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Packing convex polygons in minimum-perimeter convex hulls

Author

Listed:
  • Josef Kallrath

    (University of Florida)

  • Tatiana Romanova

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

  • Alexander Pankratov

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

  • Igor Litvinchev

    (Graduate Program in Systems Engineering, Nuevo Leon State University (UANL))

  • Luis Infante

    (Graduate Program in Systems Engineering, Nuevo Leon State University (UANL))

Abstract

The problem of packing a given set of freely translated and rotated convex polygons in a minimum-perimeter convex polygon (in particular the minimum-perimeter convex hull) is introduced. A mathematical model of the problem using the phi-function technique is provided. Problem instances with up to 6 convex polygons are solved by the global NLP solver BARON to get a minimum-perimeter convex hull. Numerical experiments for larger instances are reported using the local NLP solver IPOPT.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:1:d:10.1007_s10898-022-01194-4
    DOI: 10.1007/s10898-022-01194-4
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    References listed on IDEAS

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