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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Datum:2016
1. Verfasser: Хлуд, О. М.
Format: Artikel
Sprache:Russian
Veröffentlicht: Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України 2016
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Online Zugang:https://journals.uran.ua/jme/article/view/71880
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Назва журналу:Energy Technologies & Resource Saving

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Energy Technologies & Resource Saving
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Zusammenfassung: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