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New Greedy-Like Heuristics for the Multidimensional 0-1 Knapsack Problem

Author

Listed:
  • Richard Loulou

    (McGill University, Montreal, Quebec)

  • Eleftherios Michaelides

    (McGill University, Montreal, Quebec)

Abstract

In this paper, we develop four heuristic methods to obtain approximate solutions to the multidimensional 0-1 knapsack problem. The four methods are tested on a number of problems of various sizes. The solutions are compared to the rigorous optimum as well as to a heuristic method of Toyoda. They are statistically better than the latter, with average relative errors of the order of less than 1%.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:6:p:1101-1114
    DOI: 10.1287/opre.27.6.1101
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    Cited by:

    1. 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.
    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. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    4. Niederhoff, Julie A., 2007. "Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions," European Journal of Operational Research, Elsevier, vol. 176(2), pages 941-955, January.
    5. Cao, Chengxuan & Gao, Ziyou & Li, Keping, 2012. "Capacity allocation problem with random demands for the rail container carrier," European Journal of Operational Research, Elsevier, vol. 217(1), pages 214-221.
    6. Wu, Jigang & Srikanthan, Thambipillai & Yan, Chengbin, 2008. "Algorithmic aspects for power-efficient hardware/software partitioning," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1204-1215.
    7. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria combinatorial optimization," Working papers 3756-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Yalçin Akçay & Susan H. Xu, 2004. "Joint Inventory Replenishment and Component Allocation Optimization in an Assemble-to-Order System," Management Science, INFORMS, vol. 50(1), pages 99-116, January.
    9. 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.
    10. 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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