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Packing non-identical circles within a rectangle with open length

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  • Yaohua He
  • Yong Wu

Abstract

Packing non-identical circles inside a rectangle witnesses a wide range of industrial applications. However, the non-convex constraints in this problem make it intractable using exact analytical approaches. Even via heuristic methods, the solution time for industrial-scale instances sometimes is too long to be acceptable. This article aims to challenge the existing methods for the benchmark instances. The most significant contributions of this work are: firstly, we proposed three types of packing positions for selection and used human intelligence to convert an arbitrary circle sequence into a feasible compact layout; secondly, diverse position selection criteria have been tested, and it is found that the criterion commonly used in the literature is not the best; thirdly, the traditional genetic algorithm is adapted with lower crossover rate but higher mutation rate particularly, and a minor-adjustment operator with the purpose of exploring the neighborhood of the current best solutions is introduced. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:3:p:1187-1215
    DOI: 10.1007/s10898-012-9948-6
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. Birgin, E. G. & Martinez, J. M. & Ronconi, D. P., 2005. "Optimizing the packing of cylinders into a rectangular container: A nonlinear approach," European Journal of Operational Research, Elsevier, vol. 160(1), pages 19-33, January.
    5. Wu, Yong & Li, Wenkai & Goh, Mark & de Souza, Robert, 2010. "Three-dimensional bin packing problem with variable bin height," European Journal of Operational Research, Elsevier, vol. 202(2), pages 347-355, April.
    6. 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. 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.

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