A problem of packing of homothetic convex polytopes

1Stoyan, Yu.G, 1Chugay, AM
1A. N. Podgorny Institute for Mechanical Engineering Problems of the NAS of Ukraine, Kharkiv
Dopov. Nac. akad. nauk Ukr. 2017, 10:28-33
https://doi.org/10.15407/dopovidi2017.10.028
Section: Information Science and Cybernetics
Language: Ukrainian
Abstract: 

On the ground of an Φ-function for two convex polytopes, a mathematical model of the problem of packing of homothetic convex polytopes into a cuboid of a minimum volume is constructed. A number of characteristics of the mathematical model are pointed out. Based on the characteristics, a way of construction of starting points, a rapid algorithm of searching for local minima, and an original approach to the directed non-exhaustive search for local extrema to obtain a good approximation to a global extremum are offered. Numerical results are given.

Keywords: homothetic polytopes, optimization, packing, rotations
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