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Merging and Sorting Applied to the Zero-One Knapsack Problem

Author

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  • J. H. Ahrens

    (Nova Scotia Technical College, Halifax, Nova Scotia)

  • G. Finke

    (Nova Scotia Technical College, Halifax, Nova Scotia)

Abstract

Branch-and-bound algorithms are adequate for the solution of a wide range of 0-1 knapsack problems. It is shown that the simplest method of branching is as good as any. However, problems with highly correlated large weights and values quickly become unsolvable in a reasonable time. This paper develops algorithms that are aimed specifically at the hardest possible examples. The new methods use merging and sorting ideas and require a moderate amount of additional memory space. They are, however, faster by factors far in excess of 1,000 in many cases, thereby extending considerably the range of practically solvable 0-1 knapsack problems.

Suggested Citation

  • J. H. Ahrens & G. Finke, 1975. "Merging and Sorting Applied to the Zero-One Knapsack Problem," Operations Research, INFORMS, vol. 23(6), pages 1099-1109, December.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:6:p:1099-1109
    DOI: 10.1287/opre.23.6.1099
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    Cited by:

    1. Chia‐Shin Chung & Ming S. Hung & Walter O. Rom, 1988. "A hard knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 85-98, February.

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