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Exact algorithms for the solution of the grey pattern quadratic assignment problem

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  • Zvi Drezner
  • Alfonsas Misevičius
  • Gintaras Palubeckis

Abstract

We propose an exact algorithm to find the optimal solution to the grey pattern problem which is a special instance of the quadratic assignment problem. A very effective branch and bound algorithm is constructed. The special structure of the problem is exploited and optimal solutions for many problem instances established. One instance based on 64 facilities, organized in an 8 by 8 pattern, that was extensively researched in the literature was optimally solved in 15 s of computer time while existing papers report solution times of hours. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:82:y:2015:i:1:p:85-105
    DOI: 10.1007/s00186-015-0505-1
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    References listed on IDEAS

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    1. Matteo Fischetti & Michele Monaci & Domenico Salvagnin, 2012. "Three Ideas for the Quadratic Assignment Problem," Operations Research, INFORMS, vol. 60(4), pages 954-964, August.
    2. Zvi Drezner & Peter Hahn & Éeric Taillard, 2005. "Recent Advances for the Quadratic Assignment Problem with Special Emphasis on Instances that are Difficult for Meta-Heuristic Methods," Annals of Operations Research, Springer, vol. 139(1), pages 65-94, October.
    3. E. L. Lawler, 1973. "Optimal Sequencing of a Single Machine Subject to Precedence Constraints," Management Science, INFORMS, vol. 19(5), pages 544-546, January.
    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. Z Drezner & A Suzuki, 2010. "Covering continuous demand in the plane," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 878-881, May.
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    1. Brimberg, Jack & Kalczynski, Pawel & Drezner, Zvi, 2024. "Different formulations of the gray pattern problem and their optimal solutions," European Journal of Operational Research, Elsevier, vol. 316(1), pages 61-71.
    2. Pawel Kalczynski & Zvi Goldstein & Zvi Drezner, 2023. "An Efficient Heuristic for the k-Partitioning Problem," SN Operations Research Forum, Springer, vol. 4(4), pages 1-21, December.

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