A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids
•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 c...
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| Published in: | European journal of operational research Vol. 272; no. 2; pp. 447 - 464 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
16-01-2019
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| Abstract | •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. |
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| AbstractList | •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. |
| Author | Birgin, E.G. Lobato, R.D. |
| Author_xml | – sequence: 1 givenname: E.G. surname: Birgin fullname: Birgin, E.G. email: egbirgin@ime.usp.br organization: Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo 05508-090, SP, Brazil – sequence: 2 givenname: R.D. surname: Lobato fullname: Lobato, R.D. email: lobato@ime.usp.br organization: Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific Computing, State University of Campinas, Rua Sérgio Buarque de Holanda 651, Campinas 13083-859, SP, Brazil |
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| Keywords | Matheuristic Algorithms Nonlinear programming Packing Ellipsoids |
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| Title | A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids |
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