Packing Different Cuboids with Rotations and Spheres into a Cuboid | Zendy

Yu. G. Stoyan | Zendy; A. M. Chugay | Zendy

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Packing Different Cuboids with Rotations and Spheres into a Cuboid

Author(s) -

Yu. G. Stoyan,

A. M. Chugay

Publication year - 2014

Publication title -

advances in decision sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.178

H-Index - 13

eISSN - 2090-3367

pISSN - 2090-3359

DOI - 10.1155/2014/571743

Subject(s) - cuboid , spheres , packing problems , computer science , construct (python library) , mathematical optimization , algorithm , mathematics , geometry , physics , programming language , astronomy

The paper considers a packing optimization problem of different spheres and cuboids into a cuboid of the minimal height. Translations and continuous rotations of cuboids are allowed. In the paper, we offer a way of construction of special functions (Φ-functions) describing how rotations can be dealt with. These functions permit us to construct the mathematical model of the problem as a classical mathematical programming problem. Basic characteristics of the mathematical model are investigated. When solving the problem, the characteristics allow us to apply a number of original and state-of-the-art efficient methods of local and global optimization. Numerical examples of packing from 20 to 300 geometric objects are given

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