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


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  • Castillo, Ignacio
  • Kampas, Frank J.
  • Pintér, János D.
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    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Erkut, Erhan, 1990. "The discrete p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 46(1), pages 48-60, May.
    7. Dowsland, Kathryn A. & Dowsland, William B., 1992. "Packing problems," European Journal of Operational Research, Elsevier, vol. 56(1), pages 2-14, January.
    8. 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.
    9. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
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    Cited by:
    1. Giorgio Fasano, 2013. "A global optimization point of view to handle non-standard object packing problems," Journal of Global Optimization, Springer, vol. 55(2), pages 279-299, February.
    2. Mustafa Çağlayan & János Pintér, 2013. "Development and calibration of a currency trading strategy using global optimization," Journal of Global Optimization, Springer, vol. 56(2), pages 353-371, June.
    3. Hinostroza, Ignacio & Pradenas, Lorena & Parada, Víctor, 2013. "Board cutting from logs: Optimal and heuristic approaches for the problem of packing rectangles in a circle," International Journal of Production Economics, Elsevier, vol. 145(2), pages 541-546.
    4. Dam, E.R. van & Husslage, B.G.M. & Hertog, D. den, 2010. "One-dimensional nested maximin designs," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3448696, Tilburg University.
    5. 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.
    6. 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, vol. 17(4), pages 461-477, December.
    7. A. Grosso & A. Jamali & M. Locatelli & F. Schoen, 2010. "Solving the problem of packing equal and unequal circles in a circular container," Journal of Global Optimization, Springer, vol. 47(1), pages 63-81, May.
    8. Zvi Drezner, 2010. "On the unboundedness of facility layout problems," Computational Statistics, Springer, vol. 72(2), pages 205-216, October.
    9. Galiev, Shamil I. & Lisafina, Maria S., 2013. "Linear models for the approximate solution of the problem of packing equal circles into a given domain," European Journal of Operational Research, Elsevier, vol. 230(3), pages 505-514.
    10. Huang, Wenqi & Ye, Tao, 2011. "Global optimization method for finding dense packings of equal circles in a circle," European Journal of Operational Research, Elsevier, vol. 210(3), pages 474-481, May.
    11. János Pintér & Zoltán Horváth, 2013. "Integrated experimental design and nonlinear optimization to handle computationally expensive models under resource constraints," Journal of Global Optimization, Springer, vol. 57(1), pages 191-215, September.
    12. 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.
    13. János Pintér & Frank Kampas, 2013. "Benchmarking nonlinear optimization software in technical computing environments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(1), pages 133-162, April.


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