This application optimizes the packing of circles (of varying radii) in a square, such that the side-length of the square is minimized.  One solution for 20 circles (with integer radii of 1 to 20) 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, 20 circles generates 230 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.