Packing of various radii solid spheres into a parallelepiped. (Q1421061)

Packing various solid spheres into a parallelepiped with minimal height is the problem considered in this paper. To solve this problem the following general approach is suggested: 1. Compute a number of extreme points of the feasible region according to randomly generated sequences of spheres. 2. Among these extreme points chose a best one; it determines the center of a neighborhood. 3. By use of the decremental neighborhood search improve upon these points and take the best as the center of a new neighborhood. 4. Use several of the best extreme points found in the last neighborhood as starting points to calculate local minima and an approximation of a global minimum. Numerical results for examples with up to 60 spheres are presented.