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

E.G. Birgin and R.D. Lobato

European Journal of Operational Research, 2019, vol. 272, issue 2, 447-464

Abstract: 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.

Keywords: Packing; Ellipsoids; Nonlinear programming; Algorithms; Matheuristic (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:272:y:2019:i:2:p:447-464

DOI: 10.1016/j.ejor.2018.07.006

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