IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v285y2020i2p429-443.html
   My bibliography  Save this article

Packing ellipsoids in an optimized cylinder

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221720300886
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2020.01.051?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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. 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.
    4. 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.
    5. 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.
    6. Donald Jones, 2014. "A fully general, exact algorithm for nesting irregular shapes," Journal of Global Optimization, Springer, vol. 59(2), pages 367-404, July.
    7. 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.
    8. Josef Kallrath, 2017. "Packing ellipsoids into volume-minimizing rectangular boxes," Journal of Global Optimization, Springer, vol. 67(1), pages 151-185, January.
    9. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    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. Frank J. Kampas & János D. Pintér & Ignacio Castillo, 2020. "Packing ovals in optimized regular polygons," Journal of Global Optimization, Springer, vol. 77(1), pages 175-196, May.
    5. 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.
    6. Tiago Montanher & Arnold Neumaier & Mihály Csaba Markót & Ferenc Domes & Hermann Schichl, 2019. "Rigorous packing of unit squares into a circle," Journal of Global Optimization, Springer, vol. 73(3), pages 547-565, March.
    7. Ryu, Joonghyun & Lee, Mokwon & Kim, Donguk & Kallrath, Josef & Sugihara, Kokichi & Kim, Deok-Soo, 2020. "VOROPACK-D: Real-time disk packing algorithm using Voronoi diagram," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    8. 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.
    9. 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.
    10. Akang Wang & Christopher L. Hanselman & Chrysanthos E. Gounaris, 2018. "A customized branch-and-bound approach for irregular shape nesting," Journal of Global Optimization, Springer, vol. 71(4), pages 935-955, August.
    11. Alexander Pankratov & Tatiana Romanova & Igor Litvinchev, 2020. "Packing Oblique 3D Objects," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    12. Cafieri, Sonia & Conn, Andrew R. & Mongeau, Marcel, 2023. "Mixed-integer nonlinear and continuous optimization formulations for aircraft conflict avoidance via heading and speed deviations," European Journal of Operational Research, Elsevier, vol. 310(2), pages 670-679.
    13. Josef Kallrath & Markus M. Frey, 2019. "Packing circles into perimeter-minimizing convex hulls," Journal of Global Optimization, Springer, vol. 73(4), pages 723-759, April.
    14. Yizhe Yang & Bingshan Liu & Haochen Li & Xin Li & Gong Wang & Shan Li, 2023. "A nesting optimization method based on digital contour similarity matching for additive manufacturing," Journal of Intelligent Manufacturing, Springer, vol. 34(6), pages 2825-2847, August.
    15. 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.
    16. Luiz H. Cherri & Adriana C. Cherri & Edilaine M. Soler, 2018. "Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations," Journal of Global Optimization, Springer, vol. 72(1), pages 89-107, September.
    17. 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.
    18. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
    19. Burak Beyhan & Cüneyt Güler & Hidayet Tağa, 2020. "An algorithm for maximum inscribed circle based on Voronoi diagrams and geometrical properties," Journal of Geographical Systems, Springer, vol. 22(3), pages 391-418, July.
    20. Igor Kierkosz & Maciej Łuczak, 2019. "A one-pass heuristic for nesting problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(1), pages 37-60.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:285:y:2020:i:2:p:429-443. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.