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A variable neighbourhood search enhanced estimation of distribution algorithm for quadratic assignment problems

Author

Listed:
  • T. G. Pradeepmon

    (National Institute of Technology Calicut
    Muthoot Institute of Technology and Science)

  • Vinay V. Panicker

    (National Institute of Technology Calicut)

  • R. Sridharan

    (National Institute of Technology Calicut)

Abstract

Quadratic Assignment Problem (QAP) is one of the most complex combinatorial optimization problems. Many real-world problems such as printed circuit board design, facility location problems, assigning gates to airplanes can be modelled as QAP. Problems of size greater than 35 is not able to solve optimally using conventional optimization methods. This warrants the use of evolutionary optimization methods for obtaining optimal or near optimal solutions for QAPs. This work proposes a hybridization on a univariate Estimation of Distribution Algorithm, namely the Population Based Incremental Learning Algorithm (PBILA), with Variable Neighbourhood Search (VNS) for solving QAPs. The proposed algorithm is employed to solve benchmark instances of QAP and the results are reported. The results of this work reveals that PBILA on its own is not efficient for solving the QAPs. However, when hybridised with VNS, the algorithm performs well providing best known solutions for 95 test instances out of the 101 instances considered. For most of the test instances, the percentage deviation is less than one percentage. The overall average percentage deviation of the obtained solutions from the best-known solutions is 0.037%, which is a significant improvement when compared with state-of-the-art algorithms.

Suggested Citation

  • T. G. Pradeepmon & Vinay V. Panicker & R. Sridharan, 2021. "A variable neighbourhood search enhanced estimation of distribution algorithm for quadratic assignment problems," OPSEARCH, Springer;Operational Research Society of India, vol. 58(1), pages 203-233, March.
    • Handle: RePEc:spr:opsear:v:58:y:2021:i:1:d:10.1007_s12597-020-00475-4
    DOI: 10.1007/s12597-020-00475-4
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    References listed on IDEAS

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    1. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
    2. Alexander Barvinok & Tamon Stephen, 2003. "The Distribution of Values in the Quadratic Assignment Problem," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 64-91, February.
    3. Drezner, Zvi, 2005. "The extended concentric tabu for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 160(2), pages 416-422, January.
    4. Zvi Drezner, 2015. "The Quadratic Assignment Problem," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 345-363, Springer.
    5. Pitsoulis, Leonidas S. & Pardalos, Panos M. & Hearn, Donald W., 2001. "Approximate solutions to the turbine balancing problem," European Journal of Operational Research, Elsevier, vol. 130(1), pages 147-155, April.
    6. Anderson, E. J., 1996. "Mechanisms for local search," European Journal of Operational Research, Elsevier, vol. 88(1), pages 139-151, January.
    7. Stefan Helber & Daniel Böhme & Farid Oucherif & Svenja Lagershausen & Steffen Kasper, 2016. "A hierarchical facility layout planning approach for large and complex hospitals," Flexible Services and Manufacturing Journal, Springer, vol. 28(1), pages 5-29, June.
    8. Jadranka Skorin-Kapov, 1990. "Tabu Search Applied to the Quadratic Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 33-45, February.
    9. Osman, Hany & Demirli, Kudret, 2012. "Economic lot and delivery scheduling problem for multi-stage supply chains," International Journal of Production Economics, Elsevier, vol. 136(2), pages 275-286.
    10. Mokhtar S. Bazaraa & Hanif D. Sherali, 1980. "Benders' partitioning scheme applied to a new formulation of the quadratic assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(1), pages 29-41, March.
    11. Charles Fleurent & Fred Glover, 1999. "Improved Constructive Multistart Strategies for the Quadratic Assignment Problem Using Adaptive Memory," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 198-204, May.
    12. Burkard, R. E. & Rendl, F., 1984. "A thermodynamically motivated simulation procedure for combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 17(2), pages 169-174, August.
    13. 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.
    14. Phen Chiak See & Kuan Yew Wong, 2008. "Application of ant colony optimisation algorithms in solving facility layout problems formulated as quadratic assignment problems: a review," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 3(6), pages 644-672.
    15. Heffley, Dennis R., 1980. "Decomposition of the Koopmans-Beckmann Problem," Regional Science and Urban Economics, Elsevier, vol. 10(4), pages 571-580, November.
    16. Li, Wu-Ji & Smith, J. MacGregor, 1995. "An algorithm for Quadratic Assignment Problems," European Journal of Operational Research, Elsevier, vol. 81(1), pages 205-216, February.
    17. L M Gambardella & É D Taillard & M Dorigo, 1999. "Ant colonies for the quadratic assignment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(2), pages 167-176, February.
    18. Yichuan Ding & Henry Wolkowicz, 2009. "A Low-Dimensional Semidefinite Relaxation for the Quadratic Assignment Problem," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 1008-1022, November.
    19. 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.
    20. Timothy Urban, 1998. "Solution procedures for the dynamic facility layout problem," Annals of Operations Research, Springer, vol. 76(0), pages 323-342, January.
    21. Connolly, David T., 1990. "An improved annealing scheme for the QAP," European Journal of Operational Research, Elsevier, vol. 46(1), pages 93-100, May.
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