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Improving the efficiency of a best-first bottom-up approach for the Constrained 2D Cutting Problem

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  • de Armas, Jesica
  • Miranda, Gara
  • León, Coromoto

Abstract

This work introduces several improvements in the solution of the Constrained 2D Cutting Problem. Such improvements combine the detection of dominated and duplicated cutting patterns with the implementation of parallel approaches for best-first search methods. The analysis of symmetries and dominances among the cutting patterns is able to discard some non-optimal or redundant builds, thus reducing the search space to be explored. The experimental evaluation demonstrates that when the domination/duplication rules are applied to an efficient parallel approach, the obtained reduction in the number of managed nodes involves a noticeable decrease in the computational effort associated with the final search process.

Suggested Citation

  • de Armas, Jesica & Miranda, Gara & León, Coromoto, 2012. "Improving the efficiency of a best-first bottom-up approach for the Constrained 2D Cutting Problem," European Journal of Operational Research, Elsevier, vol. 219(2), pages 201-213.
    • Handle: RePEc:eee:ejores:v:219:y:2012:i:2:p:201-213
    DOI: 10.1016/j.ejor.2011.11.002
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    References listed on IDEAS

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    1. Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
    2. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    3. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    4. P. Y. Wang, 1983. "Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems," Operations Research, INFORMS, vol. 31(3), pages 573-586, June.
    5. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    6. 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.
    7. Oliveira, JoseFernando & Ferreira, JoseSoeiro, 1990. "An improved version of Wang's algorithm for two-dimensional cutting problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 256-266, January.
    8. K. V. Viswanathan & A. Bagchi, 1993. "Best-First Search Methods for Constrained Two-Dimensional Cutting Stock Problems," Operations Research, INFORMS, vol. 41(4), pages 768-776, August.
    9. Fayard, Didier & Zissimopoulos, Vassilis, 1995. "An approximation algorithm for solving unconstrained two-dimensional knapsack problems," European Journal of Operational Research, Elsevier, vol. 84(3), pages 618-632, August.
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    Cited by:

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    3. Wei, Lijun & Lim, Andrew, 2015. "A bidirectional building approach for the 2D constrained guillotine knapsack packing problem," European Journal of Operational Research, Elsevier, vol. 242(1), pages 63-71.

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