2022</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>16</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2022-02-02</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On a Computationally Ill-Behaved Bilevel Problem with a Continuous and Nonconvex Lower Level</title>
    <abstract language="eng">It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to solving bilevel problems with continuous but nonconvex lower levels. Even if the lower-level problem is solved to ɛ-feasibility regarding its nonlinear constraints for an arbitrarily small but positive ɛ, the obtained bilevel solution as well as its objective value may be arbitrarily far away from the actual bilevel solution and its actual objective value. This result even holds for bilevel problems for which the nonconvex lower level is uniquely solvable, for which the strict complementarity condition holds, for which the feasible set is convex, and for which Slater's constraint qualification is satisfied for all feasible upper-level decisions. Since the consideration of ɛ-feasibility cannot be avoided when solving nonconvex problems to global optimality, our result shows that computational bilevel optimization with continuous and nonconvex lower levels needs to be done with great care. Finally, we illustrate that the nonlinearities in the lower level are the key reason for the observed bad behavior by showing that linear bilevel problems behave much better at least on the level of feasible solutions.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Yasmine Beck</author>
    <author>Martin Schmidt</author>
    <author>Johannes Thürauf</author>
    <author>Daniel Bienstock</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bilevel optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonconvex lower levels</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Approximate feasibility</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Global optimization</value>
    </subject>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/484/nearly-feasible-bilevel-preprint.pdf</file>
  </doc>
  <doc>
    <id>502</id>
    <completedYear>2022</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>28</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2022-10-19</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Exact Method for Nonlinear Network Flow Interdiction Problems</title>
    <abstract language="eng">We study network flow interdiction problems with nonlinear and nonconvex flow models. The resulting model is a max-min bilevel optimization problem in which the follower's problem is nonlinear and nonconvex. In this game, the leader attacks a limited number of arcs with the goal to maximize the load shed and the follower aims at minimizing the load shed by solving a transport problem in the interdicted network. We develop an exact algorithm consisting of lower and upper bounding schemes that computes an optimal interdiction under the assumption that the interdicted network remains weakly connected. The main challenge consists of computing valid upper bounds for the maximal load shed, whereas lower bounds can directly be derived from the follower's problem. To compute an upper bound, we propose solving a specific bilevel problem, which is derived from restricting the flexibility of the follower when adjusting the load flow. This bilevel problem still has a nonlinear and nonconvex follower's problem, for which we then prove necessary and sufficient optimality conditions. Consequently, we obtain equivalent single-level reformulations of the specific bilevel model to compute upper bounds. Our numerical results show the applicability of this exact approach using the example of gas networks.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Martin Schmidt</author>
    <author>Johannes Thürauf</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Interdiction Games</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bilevel Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Potential-Based Flows</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Nonlinear Optimization</value>
    </subject>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/502/potential-based-interdiction-games-r1.pdf</file>
  </doc>
  <doc>
    <id>614</id>
    <completedYear>2026</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>Springer-Nature</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2026-01-28</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Potential-Based Flows - An Overview</title>
    <abstract language="eng">Potential-based flows provide an algebraic way to model static physical flows&#13;
in networks, for example, in gas, water, and lossless DC power networks. The flow on an&#13;
arc in the network depends on the difference of the potentials at its end-nodes, possibly&#13;
in a nonlinear way. Potential-based flows have several nice properties like uniqueness&#13;
and acyclicity. The goal of this paper is to provide an overview of the current knowledge&#13;
on these models with a focus on optimization problems on such networks. We cover&#13;
basic properties, computational complexity, monotonicity, uncertain parameters, and&#13;
the corresponding behavior of the network as well as topology optimization.</abstract>
    <parentTitle language="eng">Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks</parentTitle>
    <enrichment key="SubmissionStatus">epub ahead of print</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Marc Pfetsch</author>
    <author>Martin Schmidt</author>
    <author>Martin Skutella</author>
    <author>Johannes Thürauf</author>
    <collection role="subprojects" number="">A01</collection>
    <collection role="subprojects" number="">A07</collection>
    <collection role="subprojects" number="">B08</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/614/ch_potential_preprint.pdf</file>
  </doc>
</export-example>
