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Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem

Author

Listed:
  • Silvano Martello

    (DEIS, University of Bologna, Viale Risorgimento 2, Bologna, Italy)

  • David Pisinger

    (DIKU, University of Copenhagen, Univ.parken 1, Copenhagen, Denmark)

  • Paolo Toth

    (DEIS, University of Bologna, Viale Risorgimento 2, Bologna, Italy)

Abstract

Two new algorithms recently proved to outperform all previous methods for the exact solution of the 0-1 Knapsack Problem. This paper presents a combination of such approaches, where, in addition, valid inequalities are generated and surrogate relaxed, and a new initial core problem is adopted. The algorithm is able to solve all classical test instances, with up to 10,000 variables, in less than 0.2 seconds on a HP9000-735/99 computer. The C language implementation of the algorithm is available on the internet.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:3:p:414-424
    DOI: 10.1287/mnsc.45.3.414
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    References listed on IDEAS

    as
    1. Pisinger, David, 1995. "An expanding-core algorithm for the exact 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 87(1), pages 175-187, November.
    2. Freville, Arnaud & Plateau, Gerard, 1993. "An exact search for the solution of the surrogate dual of the 0-1 bidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 68(3), pages 413-421, August.
    3. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    4. Silvano Martello & Paolo Toth, 1984. "A Mixture of Dynamic Programming and Branch-and-Bound for the Subset-Sum Problem," Management Science, INFORMS, vol. 30(6), pages 765-771, June.
    5. Silvano Martello & Paolo Toth, 1988. "A New Algorithm for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 34(5), pages 633-644, May.
    6. Silvano Martello & Paolo Toth, 1997. "Upper Bounds and Algorithms for Hard 0-1 Knapsack Problems," Operations Research, INFORMS, vol. 45(5), pages 768-778, October.
    7. David Pisinger, 1997. "A Minimal Algorithm for the 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 45(5), pages 758-767, October.
    Full references (including those not matched with items on IDEAS)

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