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An efficient algorithm for the regular W1 packing of polygons in the infinite plane

Author

Listed:
  • P D Watson

    (University of Birmingham)

  • A M Tobias

    (University of Birmingham)

Abstract

This paper describes a new algorithm, PLANEPACK, which determines an optimal or near optimal solution for the W1 packing of identical shapes in the infinite plane. Restricted to polygons for computational convenience, it is based on the no-fit polygon/configuration space obstacle approach. The algorithm was tested on a modest set of fourteen polygons (thirteen non-interlocking and one interlocking) and yielded a feasible solution for each. The solutions were optimal for four of the non-interlocking polygons and near optimal for the other nine. As expected though, the solution for the one interlocking polygon was sub-optimal and enhancements to the algorithm would be required for such cases.

Suggested Citation

  • P D Watson & A M Tobias, 1999. "An efficient algorithm for the regular W1 packing of polygons in the infinite plane," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1054-1062, October.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:10:d:10.1057_palgrave.jors.2600807
    DOI: 10.1057/palgrave.jors.2600807
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    Citations

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    Cited by:

    1. L Huyao & H Yuanjun & J A Bennell, 2007. "The irregular nesting problem: a new approach for nofit polygon calculation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(9), pages 1235-1245, September.
    2. Qiang Luo & Yunqing Rao, 2022. "Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    3. Alvarez-Valdes, R. & Martinez, A. & Tamarit, J.M., 2013. "A branch & bound algorithm for cutting and packing irregularly shaped pieces," International Journal of Production Economics, Elsevier, vol. 145(2), pages 463-477.
    4. Elkeran, Ahmed, 2013. "A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering," European Journal of Operational Research, Elsevier, vol. 231(3), pages 757-769.
    5. Bennell, Julia A. & Oliveira, Jose F., 2008. "The geometry of nesting problems: A tutorial," European Journal of Operational Research, Elsevier, vol. 184(2), pages 397-415, January.

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