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An iterative variable-based fixation heuristic for the 0-1 multidimensional knapsack problem

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  • Wilbaut, Christophe
  • Salhi, Saïd
  • Hanafi, Saïd

Abstract

An iterative scheme which is based on a dynamic fixation of the variables is developed to solve the 0-1 multidimensional knapsack problem. Such a scheme has the advantage of generating memory information, which is used on the one hand to choose the variables to fix either permanently or temporarily and on the other hand to construct feasible solutions of the problem. Adaptations of this mechanism are proposed to explore different parts of the search space and to enhance the behaviour of the algorithm. Encouraging results are presented when tested on the correlated instances of the 0-1 multidimensional knapsack problem.

Suggested Citation

  • Wilbaut, Christophe & Salhi, Saïd & Hanafi, Saïd, 2009. "An iterative variable-based fixation heuristic for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 199(2), pages 339-348, December.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:2:p:339-348
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    1. James H. Lorie & Leonard J. Savage, 1955. "Three Problems in Rationing Capital," The Journal of Business, University of Chicago Press, vol. 28, pages 229-229.
    2. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    3. Hanafi, Said & Glover, Fred, 2007. "Exploiting nested inequalities and surrogate constraints," European Journal of Operational Research, Elsevier, vol. 179(1), pages 50-63, May.
    4. Wilbaut, Christophe & Hanafi, Said, 2009. "New convergent heuristics for 0-1 mixed integer programming," European Journal of Operational Research, Elsevier, vol. 195(1), pages 62-74, May.
    5. Vasquez, Michel & Vimont, Yannick, 2005. "Improved results on the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 165(1), pages 70-81, August.
    6. María Osorio & Fred Glover & Peter Hammer, 2002. "Cutting and Surrogate Constraint Analysis for Improved Multidimensional Knapsack Solutions," Annals of Operations Research, Springer, vol. 117(1), pages 71-93, November.
    7. Helga Meier & Nicos Christofides & Gerry Salkin, 2001. "Capital Budgeting Under Uncertainty---An Integrated Approach Using Contingent Claims Analysis and Integer Programming," Operations Research, INFORMS, vol. 49(2), pages 196-206, April.
    8. A Volgenant & I Y Zwiers, 2007. "Partial enumeration in heuristics for some combinatorial optimization problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(1), pages 73-79, January.
    9. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    10. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.
    11. H. Martin Weingartner, 1966. "Capital Budgeting of Interrelated Projects: Survey and Synthesis," Management Science, INFORMS, vol. 12(7), pages 485-516, March.
    12. M. W. P. Savelsbergh, 1994. "Preprocessing and Probing Techniques for Mixed Integer Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 6(4), pages 445-454, November.
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    Cited by:

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    3. S Salhi & A Al-Khedhairi, 2010. "Integrating heuristic information into exact methods: The case of the vertex p-centre problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1619-1631, November.
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    7. Yoon, Yourim & Kim, Yong-Hyuk & Moon, Byung-Ro, 2012. "A theoretical and empirical investigation on the Lagrangian capacities of the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 366-376.

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