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A Dynamic Programming Approach for Consistency and Propagation for Knapsack Constraints

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Abstract

Knapsack constraints are a key modeling structure in constraint programming. These constraints are normally handled with simple bounding arguments. We propose a dynamic programming structure to represent these constraints. With this structure, we are able to achieve hyper-arc consistency, to determine infeasibility before all variables are set, to generate all solutions quickly, and to provide incrementality by updating the structure after domain reduction. Testing on a difficult set of multiple knapsack instances shows significant reduction in branching.

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Authors and Affiliations

  1. GSIA, Carnegie Bosch Institute, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Michael A. Trick

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  1. Michael A. Trick
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Trick, M.A. A Dynamic Programming Approach for Consistency and Propagation for Knapsack Constraints. Annals of Operations Research 118, 73–84 (2003). https://doi.org/10.1023/A:1021801522545

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  • DOI: https://doi.org/10.1023/A:1021801522545

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