A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids

• Published in: European journal of operational research Vol. 272; no. 2; pp. 447 - 464
• Main Authors: Birgin, E.G., Lobato, R.D.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16-01-2019
• Subjects: Algorithms; Ellipsoids; Matheuristic; Nonlinear programming; Packing; Matheuristic; Algorithms; Nonlinear programming; Packing; Ellipsoids
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2018.07.006

•A matheuristic for packing a huge number of ellipsoids is introduced.•The flexibility of the approach allows considering a variety of constraints.•The computational cost scales linearly with the number of ellipsoids being packed.
The problem of packing ellipsoids in the three-dimensional space is considered in the present work. The proposed approach combines heuristic techniques with the resolution of recently introduced nonlinear programming models in order to construct solutions with a large number of ellipsoids. The introduced approach is able to pack identical and non-identical ellipsoids within a variety of containers. Moreover, it allows the inclusion of additional positioning constraints. This fact makes the proposed approach suitable for constructing large-scale solutions with specific positioning constraints in which density may not be the main issue. Numerical experiments illustrate that the introduced approach delivers good quality solutions with a computational cost that scales linearly with the number of ellipsoids; and solutions with more than a million ellipsoids are exhibited.