Packing Different Cuboids with Rotations and Spheres into a Cuboid

الملخص EN

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.