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  <doc>
    <id>8932</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName>TU Berlin</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mathematical programming for stable control and safe operation of gas transport networks</title>
    <abstract language="eng">The fight against climate change makes extreme but inevitable changes in the energy sector necessary. These in turn lead to novel and complex challenges for the transmission system operators (TSOs) of gas transport networks. In this thesis, we consider four different planning problems emerging from real-world operations and present mathematical programming models and solution approaches for all of them.&#13;
Due to regulatory requirements and side effects of renewable energy production, controlling today's gas networks with their involved topologies is becoming increasingly difficult. Based on the network station modeling concept for approximating the technical capabilities of complex subnetworks, e.g., compressor stations, we introduce a tri-level MIP model to determine important global control decisions. Its goal is to avoid changes in the network elements' settings while deviations from future inflow pressures as well as supplies and demands are minimized. A sequential linear programming inspired post-processing routine is run to derive physically accurate solutions w.r.t. the transient gas flow in pipelines. Computational experiments based on real-world data show that meaningful solutions are quickly and reliably determined. Therefore, the algorithmic approach is used within KOMPASS, a decision support system for the transient network control that we developed together with the Open Grid Europe GmbH (OGE), one of Europe's largest natural gas TSOs.&#13;
Anticipating future use cases, we adapt the aforementioned algorithmic approach for hydrogen transport. We investigate whether the natural gas infrastructure can be repurposed and how the network control changes when energy-equivalent amounts of hydrogen are transported. Besides proving the need for purpose-built compressors, we observe that, due to the reduced linepack, the network control becomes more dynamic, compression energy increases by 440% on average, and stricter regulatory rules regarding the balancing of supply and demand become necessary.&#13;
Extreme load flows expose the technical limits of gas networks and are therefore of great importance to the TSOs. In this context, we introduce the Maximum Transportation Problem and the Maximum Potential Transport Moment Problem to determine severe transport scenarios. Both can be modeled as linear bilevel programs where the leader selects supplies and demands, maximizing the follower's transport effort. To solve them, we identify solution-equivalent instances with acyclic networks, provide variable bounds regarding their KKT reformulations, apply the big-M technique, and solve the resulting MIPs. A case study shows that the obtained scenarios exceed the maximum severity values of a provided test set by at least 23%.&#13;
OGE's transmission system is 11,540km long. Monitoring it is crucial for safe operations. To this end, we discuss the idea of using uncrewed aerial vehicles and introduce the Length-Constrained Cycle Partition Problem to optimize their routing. Its goal is to find a smallest cycle partition satisfying vertex-induced length requirements. Besides a greedy-style heuristic, we propose two MIP models. Combining them with symmetry-breaking constraints as well as valid inequalities and lower bounds from conflict hypergraphs yields a highly performant solution algorithm for this class of problems.</abstract>
    <identifier type="url">https://doi.org/10.14279/depositonce-15837</identifier>
    <identifier type="doi">10.14279/depositonce-15837</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <advisor>Thorsten Koch</advisor>
    <author>Kai Hoppmann-Baum</author>
    <submitter>Kai Hoppmann-Baum</submitter>
    <collection role="persons" number="hennig">Hoppmann, Kai</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="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>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
  </doc>
  <doc>
    <id>6691</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>411</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2017-02-03</thesisDateAccepted>
    <title language="eng">Exploiting structure in non-convex quadratic optimization and gas network planning under uncertainty</title>
    <abstract language="eng">The amazing success of computational mathematical optimization over&#13;
the last decades has been driven more by insights into mathematical&#13;
structures than by the advance of computing technology. In this vein,&#13;
we address applications, where nonconvexity in the model and&#13;
uncertainty in the data pose principal difficulties.&#13;
&#13;
The first part of the thesis deals with non-convex quadratic programs.&#13;
Branch&amp;Bound methods for this problem class depend on tight&#13;
relaxations. We contribute in several ways: First, we establish a new&#13;
way to handle missing linearization variables in the well-known&#13;
Reformulation-Linearization-Technique (RLT). This is implemented&#13;
into the commercial software CPLEX. Second, we study the optimization&#13;
of a quadratic objective over the standard simplex or a knapsack&#13;
constraint. These basic structures appear as part of many complex&#13;
models. Exploiting connections to the maximum clique problem and RLT,&#13;
we derive new valid inequalities. Using exact and heuristic separation&#13;
methods, we demonstrate the impact of the new inequalities on the&#13;
relaxation and the global optimization of these problems. Third, we&#13;
strengthen the state-of-the-art relaxation for the pooling problem, a&#13;
well-known non-convex quadratic problem, which is, for example,&#13;
relevant in the petrochemical industry. We propose a novel relaxation&#13;
that captures the essential non-convex structure of the problem but is&#13;
small enough for an in-depth study. We provide a complete inner&#13;
description in terms of the extreme points as well as an outer&#13;
description in terms of inequalities defining its convex hull (which&#13;
is not a polyhedron). We show that the resulting valid convex&#13;
inequalities significantly strengthen the standard relaxation of the&#13;
pooling problem.&#13;
&#13;
The second part of this thesis focuses on a common challenge in real&#13;
world applications, namely, the uncertainty entailed in the input&#13;
data.&#13;
We study the extension of a gas transport network, e.g., from our&#13;
project partner Open Grid Europe GmbH.&#13;
For a single scenario this maps to a challenging non-convex MINLP.&#13;
As the future transport patterns are highly uncertain, we propose a&#13;
robust model to best prepare the network operator for an array of&#13;
scenarios.&#13;
We develop a custom decomposition approach that makes use of the&#13;
hierarchical structure of network extensions and the loose coupling&#13;
between the scenarios.&#13;
The algorithm used the single-scenario problem as black-box subproblem&#13;
allowing the generalization of our approach to problems with the same&#13;
structure.&#13;
The scenario-expanded version of this problem is out of reach for&#13;
today's general-purpose MINLP solvers.&#13;
Yet our approach provides primal and dual bounds for instances with up&#13;
to 256 scenarios and solves many of them to optimality.&#13;
&#13;
Extensive computational studies show the impact of our work.</abstract>
    <abstract language="deu">Der bemerkenswerte Erfolg der angewandten mathematischen Optimierung&#13;
in den letzten Dekaden ist mehr auf Einsichten in mathematische&#13;
Strukturen zurückzuführen, als auf eine Steigerung der Rechenleistung.&#13;
In diesem Sinne adressieren wir Anwendungen, in denen Nichtkonvexität&#13;
und Unsicherheit in den Daten die Hauptschwierigkeiten darstellen.&#13;
&#13;
Der erste Teil dieser Arbeit beschäftigt sich mit nichtkonvexen&#13;
quadratischen Optimierungsproblemen. Relaxierungen sind integraler&#13;
Bestandteil von \BranchAndBound{}-Lösungsmethoden für diese&#13;
Problemkategorie. Wir leisten folgende Beiträge: Erstens beschreiben&#13;
wir eine neue Art fehlende Linearisierungsvariablen, in der so&#13;
genannten Reformulation-Linearization-Technique (RLT), zu behandeln.&#13;
Diese wird inzwischen in der kommerziellen Software CPLEX verwendet.&#13;
Zweitens beschäftigen wir uns mit der Optimierung einer quadratischen&#13;
Zielfunktion über die Standardsimplex oder einen so genannten&#13;
Knapsack-Constraint. Solche grundlegenden Strukturen sind Teil vieler&#13;
komplexer Modelle. Wir benutzen bekannte Verbindungen zum maximalen&#13;
Cliquenproblem sowie zu RLT, um neue gültige Ungleichungen&#13;
herzuleiten, die die Relaxierung verstärken. Drittens beschäftigen wir uns mit dem&#13;
Pooling Problem, das z.B. in der Erdölindustrie relevant ist. Wie&#13;
leiten eine neue Relaxierung her, die die wesentliche nicht-konvexe&#13;
Struktur des Problems erfasst, aber klein genug für eine grundlegende&#13;
Untersuchung ist. Wir geben eine innere Beschreibung in Form der&#13;
Extrempunkte, sowie eine äußere Beschreibung in Form von Ungleichungen,&#13;
die die konvexe Hülle (welche im Allgemeinen kein Polyeder ist)&#13;
beschreiben, an. Wir zeigen, dass neuen die Ungleichungen die Relaxierung&#13;
des Pooling Problems erheblich verstärken.&#13;
&#13;
Der zweite Teil der Arbeit befasst sich mit einer weiteren&#13;
Herausforderung in realen Anwendungen, nämlich Unsicherheit in den&#13;
Eingabedaten. Konkret untersuchen wir die Optimierung des Ausbaus&#13;
eines Gastransportnetzes, wie z.B. von unserem Projektpartner Open&#13;
Grid Europe GmbH. Dieses Problem ist bereits bei gegebenen&#13;
Eingabedaten ein schweres nicht-konvexes gemischt-ganzzahliges&#13;
Optimierungsproblem. Da zukünftige Nutzungsmuster des Netzes mit&#13;
großer Unsicherheit behaftet sind, beschreiben wir ein robustes&#13;
Modell, um den Netzbetreiber gegen verschiedene Szenarien abzusichern.&#13;
Wir entwickeln einen speziellen Dekompositionsalgorithmus unter&#13;
Berücksichtigung der hierarchischen Struktur der Ausbauten und der&#13;
schwachen Kopplung zwischen den Szenarien. Unser Ansatz liefert primale &#13;
und duale Schranken für Instanzen mit bis&#13;
zu 256 Szenarien und löst viele beweisbar optimal.&#13;
&#13;
Umfangreiche Rechnungen bestätigen die Effizient der&#13;
vorgestellten Methoden.</abstract>
    <identifier type="url">http://dx.doi.org/10.14279/depositonce-6015</identifier>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <advisor>Thorsten Koch</advisor>
    <author>Jonas Schweiger</author>
    <submitter>Jonas Schweiger</submitter>
    <advisor>Andrea Lodi</advisor>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonconvexity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Uncertainty</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Quadratic Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Relaxations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cutting Planes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Standard Quadratic Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Pooling Problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gas Network Planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Robust Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Computations</value>
    </subject>
    <collection role="msc" number="90-02">Research exposition (monographs, survey articles)</collection>
    <collection role="msc" number="90C20">Quadratic programming</collection>
    <collection role="msc" number="90C26">Nonconvex programming, global optimization</collection>
    <collection role="msc" number="90C90">Applications of mathematical programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="MODAL-GasLab">MODAL-GasLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="schweiger">Schweiger, Jonas</collection>
    <collection role="institutes" number="enernet">Energy Network Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
  </doc>
</export-example>
