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Three Ideas for the Quadratic Assignment Problem

Author

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  • Matteo Fischetti

    (Department of Information Engineering, University of Padova, 35131 Padova, Italy)

  • Michele Monaci

    (Department of Information Engineering, University of Padova, 35131 Padova, Italy)

  • Domenico Salvagnin

    (Department of Information Engineering, University of Padova, 35131 Padova, Italy)

Abstract

We address the exact solution of the famous esc instances of the quadratic assignment problem. These are extremely hard instances that remained unsolved---even allowing for a tremendous computing power---by using all previous techniques from the literature. During this challenging task we found that three ideas were particularly useful and qualified as a breakthrough for our approach. The present paper is about describing these ideas and their impact in solving esc instances. Our method was able to solve, in a matter of seconds or minutes on a single PC, all easy cases (all esc16* plus esc32e and esc32g ). The three very hard instances esc32c, esc32d , and esc64a were solved in less than half an hour, in total, on a single PC. We also report the solution, in about five hours, of tai64c . By using a facility-flow splitting procedure, we were also able to solve to proven optimality, for the first time, esc32h (in about two hours) as well as “the big fish” esc128 . (To our great surprise, the solution of the latter required just a few seconds on a single PC.)

Suggested Citation

  • Matteo Fischetti & Michele Monaci & Domenico Salvagnin, 2012. "Three Ideas for the Quadratic Assignment Problem," Operations Research, INFORMS, vol. 60(4), pages 954-964, August.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:4:p:954-964
    DOI: 10.1287/opre.1120.1073
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    References listed on IDEAS

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    1. de Klerk, E. & Sotirov, R., 2010. "Exploiting group symmetry in semidefinite programming relaxations of the quadratic assignment problem," Other publications TiSEM 73287c80-3bc2-40c4-b02d-4, Tilburg University, School of Economics and Management.
    2. Kaufman, L. & Broeckx, F., 1978. "An algorithm for the quadratic assignment problem using Bender's decomposition," European Journal of Operational Research, Elsevier, vol. 2(3), pages 207-211, May.
    3. Burkard, R. E. & Karisch, S. & Rendl, F., 1991. "QAPLIB-A quadratic assignment problem library," European Journal of Operational Research, Elsevier, vol. 55(1), pages 115-119, November.
    4. Nyberg, Axel & Westerlund, Tapio, 2012. "A new exact discrete linear reformulation of the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 220(2), pages 314-319.
    5. de Klerk, E. & Sotirov, R., 2007. "Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem," Discussion Paper 2007-44, Tilburg University, Center for Economic Research.
    6. Eugene L. Lawler, 1963. "The Quadratic Assignment Problem," Management Science, INFORMS, vol. 9(4), pages 586-599, July.
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    Citations

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    Cited by:

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    4. Zvi Drezner & Alfonsas Misevičius & Gintaras Palubeckis, 2015. "Exact algorithms for the solution of the grey pattern quadratic assignment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 85-105, August.
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    6. Feizollahi, Mohammad Javad & Feyzollahi, Hadi, 2015. "Robust quadratic assignment problem with budgeted uncertain flows," Operations Research Perspectives, Elsevier, vol. 2(C), pages 114-123.
    7. Silva, Allyson & Coelho, Leandro C. & Darvish, Maryam, 2021. "Quadratic assignment problem variants: A survey and an effective parallel memetic iterated tabu search," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1066-1084.
    8. Martina Fischetti & Matteo Fischetti, 2023. "Integrated Layout and Cable Routing in Wind Farm Optimal Design," Management Science, INFORMS, vol. 69(4), pages 2147-2164, April.
    9. E. de Klerk & R. Sotirov & U. Truetsch, 2015. "A New Semidefinite Programming Relaxation for the Quadratic Assignment Problem and Its Computational Perspectives," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 378-391, May.
    10. Alexandre Domingues Gonçalves & Artur Alves Pessoa & Cristiana Bentes & Ricardo Farias & Lúcia Maria de A. Drummond, 2017. "A Graphics Processing Unit Algorithm to Solve the Quadratic Assignment Problem Using Level-2 Reformulation-Linearization Technique," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 676-687, November.
    11. Huizhen Zhang & Cesar Beltran-Royo & Liang Ma, 2013. "Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers," Annals of Operations Research, Springer, vol. 207(1), pages 261-278, August.

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