This website contains supplement material to the paper
E. G. Birgin and R. D. Lobato. A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids. European Journal of Operational Research (2019) 272, 447–464.
The full text is available in PDF and PS formats. We consider the problem of arranging ellipsoids (i.e., determining their centers and orientations) within a container so that the ellipsoids do not overlap each other. The ellipsoids are given by the lengths of their semi-principal axes. When the ellipsoids are identical, the objective is to pack the maximum number of ellipsoids as possible within the container. In the general case, where the ellipsoids may not be identical, the ellipsoids are given as a sequence and the objective is to pack the first ellipsoids of this sequence, being as large as possible. The general case may appear, for example, when the lengths of the semi-axes are random or when the number of different ellipsoids is finite and their expected individual densities are known.
Solutions
We provide a complete description and graphical representation of the solutions found in our experiments.
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).