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    <completedDate>2024-10-28</completedDate>
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    <title language="eng">Challenges and opportunities in quantum optimization</title>
    <parentTitle language="eng">Nature Reviews Physics</parentTitle>
    <identifier type="doi">10.1038/s42254-024-00770-9</identifier>
    <identifier type="issn">2522-5820</identifier>
    <identifier type="arxiv">2312.02279</identifier>
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    <author>Amira Abbas</author>
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    <author>Harry Buhrman</author>
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    <author>Giorgio Cortiana</author>
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    <author>Daniel J. Egger</author>
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    <author>Bryce Fuller</author>
    <author>Julien Gacon</author>
    <author>Constantin Gonciulea</author>
    <author>Sander Gribling</author>
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    <author>Stuart Hadfield</author>
    <author>Raoul Heese</author>
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    <author>Georgios Korpas</author>
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    <author>Corey O’Meara</author>
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    <author>Sebastian Pokutta</author>
    <author>Manuel Proissl</author>
    <author>Patrick Rebentrost</author>
    <author>Emre Sahin</author>
    <author>Benjamin C. B. Symons</author>
    <author>Sabine Tornow</author>
    <author>Víctor Valls</author>
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    <author>Jon Yard</author>
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    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="institutes" number="aim">Applied Algorithmic Intelligence Methods</collection>
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    <publishedYear>2024</publishedYear>
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    <language>eng</language>
    <pageFirst>107105</pageFirst>
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    <issue/>
    <volume>54</volume>
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    <completedDate>2024-03-07</completedDate>
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    <title language="eng">How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem</title>
    <abstract language="eng">It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.</abstract>
    <parentTitle language="eng">Operations Research Letters</parentTitle>
    <identifier type="doi">10.1016/j.orl.2024.107105</identifier>
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    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-90902</enrichment>
    <author>Gennesaret Tjusila</author>
    <submitter>Christoph Spiegel</submitter>
    <author>Mathieu Besançon</author>
    <author>Mark Turner</author>
    <author>Thorsten Koch</author>
    <collection role="persons" number="koch">Koch, Thorsten</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="turner">Turner, Mark Ruben</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
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  <doc>
    <id>8169</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>61</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>masterthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2020-05-05</thesisDateAccepted>
    <title language="eng">Multiperiod Optimal Power Flow Problem In Distribution System Planning</title>
    <abstract language="eng">Growing demand, distributed generation, such as renewable energy sources (RES), and the increasing role of storage systems to mitigate the volatility of RES on a medium voltage level, push existing distribution grids to their limits. Therefore, necessary network expansion needs to be evaluated to guarantee a safe and reliable  electricity supply in the future taking these challenges into account. This problem is formulated as an optimal power flow (OPF) problem which combines network expansion, volatile generation and storage systems, minimizing network expansion and generation costs. As storage  systems introduce a temporal coupling into the system, a multiperiod OPF problem is needed and analysed in this thesis. To reduce complexity, the network expansion problem is represented in a continuous nonlinear programming formulation by using fundamental properties of electrical engeneering. This formulation is validated  succesfully against a common mixed integer programming approach on a 30 and 57 bus network with respect to solution and computing time. As the OPF problem is, in general, a nonconvex, nonlinear problem and, thus, hard to solve, convex relaxations of the power flow equations have gained increasing interest. Sufficient conditions are represented which guarantee exactness of a second-order cone (SOC) relaxation of an operational OPF in radial networks. In this thesis, these conditions are enhanced for the network expansion planning problem.  Additionally, nonconvexities introduced by the choice of network expansion variables are relaxed by using McCormick envelopes. These relaxations are then applied on the multiperiod OPF and compared to the original problem on a 30 and a 57 bus network. In particular, the computational time is decreased by an order up to 10^2 by the SOC relaxation while it provides either an exact solution or a sufficient lower bound on the original problem. Finally, a sensitivity study is performed on weights of network expansion costs showing strong dependency of both the solution of performed expansion and solution time on the chosen weights.</abstract>
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    <advisor>Ralf Borndörfer</advisor>
    <author>Jaap Pedersen</author>
    <submitter>Jaap Pedersen</submitter>
    <advisor>Niels Lindner</advisor>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multiperiod optimal power flow, distribution network planning, battery storage</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="persons" number="pedersen">Pedersen, Jaap</collection>
    <collection role="institutes" number="Mathematical Algorithmic Intelligence">Mathematical Algorithmic Intelligence</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="projects" number="MODAL-EnergyLab">MODAL-EnergyLab</collection>
    <thesisGrantor>Freie Universität Berlin</thesisGrantor>
  </doc>
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