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Spreading Points Using Gradient and Tabu

Author

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  • Xiangyang Huang

    (Capital Normal University)

  • LiGuo Huang

    (Southern Methodist University)

Abstract

Large spreading (packing) problems are hard to be solved exactly. Consequently, heuristic approaches are usually used to find approximate solutions. In this paper, a hybrid heuristic method, consisting of a Neighborhood Tabu (NT) and a Perturbed Gradient (PG), is proposed for solving spreading points problems. NT applies an adaptive random technique to selecting promising candidate solutions from the neighborhood of the current local minimum and PG uses a neighborhood-based perturbed gradient algorithm to seek a better minimum, starting from the candidates. Two procedures work alternatively and cooperatively. When applied to some previously studied packings, the proposed method can improve the accuracy of the previous record solutions.

Suggested Citation

  • Xiangyang Huang & LiGuo Huang, 2023. "Spreading Points Using Gradient and Tabu," SN Operations Research Forum, Springer, vol. 4(2), pages 1-11, June.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:2:d:10.1007_s43069-023-00214-7
    DOI: 10.1007/s43069-023-00214-7
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    References listed on IDEAS

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    1. 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.
    2. Mhand Hifi & Rym M'Hallah, 2009. "A Literature Review on Circle and Sphere Packing Problems: Models and Methodologies," Advances in Operations Research, Hindawi, vol. 2009, pages 1-22, July.
    3. B. Addis & M. Locatelli & F. Schoen, 2008. "Disk Packing in a Square: A New Global Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 516-524, November.
    4. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
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