Packing cylinders and rectangular parallelepipeds with distances between them into a given region

This paper considers the problem of packing cylinders and parallelepipeds into a given region so that the height of the occupied part of the region is minimal and the distances between each pair of items, and the distance between each packed item and the frontier of the region must be greater than or equal to given distances. A mathematical model of the problem is built and some characteristics of the mathematical model are investigated. Methods for fast construction of starting points, searching for local minima, and a special non-exhaustive search of local minima to obtain good approximations to a global minimum are offered. A numerical example is given. Runtimes to obtain starting points, local minima and approximations to a global minimum are adduced.