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Packing ellipsoids in an optimized cylinder

Author

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  • Romanova, Tatiana
  • Litvinchev, Igor
  • Pankratov, Alexander

Abstract

The paper studies packing ellipsoids of revolution in a cylindrical container of minimum volume. Ellipsoids can be continuously rotated and translated. Two nonlinear mathematical programming models are introduced: exact and approximated. The latter uses an optimized multi-spherical approximation of ellisoids. For both models the phi-function technique is employed to describe analytically non-overlapping and containment constraints. Two solution approaches are proposed to solve the packing problem. Computational results for up to 500 ellipsoids are provided to demonstrate efficiency of the proposed approaches.

Suggested Citation

  • Romanova, Tatiana & Litvinchev, Igor & Pankratov, Alexander, 2020. "Packing ellipsoids in an optimized cylinder," European Journal of Operational Research, Elsevier, vol. 285(2), pages 429-443.
    • Handle: RePEc:eee:ejores:v:285:y:2020:i:2:p:429-443
    DOI: 10.1016/j.ejor.2020.01.051
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    References listed on IDEAS

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    1. Josef Kallrath & Steffen Rebennack, 2014. "Cutting ellipses from area-minimizing rectangles," Journal of Global Optimization, Springer, vol. 59(2), pages 405-437, July.
    2. Donald Jones, 2014. "A fully general, exact algorithm for nesting irregular shapes," Journal of Global Optimization, Springer, vol. 59(2), pages 367-404, July.
    3. A. Pankratov & T. Romanova & I. Litvinchev, 2019. "Packing ellipses in an optimized convex polygon," Journal of Global Optimization, Springer, vol. 75(2), pages 495-522, October.
    4. 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.
    5. Josef Kallrath, 2017. "Packing ellipsoids into volume-minimizing rectangular boxes," Journal of Global Optimization, Springer, vol. 67(1), pages 151-185, January.
    6. Pedro Rocha & A. Miguel Gomes & Rui Rodrigues & Franklina M. B. Toledo & Marina Andretta, 2016. "Constraint Aggregation in Non-linear Programming Models for Nesting Problems," Lecture Notes in Economics and Mathematical Systems, in: Raquel J. Fonseca & Gerhard-Wilhelm Weber & João Telhada (ed.), Computational Management Science, edition 1, pages 175-180, Springer.
    7. 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.
    8. Birgin, E.G. & Lobato, R.D., 2019. "A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids," European Journal of Operational Research, Elsevier, vol. 272(2), pages 447-464.
    9. Yuriy Stoyan & Tatiana Romanova & Alexander Pankratov & Andrey Chugay, 2015. "Optimized Object Packings Using Quasi-Phi-Functions," Springer Optimization and Its Applications, in: Giorgio Fasano & János D. Pintér (ed.), Optimized Packings with Applications, edition 1, chapter 0, pages 265-293, Springer.
    10. Romanova, T. & Bennell, J. & Stoyan, Y. & Pankratov, A., 2018. "Packing of concave polyhedra with continuous rotations using nonlinear optimisation," European Journal of Operational Research, Elsevier, vol. 268(1), pages 37-53.
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    Cited by:

    1. Andreas Fischer & Igor Litvinchev & Tetyana Romanova & Petro Stetsyuk & Georgiy Yaskov, 2023. "Quasi-Packing Different Spheres with Ratio Conditions in a Spherical Container," Mathematics, MDPI, vol. 11(9), pages 1-19, April.
    2. Romanova, Tatiana & Stoyan, Yurij & Pankratov, Alexander & Litvinchev, Igor & Plankovskyy, Sergiy & Tsegelnyk, Yevgen & Shypul, Olga, 2021. "Sparsest balanced packing of irregular 3D objects in a cylindrical container," European Journal of Operational Research, Elsevier, vol. 291(1), pages 84-100.
    3. Igor Litvinchev & Andreas Fischer & Tetyana Romanova & Petro Stetsyuk, 2024. "A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms," Mathematics, MDPI, vol. 12(7), pages 1-17, March.
    4. Josef Kallrath & Joonghyun Ryu & Chanyoung Song & Mokwon Lee & Deok-Soo Kim, 2021. "Near optimal minimal convex hulls of disks," Journal of Global Optimization, Springer, vol. 80(3), pages 551-594, July.
    5. Josef Kallrath & Tatiana Romanova & Alexander Pankratov & Igor Litvinchev & Luis Infante, 2023. "Packing convex polygons in minimum-perimeter convex hulls," Journal of Global Optimization, Springer, vol. 85(1), pages 39-59, January.

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