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Parallel greedy algorithms for packing unequal circles into a strip or a rectangle

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  • T. Kubach
  • A. Bortfeldt
  • H. Gehring

Abstract

Given a finite set of circles of different sizes we study the strip packing problem (SPP) as well as the Knapsack Problem (KP). The SPP asks for a placement of all circles within a rectangular strip of fixed width so that the variable length of the strip is minimized. The KP requires packing of a subset of the circles in a given rectangle so that the wasted area is minimized. To solve these problems some greedy algorithms were developed which enhance the algorithms proposed by Huang et al. (J Oper Res Soc 56:539–548, 2005). Furthermore, the new greedy algorithms were parallelized using a master slave approach. The resulting parallel methods were tested using the instances introduced by Stoyan and Yaskov (Eur J Oper Res 156:590–600, 2004). Additionally, two sets of 128 instances each for the SPP and for the KP were generated and results for these new instances are also reported. Copyright Springer-Verlag 2009

Suggested Citation

  • 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.
    • Handle: RePEc:spr:cejnor:v:17:y:2009:i:4:p:461-477
    DOI: 10.1007/s10100-009-0103-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Castillo, Ignacio & Kampas, Frank J. & Pintér, János D., 2008. "Solving circle packing problems by global optimization: Numerical results and industrial applications," European Journal of Operational Research, Elsevier, vol. 191(3), pages 786-802, December.
    5. 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.
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    Cited by:

    1. Balázs Bánhelyi & Endre Palatinus & Balázs Lévai, 2015. "Optimal circle covering problems and their applications," 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. 23(4), pages 815-832, December.
    2. 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.
    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. 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.
    5. 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.

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