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Solving circle packing problems by global optimization: Numerical results and industrial applications

Listed author(s):
  • Castillo, Ignacio
  • Kampas, Frank J.
  • Pintér, János D.
Registered author(s):

    A (general) circle packing is an optimized arrangement of N arbitrary sized circles inside a container (e.g., a rectangle or a circle) such that no two circles overlap. In this paper, we present several circle packing problems, review their industrial applications, and some exact and heuristic strategies for their solution. We also present illustrative numerical results using 'generic' global optimization software packages. Our work highlights the relevance of global optimization in solving circle packing problems, and points towards the necessary advancements in both theory and numerical practice.

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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 191 (2008)
    Issue (Month): 3 (December)
    Pages: 786-802

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    Handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:786-802
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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. Dowsland, Kathryn A. & Dowsland, William B., 1992. "Packing problems," European Journal of Operational Research, Elsevier, vol. 56(1), pages 2-14, January.
    4. 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.
    5. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    6. Haessler, Robert W. & Sweeney, Paul E., 1991. "Cutting stock problems and solution procedures," European Journal of Operational Research, Elsevier, vol. 54(2), pages 141-150, September.
    7. 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.
    8. Wang, Huaiqing & Huang, Wenqi & Zhang, Quan & Xu, Dongming, 2002. "An improved algorithm for the packing of unequal circles within a larger containing circle," European Journal of Operational Research, Elsevier, vol. 141(2), pages 440-453, September.
    9. Erkut, Erhan, 1990. "The discrete p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 46(1), pages 48-60, May.
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