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Iterated tabu search for the circular open dimension problem

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  • Fu, Zhanghua
  • Huang, Wenqi
  • Lü, Zhipeng
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    Abstract

    This paper investigates the circular open dimension problem (CODP), which consists of packing a set of circles of known radii into a strip of fixed width and unlimited length without overlapping. The objective is to minimize the length of the strip. In this paper, CODP is solved by a series of sub-problems, each corresponding to a fixed strip length. For each sub-problem, an iterated tabu search approach, named ITS, is proposed. ITS starts from a randomly generated solution and attempts to gain improvements by a tabu search procedure. After that, if the obtained solution is not feasible, a perturbation operator is subsequently employed to reconstruct the incumbent solution and an acceptance criterion is implemented to determine whether or not accept the perturbed solution. As a supplementary method, the length of the strip is determined in monotonously decreasing way, with the aid of some post-processing techniques. The search terminates and returns the best found solution after the allowed computation time has been elapsed. Computational experiments based on numerous well-known benchmark instances show that ITS produces quite competitive results, with respect to the best known results, while the computational time remains reasonable for each instance.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712007680
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    Bibliographic Info

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

    Volume (Year): 225 (2013)
    Issue (Month): 2 ()
    Pages: 236-243

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    Handle: RePEc:eee:ejores:v:225:y:2013:i:2:p:236-243

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Packing; Cutting; Tabu search; Perturbation operator; Acceptance criterion;

    References

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    1. 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.
    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. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    4. 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.
    5. James, Tabitha & Rego, Cesar & Glover, Fred, 2009. "A cooperative parallel tabu search algorithm for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 195(3), pages 810-826, June.
    6. 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.
    7. 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.
    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. 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.
    10. Lü, Zhipeng & Hao, Jin-Kao, 2010. "Adaptive Tabu Search for course timetabling," European Journal of Operational Research, Elsevier, vol. 200(1), pages 235-244, January.
    11. 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.
    12. I Al-Mudahka & M Hifi & R M'Hallah, 2011. "Packing circles in the smallest circle: an adaptive hybrid algorithm," Journal of the Operational Research Society, Palgrave Macmillan, vol. 62(11), pages 1917-1930, November.
    13. 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.
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