Algorithms of optimal ball packing into ellipsoids

The article deals with the problem of constructing a package from a set of congruent balls into closed convex sets. As the form of containers for packaging, ellipsoids are chosen. In one case, the number of package elements is considered fixed, and the maximization of the radii of package elements is chosen as the optimization criterion. In another case, the radius of the balls is fixed and the problem of finding the package with the largest number of elements is posed. Iterative algorithms for constructing optimal packages based on the imitation of pushing their centers away from each other and from the container boundary are proposed. Algorithms are developed for constructing packages on the basis of the most dense packaging of three-dimensional space, which is a lattice of various types and their combinations. A simulation of the solution of a number of problems and visualization of results is performed.