Packing Different Cuboids with Rotations and Spheres into a Cuboid. (10th March 2014)

• Record Type: Journal Article
• Authors: Stoyan, Y. G.; Chugay, A. M.
• Other Names: Dempe S. Academic Editor.
• Is Part Of: Advances in decision sciences. Volume 2014(2014)
• Publication Date: 2014-03-10
• Subjects: Decision making -- Periodicals; Decision making; Electronic journals; Periodicals; 519
• DOI: 10.1155/2014/571743
• Languages: English
• ISSNs: 2090-3359

Abstract

Abstract : 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.