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A heuristic solution procedure for the multiconstraint zero‐one knapsack problem

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  • Hasan Pirkul

Abstract

In this article a new heuristic procedure is proposed. This procedure makes use of surrogate duality in solving multiconstraint knapsack problems. Computational effort involved in the procedure is bounded by a polynomial in the number of variables. Extensive computational testing indicates that the procedure generates good feasible solutions regardless of the problem structure. In 98% of the problems solved, the solution generated by the heuristic was within 1% of the optimal solution. This procedure was also tested against other heuristics and was found to compare favorably.

Suggested Citation

  • Hasan Pirkul, 1987. "A heuristic solution procedure for the multiconstraint zero‐one knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 161-172, April.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:2:p:161-172
    DOI: 10.1002/1520-6750(198704)34:23.0.CO;2-A
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    References listed on IDEAS

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    1. Harvey M. Salkin & Cornelis A. De Kluyver, 1975. "The knapsack problem: A survey," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(1), pages 127-144, March.
    2. Harvey J. Greenberg, 1973. "The Generalized Penalty-Function/Surrogate Model," Operations Research, INFORMS, vol. 21(1), pages 162-178, February.
    3. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    4. Yoshiaki Toyoda, 1975. "A Simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems," Management Science, INFORMS, vol. 21(12), pages 1417-1427, August.
    5. Fred Glover, 1965. "A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem," Operations Research, INFORMS, vol. 13(6), pages 879-919, December.
    6. A. Victor Cabot, 1970. "An Enumeration Algorithm for Knapsack Problems," Operations Research, INFORMS, vol. 18(2), pages 306-311, April.
    7. Richard Loulou & Eleftherios Michaelides, 1979. "New Greedy-Like Heuristics for the Multidimensional 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 27(6), pages 1101-1114, December.
    8. Egon Balas, 1965. "An Additive Algorithm for Solving Linear Programs with Zero-One Variables," Operations Research, INFORMS, vol. 13(4), pages 517-546, August.
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    Cited by:

    1. José García & Paola Moraga & Matias Valenzuela & Hernan Pinto, 2020. "A db-Scan Hybrid Algorithm: An Application to the Multidimensional Knapsack Problem," Mathematics, MDPI, vol. 8(4), pages 1-22, April.
    2. Sabah Bushaj & İ. Esra Büyüktahtakın, 2024. "A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack," Journal of Global Optimization, Springer, vol. 89(3), pages 655-685, July.
    3. Al-Shihabi, Sameh, 2021. "A Novel Core-Based Optimization Framework for Binary Integer Programs- the Multidemand Multidimesional Knapsack Problem as a Test Problem," Operations Research Perspectives, Elsevier, vol. 8(C).
    4. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    5. 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.
    6. Yalçın Akçay & Haijun Li & Susan Xu, 2007. "Greedy algorithm for the general multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 150(1), pages 17-29, March.

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