This application optimizes the packing of circles in an ellipse, such that the area of the ellipse is minimized. A typical solution is visualized here.

This is a difficult global optimization problem and demands strong solvers. This application uses Maple's Global Optimization Toolbox.

Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 35 circles generates 666 constraint equations.

The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.

Applications like this are used to stress-test global optimizers.

The constraints and ellipse parameterization are taken from "Packing circles within ellipses", Birgin et al., International Transactions in Operational Research , Volume 20, Issue 3, pages 365–389, May 2013.