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A recursive branch and bound algorithm for the multidimensional knapsack problem

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  • Arne Thesen

Abstract

This paper presents an efficient branch and bound algorithm for the solution of certain multiconstrained knapsack problems. The key to this algorithm is a rigidly defined tree structure in which branching and bounding may be performed through recursive relationships. The algorithm is particularly useful when only limited amounts of core storage are available as only the current and one previous solution is saved at any one time. Execution speeds compare favorably with other algorithms. A numerical example and computational experience is given.

Suggested Citation

  • Arne Thesen, 1975. "A recursive branch and bound algorithm for the multidimensional knapsack problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(2), pages 341-353, June.
    • Handle: RePEc:wly:navlog:v:22:y:1975:i:2:p:341-353
    DOI: 10.1002/nav.3800220210
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    Cited by:

    1. 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.
    2. 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.

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