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Packing ellipsoids by nonlinear optimization

Author

Listed:
  • E. G. Birgin

    (University of São Paulo)

  • R. D. Lobato

    (University of São Paulo)

  • J. M. Martínez

    (State University of Campinas)

Abstract

In this paper, continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the n-dimensional space are introduced. Two different models for the non-overlapping and models for the inclusion of ellipsoids within half-spaces and ellipsoids are presented. By applying a simple multi-start strategy combined with a clever choice of starting guesses and a nonlinear programming local solver, illustrative numerical experiments are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-015-0395-z
    DOI: 10.1007/s10898-015-0395-z
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    References listed on IDEAS

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    8. 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.
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    Citations

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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.

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