<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>6648</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>74</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>masterthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mixed-Integer Programming for Clustering in Non-reversible Markov Processes</title>
    <abstract language="eng">The topic of this thesis is the examination of an optimization model&#13;
which stems from the clustering process of non-reversible markov processes.&#13;
We introduce the cycle clustering problem und formulate it as a mixed&#13;
integer program (MIP).&#13;
We prove that this problem is N P-hard and discuss polytopal aspects&#13;
such as facets and dimension. The focus of this thesis is the development of&#13;
solving methods for this clustering problem. We develop problem specific&#13;
primal heuristics, as well as separation methods and an approximation&#13;
algorithm. These techniques are implemented in practice as an application&#13;
for the MIP solver SCIP.&#13;
Our computational experiments show that these solving methods result&#13;
in an average speedup of ×4 compared to generic solvers and that our&#13;
application is able to solve more instances to optimality within the given&#13;
time limit of one hour.</abstract>
    <identifier type="urn">urn:nbn:de:0297-zib-66486</identifier>
    <advisor>Thorsten Koch</advisor>
    <author>Leon Eifler</author>
    <submitter>Leon Eifler</submitter>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>NESS</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Non-reversible Markov Processes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Programming</value>
    </subject>
    <collection role="msc" number="60-XX">PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)</collection>
    <collection role="msc" number="82-XX">STATISTICAL MECHANICS, STRUCTURE OF MATTER</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="SparseApproxiTN">SparseApproxiTN</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
    <file>https://opus4.kobv.de/opus4-zib/files/6648/main.pdf</file>
  </doc>
</export-example>
