Optimal packing of general ellipses in a circle

Abstract

Our objective is to find the optimal non-overlapping packing of a collection of general (non-identical) ellipses, with respect to a container circle that has minimal radius. Following the review of selected topical literature, we introduce a model development approach based on using embedded Lagrange multipliers. Our optimization model has been implemented using the computing system Mathematica. We present illustrative numerical results using the LGO nonlinear (global and local) optimization software package linked to Mathematica. Our study shows that the Lagrangian modeling approach combined with nonlinear optimization tools can effectively handle challenging ellipse packing problems with hundreds of decision variables and non-convex constraints.