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  <doc>
    <id>5713</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <completedDate>--</completedDate>
    <publishedDate>2015-12-31</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An (MI)LP-based Primal Heuristic for 3-Architecture Connected Facility Location in Urban Access Network Design</title>
    <abstract language="eng">We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks integrating wired and wireless technologies. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage represented through signal-to-interference ratios. Since the problem can prove very challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic that combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-57139</identifier>
    <identifier type="doi">10.1007/978-3-319-31204-0_19</identifier>
    <enrichment key="SourceTitle">Applications of Evolutionary Computation, LNCS 9597, pp. 283-298</enrichment>
    <author>Fabio D'Andreagiovanni</author>
    <submitter>Fabio D'Andreagiovanni</submitter>
    <author>Fabian Mett</author>
    <author>Jonad Pulaj</author>
    <series>
      <title>ZIB-Report</title>
      <number>15-62</number>
    </series>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="tele">Mathematics of Telecommunication</collection>
    <collection role="persons" number="pulaj">Pulaj, Jonad</collection>
    <collection role="projects" number="ECMath-MI4">ECMath-MI4</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5713/ZR-15-62_DAndreagiovanni_3architectureConnectedFacilityAccessNetworks.pdf</file>
  </doc>
  <doc>
    <id>7024</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <type>reportzib</type>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-08-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Chvátal’s Conjecture Holds for Ground Sets of Seven Elements</title>
    <abstract language="eng">We establish a general computational framework for Chvátal’s conjecture based on exact rational integer programming. As a result we prove Chvátal’s conjecture holds for all downsets whose union of sets contains seven elements or less. The computational proof relies on an exact branch-and-bound certificate that allows for elementary verification and is independent of the integer programming solver used.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-70240</identifier>
    <author>Leon Eifler</author>
    <submitter>Leon Eifler</submitter>
    <author>Ambros Gleixner</author>
    <author>Jonad Pulaj</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-49</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>extremal combinatorics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>exact rational integer programming</value>
    </subject>
    <collection role="msc" number="05-XX">COMBINATORICS (For finite fields, see 11Txx)</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="pulaj">Pulaj, Jonad</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</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/7024/chvatal.pdf</file>
  </doc>
  <doc>
    <id>8444</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <completedDate>--</completedDate>
    <publishedDate>2021-10-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Safe Computational Framework for Integer Programming applied to Chvátal's Conjecture</title>
    <abstract language="eng">We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems.&#13;
&#13;
At its core, the framework relies on a rational branch-and-bound certificate produced by an exact integer programming solver, SCIP, in order to circumvent floating-point roundoff errors present in most state-of-the-art solvers for mixed-integer programs.&#13;
&#13;
The resulting certificates are self-contained and checker software exists that can verify their correctness independently of the integer programming solver used to produce the certificate.&#13;
&#13;
This acts as a safeguard against programming errors that may be present in complex solver software.&#13;
&#13;
The viability of this approach is tested by applying it to finite cases of Chvátal's conjecture, a long-standing open question in extremal combinatorics.&#13;
&#13;
We take particular care to verify also the correctness of the input for this specific problem, using the Coq formal proof assistant.&#13;
As a result we are able to provide a first machine-assisted proof that&#13;
&#13;
Chvátal's conjecture holds for all downsets whose union of sets contains seven elements or less.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-84444</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Leon Eifler</author>
    <submitter>Leon Eifler</submitter>
    <author>Ambros Gleixner</author>
    <author>Jonad Pulaj</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-35</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>exact rational mixed integer programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>extremal combinatorics</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="persons" number="pulaj">Pulaj, Jonad</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8444/chvatal.pdf</file>
  </doc>
  <doc>
    <id>4408</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <type>reportzib</type>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2014-02-12</completedDate>
    <publishedDate>2013-12-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A hybrid primal heuristic for Robust Multiperiod Network Design</title>
    <abstract language="eng">We investigate the Robust Multiperiod Network Design Problem, a generalization of the classical Capacitated Network Design Problem that additionally considers multiple design periods and provides solutions protected against traffic uncertainty.&#13;
Given the intrinsic difficulty of the problem, which proves challenging even for state-of-the art commercial solvers, we propose a hybrid primal heuristic based on the combination of ant colony optimization and an exact large neighborhood search. Computational experiments on a set of realistic instances from the SNDlib show that our heuristic can find solutions of extremely good quality with low optimality gap.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-44081</identifier>
    <enrichment key="SourceTitle">To appear in EvoApplications - Proc. of EvoStar 2014, Esparcia-Alcazar, A. et al. (Eds.), Lecture Notes in Computer Science, Springer, Heidelberg</enrichment>
    <author>Fabio D'Andreagiovanni</author>
    <submitter>Fabio D'Andreagiovanni</submitter>
    <author>Jonatan Krolikowski</author>
    <author>Jonad Pulaj</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-78</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Multiperiod Network Design, Traffic Uncertainty, Robust Optimization, Multiband Robustness, Hybrid Heuristics</value>
    </subject>
    <collection role="msc" number="68-XX">COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="tele">Mathematics of Telecommunication</collection>
    <collection role="persons" number="pulaj">Pulaj, Jonad</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4408/ZR-13-78_RobustMultiperiodNetworkDesign_DAndreatiovanniEtAl.pdf</file>
  </doc>
  <doc>
    <id>5286</id>
    <completedYear/>
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    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2014-10-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Fast Hybrid Primal Heuristic for Multiband Robust Capacitated Network Design with Multiple Time Periods</title>
    <abstract language="eng">We investigate the Robust Multiperiod Network Design Problem, a generalization of the Capacitated Network Design Problem (CNDP) that, besides establishing flow routing and network capacity installation as in a canonical CNDP, also considers a planning horizon made up of multiple time periods and protection against fluctuations in traffic volumes. As a remedy against traffic volume uncertainty, we propose a Robust Optimization model based on Multiband Robustness (Büsing and D'Andreagiovanni, 2012), a refinement of classical Gamma-Robustness by Bertsimas and Sim (2004) that uses a system of multiple deviation bands. Since the resulting optimization problem may prove very challenging even for instances of moderate size solved by a state-of-the-art optimization solver, we propose a hybrid primal heuristic that combines a randomized fixing strategy inspired by ant colony optimization and an exact large neighbourhood search. Computational experiments on a set of realistic instances from the SNDlib (2010) show that our original heuristic can run fast and produce solutions of extremely high quality associated with low optimality gaps.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-52862</identifier>
    <identifier type="doi">10.1016/j.asoc.2014.10.016</identifier>
    <enrichment key="PeerReviewed">Yes</enrichment>
    <enrichment key="SourceTitle">A rev. vers. appeared in: Applied Soft Computing, 26 (2015) pp. 497-507</enrichment>
    <author>Fabio D'Andreagiovanni</author>
    <submitter>Fabio D'Andreagiovanni</submitter>
    <author>Jonatan Krolikowski</author>
    <author>Jonad Pulaj</author>
    <series>
      <title>ZIB-Report</title>
      <number>14-40</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Capacitated Network Design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Multiperiod Design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Multiband Robust Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Traffic Uncertainty</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Metaheuristic</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Ant Colony Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Exact Large Neighborhood Search</value>
    </subject>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="pulaj">Pulaj, Jonad</collection>
    <collection role="projects" number="MultiNO">MultiNO</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5286/ZR-14-40_AppSoftComputing.pdf</file>
  </doc>
  <doc>
    <id>6062</id>
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    <language>eng</language>
    <pageFirst/>
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    <edition/>
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    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-10-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Cutting Planes for Families Implying Frankl's Conjecture</title>
    <abstract language="eng">We find previously unknown families which imply Frankl’s conjecture using an algorithmic framework. The conjecture states that for any non-empty union-closed (or Frankl) family there exists an element in at least half of the sets. Poonen’s Theorem characterizes the existence of weights which determine whether a given Frankl family implies the conjecture for all Frankl families which contain it. A Frankl family is Non–Frankl-Complete (Non–FC), if it does not imply the conjecture in its elements for some Frankl family that contains it. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen’s Theorem. This method allows us to find a counterexample to a ten-year-old conjecture by R. Morris about the structure of generators for Non–FC-families.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60626</identifier>
    <author>Jonad Pulaj</author>
    <submitter>Jonad Pulaj</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>16-51</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>extremal combinatorics, extremal set theory, cutting plane, exact integer programming</value>
    </subject>
    <collection role="ccs" number="A.">General Literature</collection>
    <collection role="pacs" number="00.00.00">GENERAL</collection>
    <collection role="msc" number="05-XX">COMBINATORICS (For finite fields, see 11Txx)</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="pulaj">Pulaj, Jonad</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</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/6062/ZIB_Report_16_51.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/6062/revisedPulaj.pdf</file>
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  <doc>
    <id>1336</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-07-13</completedDate>
    <publishedDate>2011-07-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Multiperiod Network Design Problem: Lagrangian-based Solution Approaches</title>
    <abstract language="eng">We present and prove a theorem which gives the optimal dual vector for which a Lagrangian dual problem in the Single Period Design Problem (SPDP) is maximized. &#13;
Furthermore we give a straightforward generalization to the Multi-Period Design Problem (MPDP). Based on the optimal dual values derived we compute the solution of the Lagrangian relaxation and compare it &#13;
with the linear relaxation and optimal IP values.</abstract>
    <identifier type="serial">11-31</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-13367</identifier>
    <author>Anastasios Giovanidis</author>
    <submitter>Anastasios Giovanidis</submitter>
    <author>Jonad Pulaj</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-31</number>
    </series>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>Network Design</value>
    </subject>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>Lagrangian Relaxation</value>
    </subject>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="pulaj">Pulaj, Jonad</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1336/multiperiod.pdf</file>
  </doc>
  <doc>
    <id>5680</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>2015-12-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">New Conjectures For Union-Closed Families</title>
    <abstract language="eng">The Frankl conjecture, also known as the union-closed sets conjecture, states that there exists an element in at least half of the sets of any (non-empty) union-closed family. From an optimization point of view, one could instead prove that 2a is an upper bound to the number of sets in a union-closed family with n elements where each element is in at most a sets, where a and n are non-negative integers. Formulating these problems as integer programs we observe that computed optimal values do not vary with n. We formalize these observations as conjectures, and show that they are not equivalent to the Frankl conjecture while still having&#13;
wide-reaching implications if proven true. Finally, we partially prove the new conjectures and discuss possible approaches to solve them completely.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-56804</identifier>
    <author>Jonad Pulaj</author>
    <submitter>Jonad Pulaj</submitter>
    <author>Annie Raymond</author>
    <author>Dirk Theis</author>
    <series>
      <title>ZIB-Report</title>
      <number>15-57</number>
    </series>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="tele">Mathematics of Telecommunication</collection>
    <collection role="persons" number="pulaj">Pulaj, Jonad</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5680/ZIB.pdf</file>
  </doc>
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