This website contains supplement material to the paper

E. G. Birgin, R. D. Lobato and J. M. Martínez. A nonlinear programming model with implicit variables for packing ellipsoids. Journal of Global Optimization (2017) 68, 467–499.

The full text is available in PDF and PS formats. The problem of packing ellipsoids can be defined as follows. Given a set of ellipsoids, each one defined by the lengths of its semi-principal axes, and a container set, the problem consists in finding an arrangement of the ellipsoids (by means of translations and rotations) so that each ellipsoid is inside the container and the ellipsoids do not overlap each other. The container set may be allowed to vary (for example, the container could be a ball whose volume should be minimized) or may be fixed (i.e., it cannot be changed).

Solutions

We provide all instances we have used in our experiments as well as complete description and graphical representation of the solutions found by our methods.

Software

We have implemented our method for packing ellipsoids in Fortran 2003.

Download

The software is available for downloading under the GNU General Public License.

This material is based upon work supported by the Brazilian agencies FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) and CNPq (Conselho Nacional de Pesquisa e Desenvolvimento).