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Cutting and Surrogate Constraint Analysis for Improved Multidimensional Knapsack Solutions

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  • María Osorio
  • Fred Glover
  • Peter Hammer

Abstract

We use surrogate analysis and constraint pairing in multidimensional knapsack problems to fix some variables to zero and to separate the rest into two groups – those that tend to be zero and those that tend to be one, in an optimal integer solution. Using an initial feasible integer solution, we generate logic cuts based on our analysis before solving the problem with branch and bound. Computational testing, including the set of problems in the OR-library and our own set of difficult problems, shows our approach helps to solve difficult problems in a reasonable amount of time and, in most cases, with a fewer number of nodes in the search tree than leading commercial software. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:117:y:2002:i:1:p:71-93:10.1023/a:1021513321301
    DOI: 10.1023/A:1021513321301
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    Citations

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    Cited by:

    1. Hanafi, Said & Glover, Fred, 2007. "Exploiting nested inequalities and surrogate constraints," European Journal of Operational Research, Elsevier, vol. 179(1), pages 50-63, May.
    2. Glover, Fred, 2013. "Advanced greedy algorithms and surrogate constraint methods for linear and quadratic knapsack and covering problems," European Journal of Operational Research, Elsevier, vol. 230(2), pages 212-225.
    3. Elendner, Thomas & Femerling, R., 2003. "Allocation of in-house services: Experimental comparison of allocation mechanisms," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 577, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Fortin, D. & Tseveendorj, I., 2009. "A trust branching path heuristic for zero-one programming," European Journal of Operational Research, Elsevier, vol. 197(2), pages 439-445, September.
    5. Xin Tang & Ameur Soukhal & Vincent T’kindt, 2014. "Preprocessing for a map sectorization problem by means of mathematical programming," Annals of Operations Research, Springer, vol. 222(1), pages 551-569, November.
    6. 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.
    7. Yuji Nakagawa & Ross J. W. James & César Rego & Chanaka Edirisinghe, 2014. "Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models," Management Science, INFORMS, vol. 60(3), pages 695-707, March.
    8. Vincent T’kindt & Federico Della Croce & Jean-Louis Bouquard, 2007. "Enumeration of Pareto Optima for a Flowshop Scheduling Problem with Two Criteria," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 64-72, February.
    9. 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.
    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. 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.
    12. Boyer, V. & Elkihel, M. & El Baz, D., 2009. "Heuristics for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 199(3), pages 658-664, December.

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