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Packing ovals in optimized regular polygons

Author

Listed:
  • Frank J. Kampas

    (Physicist at Large Consulting LLC)

  • János D. Pintér

    (Lehigh University)

  • Ignacio Castillo

    (Wilfrid Laurier University)

Abstract

We present a model development framework and numerical solution approach to the general problem-class of packing convex objects into optimized convex containers. Specifically, we discuss the problem of packing ovals (egg-shaped objects, defined here as generalized ellipses) into optimized regular polygons in $$ {\mathbb{R}}^{2} $$R2. Our solution strategy is based on the use of embedded Lagrange multipliers, followed by nonlinear optimization. Credible numerical results are attained using randomized starting solutions, refined by a single call to a local optimization solver. We obtain visibly good quality packings for packing 4 to 10 ovals into regular polygons with 3 to 10 sides in all 224 test problems presented here. Our modeling and solution approach can be extended towards handling other difficult packing problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:1:d:10.1007_s10898-019-00824-8
    DOI: 10.1007/s10898-019-00824-8
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    References listed on IDEAS

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    Cited by:

    1. Andreas Fischer & Igor Litvinchev & Tetyana Romanova & Petro Stetsyuk & Georgiy Yaskov, 2024. "Packing spheres with quasi-containment conditions," Journal of Global Optimization, Springer, vol. 90(3), pages 671-689, November.
    2. 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.
    3. Frank J. Kampas & János D. Pintér & Ignacio Castillo, 2023. "Model Development and Solver Demonstrations Using Randomized Test Problems," SN Operations Research Forum, Springer, vol. 4(1), pages 1-15, March.

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