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Cost Based Filtering for the Constrained Knapsack Problem

Author

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  • Torsten Fahle
  • Meinolf Sellmann

Abstract

We present cost based filtering methods for Knapsack Problems (KPs). Cost based filtering aims at fixing variables with respect to the objective function. It is an important technique when solving complex problems such as Quadratic Knapsack Problems, or KPs with additional constraints (Constrained Knapsack Problems (CKPs)). They evolve, e.g., when Constraint Based Column Generation is applied to appropriate optimization problems. We develop new reduction algorithms for KP. They are used as propagation routines for the CKP with Θ(nlog n) preprocessing time and Θ(n) time per call. This sums up to an amortized time Θ(n) for Ω(log n) incremental calls where the subsequent problems may differ with respect to arbitrary sets of necessarily included and excluded items. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Torsten Fahle & Meinolf Sellmann, 2002. "Cost Based Filtering for the Constrained Knapsack Problem," Annals of Operations Research, Springer, vol. 115(1), pages 73-93, September.
    • Handle: RePEc:spr:annopr:v:115:y:2002:i:1:p:73-93:10.1023/a:1021193019522
    DOI: 10.1023/A:1021193019522
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    Cited by:

    1. Benoist, Thierry & Bourreau, Eric & Rottembourg, Benoit, 2007. "The TV-Break Packing Problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1371-1386, February.
    2. Stefano Gualandi & Federico Malucelli, 2012. "Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 81-100, February.
    3. Roberto Rossi & S. Tarim & Brahim Hnich & Steven Prestwich, 2012. "Constraint programming for stochastic inventory systems under shortage cost," Annals of Operations Research, Springer, vol. 195(1), pages 49-71, May.
    4. Stefano Gualandi & Federico Malucelli, 2013. "Constraint Programming-based Column Generation," Annals of Operations Research, Springer, vol. 204(1), pages 11-32, April.

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