# Packing ellipses in an optimized rectangular container

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## Abstract

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.

## Keywords

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

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