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Greedy algorithms for packing unequal circles into a rectangular container

Author

Listed:
  • W Q Huang

    (HuaZhong University of Science and Technology)

  • Y Li

    (Université de Picardie Jules Verne)

  • H Akeb

    (Université de Picardie Jules Verne)

  • C M Li

    (Université de Picardie Jules Verne)

Abstract

In this paper, we study the problem of packing unequal circles into a two-dimensional rectangular container. We solve this problem by proposing two greedy algorithms. The first algorithm, denoted by B1.0, selects the next circle to place according to the maximum-hole degree rule, that is inspired from human activity in packing. The second algorithm, denoted by B1.5, improves B1.0 with a self-look-ahead search strategy. The comparisons with the published methods on several instances taken from the literature show the good performance of our approach.

Suggested Citation

  • W Q Huang & Y Li & H Akeb & C M Li, 2005. "Greedy algorithms for packing unequal circles into a rectangular container," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 539-548, May.
    • Handle: RePEc:pal:jorsoc:v:56:y:2005:i:5:d:10.1057_palgrave.jors.2601836
    DOI: 10.1057/palgrave.jors.2601836
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    References listed on IDEAS

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    1. Hifi, Mhand & Paschos, Vangelis Th. & Zissimopoulos, Vassilis, 2004. "A simulated annealing approach for the circular cutting problem," European Journal of Operational Research, Elsevier, vol. 159(2), pages 430-448, December.
    2. George, John A. & George, Jennifer M. & Lamar, Bruce W., 1995. "Packing different-sized circles into a rectangular container," European Journal of Operational Research, Elsevier, vol. 84(3), pages 693-712, August.
    3. Stoyan, Yu. G. & Yas'kov, G., 2004. "A mathematical model and a solution method for the problem of placing various-sized circles into a strip," European Journal of Operational Research, Elsevier, vol. 156(3), pages 590-600, August.
    4. Fraser, Hamish J. & George, John A., 1994. "Integrated container loading software for pulp and paper industry," European Journal of Operational Research, Elsevier, vol. 77(3), pages 466-474, September.
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    Cited by:

    1. Wei, Lijun & Oon, Wee-Chong & Zhu, Wenbin & Lim, Andrew, 2012. "A reference length approach for the 3D strip packing problem," European Journal of Operational Research, Elsevier, vol. 220(1), pages 37-47.
    2. T. Kubach & A. Bortfeldt & H. Gehring, 2009. "Parallel greedy algorithms for packing unequal circles into a strip or a rectangle," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(4), pages 461-477, December.
    3. Yaohua He & Yong Wu, 2013. "Packing non-identical circles within a rectangle with open length," Journal of Global Optimization, Springer, vol. 56(3), pages 1187-1215, July.
    4. Stoyan, Yu. & Chugay, A., 2009. "Packing cylinders and rectangular parallelepipeds with distances between them into a given region," European Journal of Operational Research, Elsevier, vol. 197(2), pages 446-455, September.
    5. López, C.O. & Beasley, J.E., 2016. "A formulation space search heuristic for packing unequal circles in a fixed size circular container," European Journal of Operational Research, Elsevier, vol. 251(1), pages 64-73.
    6. Ronald E. Giachetti & Jean Carlo Sanchez, 2009. "A model to design recreational boat mooring fields," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 158-174, March.
    7. Fu, Zhanghua & Huang, Wenqi & Lü, Zhipeng, 2013. "Iterated tabu search for the circular open dimension problem," European Journal of Operational Research, Elsevier, vol. 225(2), pages 236-243.
    8. Zeng, Zhizhong & Yu, Xinguo & He, Kun & Huang, Wenqi & Fu, Zhanghua, 2016. "Iterated Tabu Search and Variable Neighborhood Descent for packing unequal circles into a circular container," European Journal of Operational Research, Elsevier, vol. 250(2), pages 615-627.
    9. K A Dowsland & M Gilbert & G Kendall, 2007. "A local search approach to a circle cutting problem arising in the motor cycle industry," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(4), pages 429-438, April.
    10. Hifi, Mhand & Yousef, Labib, 2019. "A local search-based method for sphere packing problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 482-500.

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