Registration Number
0223U000298,
0122U001708
, R & D reports
Title
To develop parallel methods of non-smooth optimization for packing of spherical and cubic objects. Stage 2. To develop
mathematical models, methods and parallel algorithms for problems of packing of cubic objects
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Head
Stetsiuk Petro I., д.ф.-м.н.
Registration Date
06-01-2023
Organization
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine
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1. A non-smooth optimization model was developed for the special problem (sides of all cubes are parallel) of balanced sparse packing (permissible distances between objects are given) of cubes of different sizes into a cubic container in n-dimensional space.
2. A quadratic optimization model was developed for the problem of balanced sparse packing of cubes into a cube, provided that the sides of all cubes are parallel to the coordinate axes.
3. A mathematical model was developed for the problem of balanced sparse packing of Lp-spheres in an Lp-sphere of minimum radius. At p=1 and p=∞ we get the packing of cubes into cubic containers, and at p=2 we get the packing of spheres into a spherical container.
4. Sequential and parallel algorithms were developed (multistart in combination with a modification of the r-algorithm) for finding the best solution to problems of packing cubic objects.
Product Description
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Berezovskyi Oleg A.
Hlazunov Mykola M.
Lykhovyd Oleksii P.
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2023-01-06
