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  <doc>
    <id>6037</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-12-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Presolve Reductions in Mixed Integer Programming</title>
    <abstract language="eng">Mixed integer programming has become a very powerful tool for modeling and&#13;
solving real-world planning and scheduling problems, with the breadth of&#13;
applications appearing to be almost unlimited.   A critical component in&#13;
the solution of these mixed-integer programs is a set of routines commonly&#13;
referred to as presolve.  Presolve can be viewed as a collection of&#13;
preprocessing techniques that reduce the size of and, more importantly,&#13;
improve the ``strength'' of the given model formulation, that is, the degree&#13;
to which the constraints of the formulation accurately describe the&#13;
underlying polyhedron of integer-feasible solutions.  As our computational&#13;
results will show, presolve is a key factor in the speed with which we can&#13;
solve mixed-integer programs, and is often the difference between a model&#13;
being intractable and solvable, in some cases easily solvable.  In this&#13;
paper we describe the presolve functionality in the Gurobi commercial&#13;
mixed-integer programming code.&#13;
This includes an overview, or taxonomy of the different methods that are&#13;
employed, as well as more-detailed descriptions of several of the techniques,&#13;
with some of them appearing, to our knowledge, for the first time in the&#13;
literature.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60370</identifier>
    <author>Tobias Achterberg</author>
    <submitter>Tobias Achterberg</submitter>
    <author>Robert E. Bixby</author>
    <author>Zonghao Gu</author>
    <author>Edward Rothberg</author>
    <author>Dieter Weninger</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integer programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>presolving</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gurobi</value>
    </subject>
    <collection role="ccs" number="D.">Software</collection>
    <collection role="msc" number="90-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="90C11">Mixed integer programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="achterberg">Achterberg, Tobias</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</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/6037/Presolve.pdf</file>
  </doc>
</export-example>
