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  <doc>
    <id>4874</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2013-06-21</thesisDateAccepted>
    <title language="eng">Line Planning and Connectivity</title>
    <abstract language="eng">This thesis introduces the Steiner connectivity problem. It is a generalization of the well&#13;
known Steiner tree problem. Given a graph G = (V, E) and a subset T ⊆ V of the nodes,&#13;
the Steiner tree problem consists in finding a cost minimal set of edges connecting all&#13;
nodes in T . The Steiner connectivity problem chooses, instead of edges, from a given set&#13;
of paths a subset to connect all nodes in T . We show in the first part of this thesis that&#13;
main results about complexity, approximation, integer programming formulations, and&#13;
polyhedra can be generalized from the Steiner tree problem to the Steiner connectivity&#13;
problem.&#13;
An example for a straightforward generalization are the Steiner partition inequalities, a&#13;
fundamental class of facet defining inequalities for the Steiner tree problem. They can be&#13;
defined for the Steiner connectivity problem in an analogous way as for the Steiner tree&#13;
problem. An example for a generalization that needs more effort is the definition of a&#13;
directed cut formulation and the proof that this dominates the canonical undirected cut&#13;
formulation enriched by all Steiner partition inequalities. For the Steiner connectivity&#13;
problem this directed cut formulation leads to extended formulations, a concept that is&#13;
not necessary for the Steiner tree problem. There are also major differences between&#13;
both problems. For instance, the case T = V for the Steiner connectivity problem is&#13;
equivalent to a set covering problem and, hence, not a polynomial solvable case as in the&#13;
Steiner tree problem.&#13;
The Steiner connectivity problem is not only an interesting generalization of the Steiner&#13;
tree problem but also the underlying connectivity problem in line planning with inte-&#13;
grated passenger routing. The integrated line planning and passenger routing problem&#13;
is an important planning problem in service design of public transport and the topic of&#13;
the second part. Given is the infrastructure network of a public transport system where&#13;
the edges correspond to streets and tracks and the nodes correspond to stations/stops&#13;
of lines. The task is to find paths in the infrastructure network for lines and passengers&#13;
such that the capacities of the lines suffice to transport all passengers. Existing models&#13;
in the literature that integrate a passenger routing in line planning either treat transfers&#13;
in a rudimentary way and, hence, neglect an important aspect for the choice of the pas-&#13;
senger routes, or they treat transfers in a too comprehensive way and cannot be solved&#13;
for large scale real world problems. We propose a new model that focuses on direct&#13;
connections. The attractiveness of transfer free connections is increased by introducing a transfer penalty for each non-direct connection. In this way, a passenger routing is&#13;
computed that favors direct connections.&#13;
For the computation of this model we also implemented algorithms influenced by the&#13;
results for the Steiner connectivity problem. We can compute with our model good&#13;
solutions that minimize a weighted sum of line operating costs and passengers travel&#13;
times. These solutions improve the solutions of an existing approach, that does not&#13;
consider direct connections, by up to 17%. In contrast to a comprehensive approach,&#13;
that considers every transfer and for which we could not even solve the root LP within&#13;
10 hours for large instances, the solutions of the new model, computed in the same time,&#13;
are close to optimality (&lt;1%) or even optimal for real world instances. In a project with&#13;
the Verkehr in Potsdam GmbH to compute the line plan for 2010 we showed that our&#13;
approach is applicable in practice and can be used to solve real world problems.</abstract>
    <identifier type="isbn">978-3-8439-1062-0</identifier>
    <identifier type="url">www.zib.de/karbstein/scplpp.pdf</identifier>
    <advisor>Ralf Borndörfer</advisor>
    <author>Marika Karbstein</author>
    <submitter>Marika Karbstein</submitter>
    <advisor>Martin Grötschel</advisor>
    <collection role="msc" number="90B20">Traffic problems</collection>
    <collection role="msc" number="90C10">Integer programming</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
  </doc>
  <doc>
    <id>1018</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-10-15</completedDate>
    <publishedDate>2007-10-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Constraint Integer Programming</title>
    <abstract language="eng">This thesis introduces the novel paradigm of constraint integer programming (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method.</abstract>
    <abstract language="deu">Diese Arbeit stellt einen integrierten Ansatz aus Constraint Programming (CP) und Gemischt-Ganzzahliger Programmierung (Mixed Integer Programming, MIP) vor, den wir Constraint Integer Programming (CIP) nennen. Sowohl Modellierungs- als auch Lösungstechniken beider Felder fließen in den neuen integrierten Ansatz ein, um die unterschiedlichen Stärken der beiden Gebiete zu kombinieren. Als weiteren Beitrag stellen wir der wissenschaftlichen Gemeinschaft die Software SCIP zur Verfügung, die ein Framework für Constraint Integer Programming darstellt und zusätzlich Techniken des SAT-Lösens beinhaltet. SCIP ist im Source Code für akademische und nicht-kommerzielle Zwecke frei erhältlich. Unser Ansatz des Constraint Integer Programming ist eine Verallgemeinerung von MIP, die zusätzlich die Verwendung beliebiger Constraints erlaubt, solange sich diese durch lineare Bedingungen ausdrücken lassen falls alle ganzzahligen Variablen auf feste Werte eingestellt sind. Die Constraints werden von einer beliebigen Kombination aus CP- und MIP-Techniken behandelt. Dies beinhaltet insbesondere die Domain Propagation, die Relaxierung der Constraints durch lineare Ungleichungen, sowie die Verstärkung der Relaxierung durch dynamisch generierte Schnittebenen. Die derzeitige Version von SCIP enthält alle Komponenten, die für das effiziente Lösen von Gemischt-Ganzzahligen Programmen benötigt werden. Die vorliegende Arbeit liefert eine ausführliche Beschreibung dieser Komponenten und bewertet verschiedene Varianten in Hinblick auf ihren Einfluß auf das Gesamt-Lösungsverhalten anhand von aufwendigen praktischen Experimenten. Dabei wird besonders auf die algorithmischen Aspekte eingegangen. Der zweite Hauptteil der Arbeit befasst sich mit der Chip-Design-Verifikation, die ein wichtiges Thema innerhalb des Fachgebiets der Electronic Design Automation darstellt. Chip-Hersteller müssen sicherstellen, dass der logische Entwurf einer Schaltung der gegebenen Spezifikation entspricht. Andernfalls würde der Chip fehlerhaftes Verhalten aufweisen, dass zu Fehlfunktionen innerhalb des Gerätes führen kann, in dem der Chip verwendet wird. Ein wichtiges Teilproblem in diesem Feld ist das Eigenschafts-Verifikations-Problem, bei dem geprüft wird, ob der gegebene Schaltkreisentwurf eine gewünschte Eigenschaft aufweist. Wir zeigen, wie dieses Problem als Constraint Integer Program modelliert werden kann und geben eine Reihe von problemspezifischen Algorithmen an, die die Struktur der einzelnen Constraints und der Gesamtschaltung ausnutzen. Testrechnungen auf Industrie-Beispielen vergleichen unseren Ansatz mit den bisher verwendeten SAT-Techniken und belegen den Erfolg unserer Methode.</abstract>
    <identifier type="opus3-id">1038</identifier>
    <identifier type="urn">urn:nbn:de:kobv:83-opus-16117</identifier>
    <author>Tobias Achterberg</author>
    <submitter>unknown unknown</submitter>
    <advisor>Martin Grötschel</advisor>
    <advisor>Robert E. Bixby</advisor>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Ganzzahlige Programmierung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Constraint Programmierung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>SAT</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Chip-Verifikation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integer programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>constraint programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>SAT</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>chip verification</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="ccs" number="B.8.1">Reliability, Testing, and Fault-Tolerance (NEW)</collection>
    <collection role="ccs" number="G.1.6">Optimization</collection>
    <collection role="msc" number="90C10">Integer programming</collection>
    <collection role="msc" number="90C11">Mixed integer programming</collection>
    <collection role="collections" number="">Dissertationen</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="achterberg">Achterberg, Tobias</collection>
    <collection role="projects" number="VeriCount">VeriCount</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
    <file>https://opus4.kobv.de/opus4-zib/files/1018/achterberg_tobias.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1018/Achterberg_Constraint_Integer_ProgrammingDissZweite_Vers.pdf</file>
  </doc>
  <doc>
    <id>1040</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-06-14</completedDate>
    <publishedDate>2007-06-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Design of Survivable Optical Networks by Mathematical Optimization</title>
    <abstract language="eng">Abstract The cost-efficient design of survivable optical telecommunication networks is the topic of this thesis. In cooperation with network operators, we have developed suitable concepts and mathematical optimization methods to solve this comprehensive planning task in practice. Optical technology is more and more employed in modern telecommunication networks. Digital information is thereby transmitted as short light pulses through glass fibers. Moreover, the optical medium allows for simultaneous transmissions on a single fiber by use of different wavelengths. Recent optical switches enable a direct forwarding of optical channels in the network nodes without the previously required signal retransformation to electronics. Their integration creates ongoing optical connections,which are called lightpaths. We study the problem of finding cost-efficient configurations of optical networks which meet specified communication requirements. A configuration comprises the determination of all lightpaths to establish as well as the detailed allocation of all required devices and systems. We use a flexible modeling framework for a realistic representation of the networks and their composition. For different network architectures, we formulate integer linear programs which model the design task in detail. Moreover, network survivability is an important issue due to the immense bandwidths offered by optical technology. Operators therefore request for designs which perpetuate protected connections and guarantee for a defined minimum throughput in case of malfunctions. In order to achieve an effective realization of scalable protection, we present a novel survivability concept tailored to optical networks and integrate several variants into the models. Our solution approach is based on a suitable model decomposition into two subtasks which separates two individually hard subproblems and enables this way to compute cost-efficient designs with approved quality guarantee. The first subtask consists of routing the connections with corresponding dimensioning of capacities and constitutes a common core task in the area of network planning. Sophisticated methods for such problems have already been developed and are deployed by appropriate integration. The second subtask is characteristic for optical networks and seeks for a conflict-free assignment of available wavelengths to the lightpaths using a minimum number of involved wavelength converters. For this coloring-like task, we derive particular models and study methods to estimate the number of unavoidable conversions. As constructive approach, we develop heuristics and an exact branch-and-price algorithm. Finally, we carry out an extensive computational study on realistic data, provided by our industrial partners. As twofold purpose, we demonstrate the potential of our approach for computing good solutions with quality guarantee, and we exemplify its flexibility for application to network design and analysis.</abstract>
    <identifier type="opus3-id">1074</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10408</identifier>
    <enrichment key="SourceTitle">Ersch. als Buchveröffentlichung: Design of Survivable Optical Networks by Mathematical Optimization, (2007), Cuvillier, ISBN 978-3-86727-253-7.</enrichment>
    <author>Adrian Zymolka</author>
    <submitter>unknown unknown</submitter>
    <advisor>U. Pinkall</advisor>
    <advisor>Martin Grötschel</advisor>
    <advisor>Sven Krumke</advisor>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>network design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optical networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integer programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mathematical optimization</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="90B18">Communication networks [See also 68M10, 94A05]</collection>
    <collection role="msc" number="90C10">Integer programming</collection>
    <collection role="msc" number="90C35">Programming involving graphs or networks [See also 90C27]</collection>
    <collection role="msc" number="90C90">Applications of mathematical programming</collection>
    <collection role="collections" number="">Dissertationen</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
    <file>https://opus4.kobv.de/opus4-zib/files/1040/Dissertation_Zymolka.pdf</file>
  </doc>
  <doc>
    <id>5095</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2014-05-27</thesisDateAccepted>
    <title language="eng">The Hypergraph Assignment Problem</title>
    <abstract language="eng">This thesis deals with the hypergraph assignment problem (HAP), a set partitioning problem in a special type of hypergraph. The HAP generalizes the assignment problem from bipartite graphs to what we call bipartite hypergraphs, and is motivated by applications in railway vehicle rotation planning. The main contributions of this thesis concern complexity, polyhedral results, analyses of random instances, and primal methods for the HAP. We prove that the HAP is NP-hard and APX-hard even for small hyperedge sizes and hypergraphs with a special partitioned structure. We also study the complexity of the set packing and covering relaxations of the HAP, and present for certain cases polynomial exact or approximation algorithms. A complete linear description is known for the assignment problem. We therefore also study the HAP polytope. There, we have a huge number of facet-defining inequalities already for a very small problem size. We describe a method for dividing the inequalities into equivalence classes without resorting to a normal form. Within each class, facets are related by certain symmetries and it is sufficient to list one representative of each class to give a complete picture of the structural properties of the polytope. We propose the algorithm "HUHFA" for the classification that is applicable not only to the HAP but combinatorial optimization problems involving symmetries in general. In the largest possible HAP instance for which we could calculate the complete linear description, we have 14049 facets, which can be divided into 30 symmetry classes. We can combinatorially interpret 16 of these classes. This is possible by employing cliques to generalize the odd set inequalities for the matching problem. The resulting inequalities are valid for the polytope associated with the set packing problem in arbitrary hypergraphs and have a clear combinatorial meaning. An analysis of random instances provides a better insight into the structure of hyperassignments. Previous work has extensively analyzed random instances for the assignment problem theoretically and practically. As a generalization of these results for the HAP, we prove bounds on the expected value of a minimum cost hyperassignment that uses half of the maximum possible number of hyperedges that are not edges. In a certain complete partitioned hypergraph G2,2n with i. i. d. exponential random variables with mean 1 as hyperedge costs it lies between 0.3718 and 1.8310 if the vertex number tends to infinity. Finally, we develop an exact combinatorial solution algorithm for the HAP that combines three methods: A very large-scale neighborhood search, the composite columns method for the set partitioning problem, and the network simplex algorithm.</abstract>
    <abstract language="deu">Diese Arbeit beschäftigt sich mit dem Hypergraph Assignment Problem (Abkürzung "HAP", dt.: Zuordnungsproblem auf Hypergraphen), einem Mengenzerlegungsproblem auf einem speziellen Typ von Hypergraphen. Das HAP verallgemeinert das Zuordnungsproblem von bipartiten Graphen auf eine Struktur, die wir bipartite Hypergraphen nennen, und ist durch eine Anwendung in der Umlaufplanung im Schienenverkehr motiviert. Die Hauptresultate betreffen die Komplexität, polyedrische Ergebnisse, die Analyse von Zufallsinstanzen sowie primale Methoden für das HAP. Wir beweisen, dass das HAP NP-schwer und APX-schwer ist, sogar wenn wir uns auf kleine Hyperkantengrößen und Hypergraphen mit einer speziellen, partitionierten Struktur beschränken. Darüber hinaus untersuchen wir die Komplexität der Mengenpackungs- sowie Mengenüberdeckungsrelaxierung und geben für bestimmte Fälle Approximations- und exakte Algorithmen mit einer polynomiellen Laufzeit an. Für das Polytop des Zuordnungsproblems ist eine vollständige lineare Beschreibung bekannt. Wir untersuchen daher auch das HAP-Polytop. Dafür ist die Anzahl der Facettenungleichungen schon für sehr kleine Problemgrößen sehr groß. Wir beschreiben eine Methode zur Aufteilung der Ungleichungen in Äquivalenzklassen, die ohne die Verwendung von Normalformen auskommt. Die Facetten in jeder Klasse können durch Symmetrien ineinander überführt werden. Es genügt, einen Repräsentanten aus jeder Klasse anzugeben, um ein vollständiges Bild der Polytopstruktur zu erhalten. Wir beschreiben den Algorithmus "HUHFA", der diese Klassifikation nicht nur für das HAP, sondern für beliebige kombinatorische Optimierungsprobleme, die Symmetrien enthalten, durchführt. Die größtmögliche HAP-Instanz, für die wir die vollständige lineare Beschreibung berechnen konnten, hat 14049 Facetten, die in 30 Symmetrieklassen aufgeteilt werden können. Wir können 16 dieser Klassen kombinatorisch interpretieren. Dafür verallgemeinern wir Odd-Set-Ungleichungen für das Matchingproblem unter Verwendung von Cliquen. Die Ungleichungen, die wir erhalten, sind gültig für Mengenpackungsprobleme in beliebigen Hypergraphen und haben eine klare kombinatorische Bedeutung. Die Analyse von Zufallsinstanzen erlaubt einen besseren Einblick in die Struktur von Hyperzuordnungen. Eine solche ausführliche Analyse wurde in der Literatur theoretisch und praktisch bereits für das Zuordnungsproblem durchgeführt. Als eine Verallgemeinerung dieser Ergebnisse für das HAP beweisen wir Schranken für den Erwartungswert einer Hyperzuordnung mit minimalen Kosten, die genau die Hälfte der maximal möglichen Anzahl an Hyperkanten, die keine Kanten sind, benutzt. In einem sog. vollständigen partitionierten Hypergraphen G2,2n mit Hyperkantenkosten, die durch unabhängig identisch exponentiell verteilte Zufallsvariablen mit Erwartungswert 1 bestimmt sind, liegt dieser Wert zwischen 0.3718 und 1.8310, wenn die Knotenanzahl gegen unendlich strebt. Schließlich entwickeln wir eine exakte kombinatorische Lösungsmethode für das HAP, die drei Ansätze kombiniert: Eine Nachbarschaftssuche mit Nachbarschaften exponentieller Größe, die Composite-Columns-Methode für das Mengenzerlegungsproblem sowie den Netzwerksimplexalgorithmus.</abstract>
    <identifier type="url">http://opus4.kobv.de/opus4-tuberlin/frontdoor/index/index/docId/5321</identifier>
    <advisor>Ralf Borndörfer</advisor>
    <author>Olga Heismann</author>
    <submitter>Olga Heismann</submitter>
    <advisor>Martin Grötschel</advisor>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>assignment</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bipartite</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyperassignment</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hypergraph</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>set partitioning</value>
    </subject>
    <collection role="msc" number="05C65">Hypergraphs</collection>
    <collection role="msc" number="52B15">Symmetry properties of polytopes</collection>
    <collection role="msc" number="90C10">Integer programming</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="projects" number="MATHEON-B22">MATHEON-B22</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
  </doc>
</export-example>
