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A level-2 reformulation-linearization technique bound for the quadratic assignment problem

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  • Adams, Warren P.
  • Guignard, Monique
  • Hahn, Peter M.
  • Hightower, William L.

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  • Adams, Warren P. & Guignard, Monique & Hahn, Peter M. & Hightower, William L., 2007. "A level-2 reformulation-linearization technique bound for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 180(3), pages 983-996, August.
    • Handle: RePEc:eee:ejores:v:180:y:2007:i:3:p:983-996
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    References listed on IDEAS

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    1. Hahn, Peter & Grant, Thomas & Hall, Nat, 1998. "A branch-and-bound algorithm for the quadratic assignment problem based on the Hungarian method," European Journal of Operational Research, Elsevier, vol. 108(3), pages 629-640, August.
    2. Warren P. Adams & Hanif D. Sherali, 1986. "A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems," Management Science, INFORMS, vol. 32(10), pages 1274-1290, October.
    3. Peter Hahn & Thomas Grant, 1998. "Lower Bounds for the Quadratic Assignment Problem Based upon a Dual Formulation," Operations Research, INFORMS, vol. 46(6), pages 912-922, December.
    4. 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.
    5. Eugene L. Lawler, 1963. "The Quadratic Assignment Problem," Management Science, INFORMS, vol. 9(4), pages 586-599, July.
    6. Mauricio G. C. Resende & K. G. Ramakrishnan & Zvi Drezner, 1995. "Computing Lower Bounds for the Quadratic Assignment Problem with an Interior Point Algorithm for Linear Programming," Operations Research, INFORMS, vol. 43(5), pages 781-791, October.
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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. Lucas A. Waddell & Jerry L. Phillips & Tianzhu Liu & Swarup Dhar, 2023. "An LP-based characterization of solvable QAP instances with chess-board and graded structures," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-23, July.
    3. Pessoa, Artur Alves & Hahn, Peter M. & Guignard, Monique & Zhu, Yi-Rong, 2010. "Algorithms for the generalized quadratic assignment problem combining Lagrangean decomposition and the Reformulation-Linearization Technique," European Journal of Operational Research, Elsevier, vol. 206(1), pages 54-63, October.
    4. Nihal Berktaş & Hande Yaman, 2021. "A Branch-and-Bound Algorithm for Team Formation on Social Networks," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1162-1176, July.
    5. Richárd Molnár-Szipai & Anita Varga, 2019. "Integrating combinatorial algorithms into a linear programming solver," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 475-482, June.
    6. W. Hager, 2009. "COAP 2008 best paper award: Paper of P.M. Hahn, B.-J. Kim, M. Guignard, J.M. Smith and Y.-R. Zhu," Computational Optimization and Applications, Springer, vol. 44(3), pages 525-530, December.
    7. Bodur, Merve & Dash, Sanjeeb & Günlük, Oktay, 2017. "A new lift-and-project operator," European Journal of Operational Research, Elsevier, vol. 257(2), pages 420-428.
    8. Peter M. Hahn & Yi-Rong Zhu & Monique Guignard & William L. Hightower & Matthew J. Saltzman, 2012. "A Level-3 Reformulation-Linearization Technique-Based Bound for the Quadratic Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 24(2), pages 202-209, May.
    9. Ketan Date & Rakesh Nagi, 2019. "Level 2 Reformulation Linearization Technique–Based Parallel Algorithms for Solving Large Quadratic Assignment Problems on Graphics Processing Unit Clusters," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 771-789, October.
    10. Palubeckis, Gintaras, 2015. "Fast simulated annealing for single-row equidistant facility layout," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 287-301.
    11. Rostami, Borzou & Malucelli, Federico & Belotti, Pietro & Gualandi, Stefano, 2016. "Lower bounding procedure for the asymmetric quadratic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 584-592.
    12. Hahn, Peter M. & Kim, Bum-Jin & Stutzle, Thomas & Kanthak, Sebastian & Hightower, William L. & Samra, Harvind & Ding, Zhi & Guignard, Monique, 2008. "The quadratic three-dimensional assignment problem: Exact and approximate solution methods," European Journal of Operational Research, Elsevier, vol. 184(2), pages 416-428, January.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Richard J. Forrester & Lucas A. Waddell, 2022. "Strengthening a linear reformulation of the 0-1 cubic knapsack problem via variable reordering," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 498-517, August.
    18. 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.
    19. de Klerk, Etienne & -Nagy, Marianna E. & Sotirov, Renata & Truetsch, Uwe, 2014. "Symmetry in RLT-type relaxations for the quadratic assignment and standard quadratic optimization problems," European Journal of Operational Research, Elsevier, vol. 233(3), pages 488-499.
    20. 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.
    21. 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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