Packing circles within ellipses

The problem of packing circles within ellipses is considered in the present paper. A new ellipse-based system of coordinates is introduced by means of which a closed formula to compute the distance of an arbitrary point to the boundary of an ellipse exists. Nonlinear programming models for some variants of 2D and 3D packing problems involving circular items and elliptical objects are given. The resulting models are medium-sized highly challenging nonlinear programming problems for which a global solution is sought. For this purpose, multistart strategies are carefully and thoroughly explored. Numerical experiments are exhibited.