Packing different cuboids with rotations and spheres into a cuboid

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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. © 2014 Y. G. Stoyan and A. M. Chugay.




Stoyan, Y. G., & Chugay, A. M. (2014). Packing different cuboids with rotations and spheres into a cuboid. Advances in Decision Sciences, 2014.

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