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Heuristic approaches to large-scale periodic packing of irregular shapes on a rectangular sheet

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  • Costa, M. Teresa
  • Gomes, A. Miguel
  • Oliveira, José F.

Abstract

The nesting problem is a two-dimensional cutting and packing problem where the small pieces to cut have irregular shapes. A particular case of the nesting problem occurs when congruent copies of one single shape have to fill, as much as possible, a limited sheet. Traditional approaches to the nesting problem have difficulty to tackle with high number of pieces to place. Additionally, if the orientation of the given shape is not a constraint, the general nesting approaches are not particularly successful. This problem arises in practice in several industrial contexts such as footwear, metalware and furniture. A possible approach is the periodic placement of the shapes, in a lattice way. In this paper, we propose three heuristic approaches to solve this particular case of nesting problems. Experimental results are compared with published results in literature and additional results obtained from new instances are also provided.

Suggested Citation

  • Costa, M. Teresa & Gomes, A. Miguel & Oliveira, José F., 2009. "Heuristic approaches to large-scale periodic packing of irregular shapes on a rectangular sheet," European Journal of Operational Research, Elsevier, vol. 192(1), pages 29-40, January.
    • Handle: RePEc:eee:ejores:v:192:y:2009:i:1:p:29-40
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    References listed on IDEAS

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    1. 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.
    2. Stoyan, Yu G. & Patsuk, V. N., 2000. "A method of optimal lattice packing of congruent oriented polygons in the plane," European Journal of Operational Research, Elsevier, vol. 124(1), pages 204-216, July.
    3. Dowsland, Kathryn A. & Dowsland, William B., 1992. "Packing problems," European Journal of Operational Research, Elsevier, vol. 56(1), pages 2-14, January.
    4. Stoyan, Yu. G. & Pankratov, A. V., 1999. "Regular packing of congruent polygons on the rectangular sheet," European Journal of Operational Research, Elsevier, vol. 113(3), pages 653-675, March.
    5. Gomes, A. Miguel & Oliveira, Jose F., 2002. "A 2-exchange heuristic for nesting problems," European Journal of Operational Research, Elsevier, vol. 141(2), pages 359-370, September.
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    Cited by:

    1. Liu, Jingfa & Jiang, Yucong & Li, Gang & Xue, Yu & Liu, Zhaoxia & Zhang, Zhen, 2015. "Heuristic-based energy landscape paving for the circular packing problem with performance constraints of equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 166-174.
    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. Donald Jones, 2014. "A fully general, exact algorithm for nesting irregular shapes," Journal of Global Optimization, Springer, vol. 59(2), pages 367-404, July.

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