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Spotting Difficult Weakly Correlated Binary Knapsack Problems

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  • Ghosh, Diptesh
  • Bandyopadhyay, Tathagata

Abstract

In this paper, we examine the possibility of quickly deciding whether or not an instance of a binary knapsack problem is difficult for branch and bound algorithms. We first observe that the distribution of the objective function values is smooth and unimodal. We define a measure of difficulty of solving knapsack problems through branch and bound algorithms, and examine the relationship between the degree of correlation between profit and cost values, the skewness of the distribution of objective function values and the difficulty in solving weakly correlated binary knapsack problems. We see that the even though it is unlikely that an exact relationship exists for individual problem instances, some aggregate relationships may be observed. Key words: Binary Knapsack Problems; Skewness; Computational Experiments.

Suggested Citation

  • Ghosh, Diptesh & Bandyopadhyay, Tathagata, 2006. "Spotting Difficult Weakly Correlated Binary Knapsack Problems," IIMA Working Papers WP2006-01-04, Indian Institute of Management Ahmedabad, Research and Publication Department.
    • Handle: RePEc:iim:iimawp:wp01928
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    References listed on IDEAS

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    1. Silvano Martello & Paolo Toth, 1988. "A New Algorithm for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 34(5), pages 633-644, May.
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    5. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
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