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A New Lower Bound for the Quadratic Assignment Problem

Author

Listed:
  • Paolo Carraresi

    (University of Pisa, Pisa, Italy)

  • Federico Malucelli

    (University of Pisa, Pisa, Italy)

Abstract

We introduce a new lower bound for the quadratic assignment problem based on a sequence of equivalent formulations of the problem. We present a procedure for obtaining tight bounds by sequentially applying our approach in conjunction with the A. Assad and W. Xu bound and the N. Christofides and M. Gerrard bound.

Suggested Citation

  • Paolo Carraresi & Federico Malucelli, 1992. "A New Lower Bound for the Quadratic Assignment Problem," Operations Research, INFORMS, vol. 40(1-supplem), pages 22-27, February.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:1-supplement-1:p:s22-s27
    DOI: 10.1287/opre.40.1.S22
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    Citations

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    Cited by:

    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. Spiliopoulos, K. & Sofianopoulou, S., 1998. "An optimal tree search method for the manufacturing systems cell formation problem," European Journal of Operational Research, Elsevier, vol. 105(3), pages 537-551, March.
    3. Frank Meijer & Renata Sotirov, 2020. "The quadratic cycle cover problem: special cases and efficient bounds," Journal of Combinatorial Optimization, Springer, vol. 39(4), pages 1096-1128, May.
    4. Vittorio Maniezzo, 1999. "Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 358-369, November.
    5. de Meijer, Frank, 2023. "Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization," Other publications TiSEM b1f1088c-95fe-4b8a-9e15-c, Tilburg University, School of Economics and Management.
    6. A Diponegoro & B R Sarker, 2003. "Machine assignment in a nonlinear multi-product flowline," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 472-489, May.
    7. Rostami, Borzou & Chassein, André & Hopf, Michael & Frey, Davide & Buchheim, Christoph & Malucelli, Federico & Goerigk, Marc, 2018. "The quadratic shortest path problem: complexity, approximability, and solution methods," European Journal of Operational Research, Elsevier, vol. 268(2), pages 473-485.
    8. Ball, Michael O. & Kaku, Bharat K. & Vakhutinsky, Andrew, 1998. "Network-based formulations of the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 104(1), pages 241-249, January.
    9. Mans, Bernard & Mautor, Thierry & Roucairol, Catherine, 1995. "A parallel depth first search branch and bound algorithm for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 81(3), pages 617-628, March.
    10. Solimanpur, M. & Vrat, P. & Shankar, R., 2004. "Ant colony optimization algorithm to the inter-cell layout problem in cellular manufacturing," European Journal of Operational Research, Elsevier, vol. 157(3), pages 592-606, September.
    11. Hao Hu & Renata Sotirov, 2021. "The linearization problem of a binary quadratic problem and its applications," Annals of Operations Research, Springer, vol. 307(1), pages 229-249, December.
    12. 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.

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