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A Dynamic Programming Approach for Consistency and Propagation for Knapsack Constraints

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  • Michael Trick

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. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Michael Trick, 2003. "A Dynamic Programming Approach for Consistency and Propagation for Knapsack Constraints," Annals of Operations Research, Springer, vol. 118(1), pages 73-84, February.
    • Handle: RePEc:spr:annopr:v:118:y:2003:i:1:p:73-84:10.1023/a:1021801522545
    DOI: 10.1023/A:1021801522545
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    Cited by:

    1. Gilles Pesant, 2015. "Achieving Domain Consistency and Counting Solutions for Dispersion Constraints," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 690-703, November.
    2. Malapert, Arnaud & Guéret, Christelle & Rousseau, Louis-Martin, 2012. "A constraint programming approach for a batch processing problem with non-identical job sizes," European Journal of Operational Research, Elsevier, vol. 221(3), pages 533-545.
    3. Fabio Furini & Enrico Malaguti & Dimitri Thomopulos, 2016. "Modeling Two-Dimensional Guillotine Cutting Problems via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 736-751, November.
    4. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    5. Nicolas Beldiceanu & Mats Carlsson & Sophie Demassey & Emmanuel Poder, 2011. "New filtering for the cumulative constraint in the context of non-overlapping rectangles," Annals of Operations Research, Springer, vol. 184(1), pages 27-50, April.

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