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New filtering for the cumulative constraint in the context of non-overlapping rectangles

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  • Nicolas Beldiceanu
  • Mats Carlsson
  • Sophie Demassey
  • Emmanuel Poder

Abstract

This article describes new filtering methods for the cumulative constraint. The first method introduces the so called longest closed hole and longest open hole problems. For these two problems it first provides bounds and exact methods and then shows how to use them in the context of the non-overlapping constraint. The second method introduces balancing knapsack constraints which relate the total height of the tasks that end at a specific time-point with the total height of the tasks that start at the same time-point. Experiments on tight rectangle packing problems show that these methods drastically reduce both the time and the number of backtracks for finding all solutions as well as for finding the first solution. For example, we found without backtracking all solutions to 65 perfect square instances of order 22–25 and sizes ranging from 192×192 to 661×661. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:184:y:2011:i:1:p:27-50:10.1007/s10479-010-0731-0
    DOI: 10.1007/s10479-010-0731-0
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    References listed on IDEAS

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    1. 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.
    2. Clautiaux, Francois & Carlier, Jacques & Moukrim, Aziz, 2007. "A new exact method for the two-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1196-1211, December.
    3. Luc Mercier & Pascal Van Hentenryck, 2008. "Edge Finding for Cumulative Scheduling," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 143-153, February.
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    Cited by:

    1. Gleb Belov & Heide Rohling, 2013. "LP Bounds in an Interval-Graph Algorithm for Orthogonal-Packing Feasibility," Operations Research, INFORMS, vol. 61(2), pages 483-497, April.

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