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Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region

Author

Listed:
  • Y G Stoyan

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine)

  • M V Zlotnik

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine)

  • A M Chugay

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine)

Abstract

This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the Φ-function technique, a mathematical model of the problem is constructed and its characteristics are investigated. Based on the characteristics, a solution approach to the problem is offered. The approach includes the following methods: an optimization method by groups of variables to construct starting points, a modification of the Zoutendijk feasible direction method to search for local minima and a special non-exhaustive search of local minima to find an approximation to a global minimum. A number of numerical results are given. The numerical results are compared with the best known ones.

Suggested Citation

  • Y G Stoyan & M V Zlotnik & A M Chugay, 2012. "Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(3), pages 379-391, March.
    • Handle: RePEc:pal:jorsoc:v:63:y:2012:i:3:p:379-391
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    Citations

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    Cited by:

    1. E. G. Birgin & R. D. Lobato & J. M. Martínez, 2017. "A nonlinear programming model with implicit variables for packing ellipsoids," Journal of Global Optimization, Springer, vol. 68(3), pages 467-499, July.
    2. E. G. Birgin & R. D. Lobato & J. M. Martínez, 2016. "Packing ellipsoids by nonlinear optimization," Journal of Global Optimization, Springer, vol. 65(4), pages 709-743, August.
    3. Leao, Aline A.S. & Toledo, Franklina M.B. & Oliveira, José Fernando & Carravilla, Maria Antónia & Alvarez-Valdés, Ramón, 2020. "Irregular packing problems: A review of mathematical models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 803-822.
    4. Lai, Xiangjing & Hao, Jin-Kao & Yue, Dong & Lü, Zhipeng & Fu, Zhang-Hua, 2022. "Iterated dynamic thresholding search for packing equal circles into a circular container," European Journal of Operational Research, Elsevier, vol. 299(1), pages 137-153.
    5. Lastra-Díaz, Juan J. & Ortuño, M. Teresa, 2024. "Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts," European Journal of Operational Research, Elsevier, vol. 313(1), pages 69-91.

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