A problem of packing of homothetic convex polytopes

Authors

  • Yu.G. Stoyan Podgorny Institute for Mechanical Engineering Problems of the NAS of Ukraine, Kharkiv
  • A.M. Chugay Podgorny Institute for Mechanical Engineering Problems of the NAS of Ukraine, Kharkiv

DOI:

https://doi.org/10.15407/dopovidi2017.10.028

Keywords:

homothetic polytopes, optimization, packing, rotations

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.

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References

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Published

21.09.2024

How to Cite

Stoyan, Y., & Chugay, A. (2024). A problem of packing of homothetic convex polytopes . Reports of the National Academy of Sciences of Ukraine, (10), 28–33. https://doi.org/10.15407/dopovidi2017.10.028

Issue

No. 10 (2017): Reports of the National Academy of Sciences of Ukraine

Section

Information Science and Cybernetics

License

Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine

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