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A hard knapsack problem

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  • Chia‐Shin Chung
  • Ming S. Hung
  • Walter O. Rom

Abstract

In this article we develop a class of general knapsack problems which are hard for branch and bound algorithms. The number of alternate optimal solutions for these problems grows exponentially with problem parameters. In addition the LP bound is shown to be ineffective. Computational tests indicate that these problems are truly difficult for even very small problems. Implications for the testing of algorithms using randomly generated problems is discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:1:p:85-98
    DOI: 10.1002/1520-6750(198802)35:13.0.CO;2-D
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    References listed on IDEAS

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    1. Vasek Chvátal, 1980. "Hard Knapsack Problems," Operations Research, INFORMS, vol. 28(6), pages 1402-1411, December.
    2. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    3. R. L. Bulfin & R. G. Parker & C. M. Shetty, 1979. "Computational results with a branch‐and‐bound algorithm for the general knapsack problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(1), pages 41-46, March.
    4. A. Victor Cabot, 1970. "An Enumeration Algorithm for Knapsack Problems," Operations Research, INFORMS, vol. 18(2), pages 306-311, April.
    5. 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.
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    Cited by:

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    2. Zonghao Gu & George L. Nemhauser & Martin W. P. Savelsbergh, 1999. "Lifted Cover Inequalities for 0-1 Integer Programs: Complexity," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 117-123, February.

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