Title | A problem of packing of homothetic convex polytopes |
Publication Type | Journal Article |
Year of Publication | 2017 |
Authors | Stoyan, Yu.G, Chugay, AM |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2017.10.028 |
Issue | 10 |
Section | Information Science and Cybernetics |
Pagination | 28-33 |
Date Published | 10/2017 |
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 |
References:
- Wang, Y., Lin, C. L. & Miller, J. D. (2016) 3D image segmentation for analysis of multisize particles in a packed particle bed. Powder Technology. 301, pp. 160-168. https://doi.org/10.1016/j.powtec.2016.05.012
- Liu, X., Liu, J. & Cao, A. (2015) HAPE3D-a new constructive algorithm for the 3D irregular packing problem. Frontiers Inf. Technol. Electronic Eng., No. 16. pp. 380-390. https://doi.org/10.1631/FITEE.1400421
- Verkhoturov, M., Petunin, A., Verkhoturova, G., Danilov, K. & Kurennov, D. (2016) The 3D Object Packing Problem into a Parallelepiped Container Based on Discrete-Logical Representation. IFAC-PapersOnLine, 49, No. 12, pp. 001-005. https://doi.org/10.1016/j.ifacol.2016.07.540
- Fasano, G. & Pinter, J. (Eds.) (2015). Optimized packings with applications. New York: Springer. https://doi.org/10.1007/978-3-319-18899-7
- Youn-Kyoung, Joung, Sang, & Do, Noh. (2014). Intelligent 3D packing using a grouping algorithm for automotive container engineering. J. Computational Design and Engineering, 1, No. 2, pp. 140-151. https://doi.org/10.7315/JCDE.2014.014
- Stoyan, Yu. & Chugay, A. (2012). Mathematical modeling of the interaction of non-oriented convex polytopes. Cybern. Syst Anal.. No. 48, pp. 837-845. https://doi.org/10.1007/s10559-012-9463-2