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

Silvano Martello, David Pisinger and Paolo Toth
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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

Management Science, 1999, vol. 45, issue 3, 414-424

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.

Keywords: Knapsack problem; dynamic programming; branch-and-bound; surrogate relaxation (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (64)

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