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A New Algorithm for the 0-1 Knapsack Problem

Author

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  • Silvano Martello

    (DEIS, University of Bologna, Italy)

  • Paolo Toth

    (DEIS, University of Bologna, Italy)

Abstract

We present a new algorithm for the optimal solution of the 0-1 Knapsack problem, which is particularly effective for large-size problems. The algorithm is based on determination of an appropriate small subset of items and the solution of the corresponding "core problem": from this we derive a heuristic solution for the original problem which, with high probability, can be proved to be optimal. The algorithm incorporates a new method of computation of upper bounds and efficient implementations of reduction procedures. The corresponding Fortran code is available. We report computational experiments on small-size and large-size random problems, comparing the proposed code with all those available in the literature.

Suggested Citation

  • Silvano Martello & Paolo Toth, 1988. "A New Algorithm for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 34(5), pages 633-644, May.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:5:p:633-644
    DOI: 10.1287/mnsc.34.5.633
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    Keywords

    Knapsack problem; branch-and-bound;

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