Solving the problem of optimal packing of homothetic ellipsoids into a container of minimal volume
The paper studies the packing problem of homothetic the same oriented ellipsoids into a container of minimal volume. The container can be a rectangular parallelepiped or an ellipsoid. We formulate the model in the form of a nonlinear programming problem. To constract the non-overlapping and containm...
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| Date: | 2016 |
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| Main Author: | |
| Format: | Article |
| Language: | Russian |
| Published: |
Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України
2016
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| Subjects: | |
| Online Access: | https://journals.uran.ua/jme/article/view/71880 |
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| Journal Title: | Energy Technologies & Resource Saving |
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Energy Technologies & Resource Saving| Summary: | The paper studies the packing problem of homothetic the same oriented ellipsoids into a container of minimal volume. The container can be a rectangular parallelepiped or an ellipsoid. We formulate the model in the form of a nonlinear programming problem. To constract the non-overlapping and containment constraints using of phi-function technique. We propose the efficient algorithm, which employes a homothetic transformation of ellipsoids and the optimization procedure Local Optimization with Feasible Region Transformation (LOFRT), which allow us to reduce considerably the dimension of the problem and computational time. Our algorithm also involves generating a number of random starting points. We choose the best local minimum as the solution of the problem. Our model can be realized by the current state-of-the art local or global solvers. A several computational results are provided |
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