IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v30y2015i4d10.1007_s10878-013-9689-6.html
   My bibliography  Save this article

Generating QAP instances with known optimum solution and additively decomposable cost function

Author

Listed:
  • Mădălina M. Drugan

    (Vrije Universiteit Brussel)

Abstract

Quadratic assignment problems (QAPs) is a NP-hard combinatorial optimization problem. QAPs are often used to compare the performance of meta-heuristics. In this paper, we propose a QAP problem instance generator that can be used for benchmarking for heuristic algorithms. Our QAP generator combines small size QAPs with known optimum solution into a larger size QAP instance. We call these instances composite QAPs (cQAPs), and we show that the cost function of cQAPs is additively decomposable. We give mild conditions for which a cQAP instance has known optimum solution. We generate cQAP instances using uniform distributions with different bounds for the component QAPs and for the rest of the cQAP elements. Numerical and analytical techniques that measure the difficulty of the cQAP instances in comparison with other QAPs from the literature are introduced. These methods point out that some cQAP instances are difficult for local search with many local optimum of various values, low epistasis and non-trivial asymptotic behaviour.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:4:d:10.1007_s10878-013-9689-6
    DOI: 10.1007/s10878-013-9689-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-013-9689-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-013-9689-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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. S. W. Hadley & F. Rendl & H. Wolkowicz, 1992. "A New Lower Bound Via Projection for the Quadratic Assignment Problem," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 727-739, August.
    4. Krokhmal, Pavlo A. & Pardalos, Panos M., 2009. "Random assignment problems," European Journal of Operational Research, Elsevier, vol. 194(1), pages 1-17, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Jiming Peng & Tao Zhu & Hezhi Luo & Kim-Chuan Toh, 2015. "Semi-definite programming relaxation of quadratic assignment problems based on nonredundant matrix splitting," Computational Optimization and Applications, Springer, vol. 60(1), pages 171-198, January.
    4. 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.
    5. Yong Xia & Wajeb Gharibi, 2015. "On improving convex quadratic programming relaxation for the quadratic assignment problem," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 647-667, October.
    6. 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.
    7. 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.
    8. Sana Bouajaja & Najoua Dridi, 2017. "A survey on human resource allocation problem and its applications," Operational Research, Springer, vol. 17(2), pages 339-369, July.
    9. 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.
    10. 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.
    11. 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.
    12. Ting Pong & Hao Sun & Ningchuan Wang & Henry Wolkowicz, 2016. "Eigenvalue, quadratic programming, and semidefinite programming relaxations for a cut minimization problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 333-364, March.
    13. Yunpeng Sun & Ruoya Jia & Asif Razzaq & Qun Bao, 2023. "RETRACTED ARTICLE: Drivers of China’s geographical renewable energy development: evidence from spatial association network structure approaches," Economic Change and Restructuring, Springer, vol. 56(6), pages 4115-4163, December.
    14. Ortega, Josué & Klein, Thilo, 2022. "Improving Efficiency and Equality in School Choice," QBS Working Paper Series 2022/02, Queen's University Belfast, Queen's Business School.
    15. Herrán, Alberto & Manuel Colmenar, J. & Duarte, Abraham, 2021. "An efficient variable neighborhood search for the Space-Free Multi-Row Facility Layout problem," European Journal of Operational Research, Elsevier, vol. 295(3), pages 893-907.
    16. Kammerdiner, A.R. & Pasiliao, E.L., 2014. "In and out forests on combinatorial landscapes," European Journal of Operational Research, Elsevier, vol. 236(1), pages 78-84.
    17. Ricardo M. Lima & Ignacio E. Grossmann, 2017. "On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study," Computational Optimization and Applications, Springer, vol. 66(1), pages 1-37, January.
    18. Michela Ricciardi Celsi & Lorenzo Ricciardi Celsi, 2024. "Quantum Computing as a Game Changer on the Path towards a Net-Zero Economy: A Review of the Main Challenges in the Energy Domain," Energies, MDPI, vol. 17(5), pages 1-22, February.
    19. Papahristodoulou, Christos, 2009. "The optimal layout of football players: A case study for AC Milan," MPRA Paper 20102, University Library of Munich, Germany.
    20. Alistair Wilson & Mariagiovanna Baccara & Ayse Imrohoroglu & Leeat Yariv, 2009. "A Field Study on Matching with Network Externalities," Working Paper 486, Department of Economics, University of Pittsburgh, revised Sep 2011.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:30:y:2015:i:4:d:10.1007_s10878-013-9689-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.