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  <doc>
    <id>7814</id>
    <completedYear/>
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    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2020-04-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Estimating the Size of Branch-And-Bound Trees</title>
    <abstract language="eng">This paper investigates the estimation of the size of Branch-and-Bound (B&amp;B) trees for solving mixed-integer programs. We first prove that the size of the B&amp;B tree cannot be approximated within a factor of~2 for general binary programs, unless P equals NP. Second, we review measures of the progress of the B&amp;B search, such as the gap, and propose a new measure, which we call leaf frequency.&#13;
&#13;
We study two simple ways to transform these progress measures into B&amp;B tree size estimates, either as a direct projection, or via double-exponential smoothing, a standard time-series forecasting technique. We then combine different progress measures and their trends into nontrivial estimates using Machine Learning techniques, which yields more precise estimates than any individual measure. The best method we have identified uses all individual measures as features of a random forest model.&#13;
In a large computational study, we train and validate all methods on the publicly available MIPLIB and Coral general purpose benchmark sets. On average, the best method estimates B&amp;B tree sizes within a factor of 3 on the set of unseen test instances even during the early stage of the search, and improves in accuracy as the search progresses. It also achieves a factor 2 over the entire search on each out of six additional sets of homogeneous instances we have tested. All techniques are available in version 7 of the branch-and-cut framework SCIP.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-78144</identifier>
    <author>Gregor Hendel</author>
    <submitter>Gregor Hendel</submitter>
    <author>Daniel Anderson</author>
    <author>Pierre Le Bodic</author>
    <author>Marc Pfetsch</author>
    <series>
      <title>ZIB-Report</title>
      <number>20-02</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mixed integer programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>machine learning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>branch and bound</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>forecasting</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="hendel">Hendel, Gregor</collection>
    <collection role="projects" number="ASTfSCM">ASTfSCM</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="Siemens">Siemens</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/7814/zibreportestimatingSearchTreeSize.pdf</file>
  </doc>
  <doc>
    <id>5364</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>2015-12-02</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Computing D-optimal experimental designs for estimating treatment contrasts under the presence of a nuisance time trend</title>
    <abstract language="eng">We prove a mathematical programming characterisation of approximate partial D-optimality under general linear constraints. We use this characterisation with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.1007/978-3-319-13881-7_10</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-53640</identifier>
    <enrichment key="SourceTitle">Appeared in: Stochastic Models, Statistics and Their ApplicationsSpringer Proceedings in Mathematics &amp; Statistics Volume 122, 2015, pp 83-91</enrichment>
    <author>Radoslav Harman</author>
    <submitter>Guillaume Sagnol</submitter>
    <author>Guillaume Sagnol</author>
    <series>
      <title>ZIB-Report</title>
      <number>15-02</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal design of experiments</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nuisance trend</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>branch and bound</value>
    </subject>
    <collection role="msc" number="62-XX">STATISTICS</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="persons" number="sagnol">Sagnol, Guillaume</collection>
    <collection role="projects" number="ZIB-OptDes">ZIB-OptDes</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5364/POP-SMSA-ZIB.pdf</file>
  </doc>
  <doc>
    <id>685</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2002-04-08</completedDate>
    <publishedDate>2002-04-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Making the Yellow Angels Fly: Online Dispatching Of Service Vehicles in Real Time</title>
    <abstract language="eng">Combinatorial online optimization is an area with lots of applications and potential for significant progress, both in theory and practice. In this short note we sketch the ADACproblem, a typical large-scale online optimization problem, discuss some theoretical and pratical issues coming up, and explain, very briefly, how we approach this problem mathematically. Online problems are a battlefield of heuristics with many strong claims about their solution quality. We indicate that a stronger problem orientation and the use of a little more mathematics may yield.</abstract>
    <identifier type="serial">02-18</identifier>
    <identifier type="opus3-id">686</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6858</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM News, Vol. 35, No. 4, (2002) pp. 10-11</enrichment>
    <author>Martin Grötschel</author>
    <author>Sven Krumke</author>
    <author>Jörg Rambau</author>
    <author>Luis Miguel Torres</author>
    <series>
      <title>ZIB-Report</title>
      <number>02-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>vehicle dispatching</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>soft time windows</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>real-time</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>column generation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pricing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>branch and bound</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>real world data</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>ADAC</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90B06">Transportation, logistics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="projects" number="ADAC-Dispatch">ADAC-Dispatch</collection>
    <collection role="projects" number="MATHEON-C6:Online-Reopt">MATHEON-C6:Online-Reopt</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/685/ZR-02-18.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/685/ZR-02-18.pdf</file>
  </doc>
  <doc>
    <id>648</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2001-09-25</completedDate>
    <publishedDate>2001-09-25</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Real-Time Dispatching of Guided and Unguided Automobile Service Units with Soft Time Windows</title>
    <abstract language="eng">Given a set of service requests (events), a set of guided servers (units), and a set of unguided service contractors (conts), the vehicle dispatching problem {\sl vdp} is the task to find an assignment of events to units and conts as well as tours for all units starting at their current positions and ending at their home positions (dispatch) such that the total cost of the dispatch is minimized. The cost of a dispatch is the sum of unit costs, cont costs, and event costs. Unit costs consist of driving costs, service costs and overtime costs; cont costs consist of a fixed cost per service; event costs consist of late costs linear in the late time, which occur whenever the service of the event starts later than its deadline. The program \textsf{ZIBDIP} based on dynamic column generation and set partitioning yields solutions on heavy-load real-world instances (215 events, 95 units) in less than a minute that are no worse than 1\% from optimum on state-of-the-art personal computers.</abstract>
    <identifier type="serial">01-22</identifier>
    <identifier type="opus3-id">649</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6484</identifier>
    <enrichment key="SourceTitle">Appeared in: Algorithms - ESA 2002. Proceedings of the 10th European Symposium on Algorithms, Rome, Italy, September 17-21, 2002. R. Möhring et al. (eds.) Berlin: Springer 2002. LNCS 2461, pp. 637-648</enrichment>
    <author>Sven Krumke</author>
    <author>Jörg Rambau</author>
    <author>Luis Miguel Torres</author>
    <series>
      <title>ZIB-Report</title>
      <number>01-22</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>vehicle dispatching</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>soft time windows</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>real-time</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>column generation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pricing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>branch and bound</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>real world data</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>ADAC</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90B06">Transportation, logistics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="projects" number="ADAC-Dispatch">ADAC-Dispatch</collection>
    <collection role="projects" number="MATHEON-C6:Online-Reopt">MATHEON-C6:Online-Reopt</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/648/ZR-01-22.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/648/ZR-01-22.pdf</file>
  </doc>
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