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Recent Advances for the Quadratic Assignment Problem with Special Emphasis on Instances that are Difficult for Meta-Heuristic Methods

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  • Zvi Drezner
  • Peter Hahn
  • Éeric Taillard

Abstract

This paper reports heuristic and exact solution advances for the Quadratic Assignment Problem (QAP).QAPinstances most often discussed in the literature are relatively well solved by heuristic approaches. Indeed, solutions at a fraction of one percent from the best known solution values are rapidly found by most heuristic methods. Exact methods are not able to prove optimality for these instances as soon as the problem size approaches 30 to 40. This article presents new QAP instances that are ill conditioned for many metaheuristic-based methods. However, these new instances are shown to be solved relatively well by some exact methods, since problem instances up to a size of 75 have been exactly solved. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:139:y:2005:i:1:p:65-94:10.1007/s10479-005-3444-z
    DOI: 10.1007/s10479-005-3444-z
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    Cited by:

    1. Monique Guignard, 2020. "Strong RLT1 bounds from decomposable Lagrangean relaxation for some quadratic 0–1 optimization problems with linear constraints," Annals of Operations Research, Springer, vol. 286(1), pages 173-200, March.
    2. Madalina M. Drugan, 2019. "Estimating the number of basins of attraction of multi-objective combinatorial problems," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1367-1407, May.
    3. James, Tabitha & Rego, Cesar & Glover, Fred, 2009. "A cooperative parallel tabu search algorithm for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 195(3), pages 810-826, June.
    4. Krešimir Mihić & Kevin Ryan & Alan Wood, 2018. "Randomized Decomposition Solver with the Quadratic Assignment Problem as a Case Study," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 295-308, May.
    5. Zakir Hussain Ahmed, 2016. "Experimental analysis of crossover and mutation operators on the quadratic assignment problem," Annals of Operations Research, Springer, vol. 247(2), pages 833-851, December.
    6. Peter Hahn & J. MacGregor Smith & Yi-Rong Zhu, 2010. "The Multi-Story Space Assignment Problem," Annals of Operations Research, Springer, vol. 179(1), pages 77-103, September.
    7. Zvi Drezner, 2010. "On the unboundedness of facility layout problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 205-216, October.
    8. Zvi Drezner & Jack Brimberg & Nenad Mladenović & Said Salhi, 2015. "Solving the planar p-median problem by variable neighborhood and concentric searches," Journal of Global Optimization, Springer, vol. 63(3), pages 501-514, November.
    9. Paul, G., 2011. "An efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems," European Journal of Operational Research, Elsevier, vol. 209(3), pages 215-218, March.
    10. Mădălina M. Drugan, 2015. "Generating QAP instances with known optimum solution and additively decomposable cost function," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1138-1172, November.
    11. 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.
    12. Eduardo G. Pardo & Mauricio Soto & Christopher Thraves, 2015. "Embedding signed graphs in the line," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 451-471, February.
    13. 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.
    14. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    15. Jingyang Zhou & Peter E.D. Love & Kok Lay Teo & Hanbin Luo, 2017. "An exact penalty function method for optimising QAP formulation in facility layout problem," International Journal of Production Research, Taylor & Francis Journals, vol. 55(10), pages 2913-2929, May.
    16. Zhuoxuan Jiang & Xinyuan Zhao & Chao Ding, 2021. "A proximal DC approach for quadratic assignment problem," Computational Optimization and Applications, Springer, vol. 78(3), pages 825-851, April.
    17. 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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