Packing ellipses in an optimized rectangular container

  • A. Pankratov
  • T. Romanova
  • I. Litvinchev


The paper studies packing ellipses in a rectangular container of minimum area. The problem has various applications in production, logistics, industrial design. New phi-functions are proposed to state containment constraints and quasi-phi-functions are used for analytical description of non-overlapping constraints. A mathematical model for the packing problem is stated as a nonlinear programming problem. Two algorithms to find feasible starting points for identical and non-identical ellipses are proposed. The optimization procedure is used as a compaction algorithm to search for local optimal solutions. Computational results are provided to show the efficiency of the proposed approach.


Ellipses Packing Continuous rotations Phi-function technique Mathematical modelling Nonlinear optimization 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Mechanical Engineering Problems of the National Academy of Sciences of UkraineKharkivUkraine
  2. 2.Nuevo Leon State University (UANL)MexicoMexico

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