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An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem

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  • Billionnet, Alain
  • Soutif, Eric

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  • Billionnet, Alain & Soutif, Eric, 2004. "An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 157(3), pages 565-575, September.
    • Handle: RePEc:eee:ejores:v:157:y:2004:i:3:p:565-575
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    References listed on IDEAS

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    1. Billionnet, Alain & Faye, Alain & Soutif, Eric, 1999. "A new upper bound for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 112(3), pages 664-672, February.
    2. Alberto Caprara & David Pisinger & Paolo Toth, 1999. "Exact Solution of the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 125-137, May.
    3. Michelon, Philippe & Veilleux, Louis, 1996. "Lagrangean methods for the 0-1 Quadratic Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 326-341, July.
    4. Billionnet, Alain & Calmels, Frederic, 1996. "Linear programming for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 310-325, July.
    5. Pierre Chardaire & Alain Sutter, 1995. "A Decomposition Method for Quadratic Zero-One Programming," Management Science, INFORMS, vol. 41(4), pages 704-712, April.
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    Cited by:

    1. Yuning Chen & Jin-Kao Hao, 2015. "Iterated responsive threshold search for the quadratic multiple knapsack problem," Annals of Operations Research, Springer, vol. 226(1), pages 101-131, March.
    2. Gabriel Lopez Zenarosa & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "On exact solution approaches for bilevel quadratic 0–1 knapsack problem," Annals of Operations Research, Springer, vol. 298(1), pages 555-572, March.
    3. Jesus Cunha & Luidi Simonetti & Abilio Lucena, 2016. "Lagrangian heuristics for the Quadratic Knapsack Problem," Computational Optimization and Applications, Springer, vol. 63(1), pages 97-120, January.
    4. D. Quadri & E. Soutif & P. Tolla, 2009. "Exact solution method to solve large scale integer quadratic multidimensional knapsack problems," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 157-167, February.
    5. Banda, Juan & Velasco, Jonás & Berrones, Arturo, 2017. "Dual mean field search for large scale linear and quadratic knapsack problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 158-167.
    6. Xiaochuan Shi & Lei Wu & Xiaoliang Meng, 2017. "A New Optimization Model for the Sustainable Development: Quadratic Knapsack Problem with Conflict Graphs," Sustainability, MDPI, vol. 9(2), pages 1-10, February.
    7. Fabio Furini & Emiliano Traversi, 2019. "Theoretical and computational study of several linearisation techniques for binary quadratic problems," Annals of Operations Research, Springer, vol. 279(1), pages 387-411, August.
    8. Britta Schulze & Michael Stiglmayr & Luís Paquete & Carlos M. Fonseca & David Willems & Stefan Ruzika, 2020. "On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 107-132, August.
    9. Liu, Yipeng & Koehler, Gary J., 2010. "Using modifications to Grover's Search algorithm for quantum global optimization," European Journal of Operational Research, Elsevier, vol. 207(2), pages 620-632, December.
    10. David Bergman, 2019. "An Exact Algorithm for the Quadratic Multiknapsack Problem with an Application to Event Seating," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 477-492, July.
    11. Z. Y. Wu & Y. J. Yang & F. S. Bai & M. Mammadov, 2011. "Global Optimality Conditions and Optimization Methods for Quadratic Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 241-259, November.
    12. Isma Dahmani & Mhand Hifi, 2021. "A modified descent method-based heuristic for binary quadratic knapsack problems with conflict graphs," Annals of Operations Research, Springer, vol. 298(1), pages 125-147, March.
    13. Schauer, Joachim, 2016. "Asymptotic behavior of the quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 255(2), pages 357-363.

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