An algorithm for packing balls of two types in a three-dimensional set with a non-euclidean metric

The problem of packing balls of two types into a closed bounded set in three-dimensional space with the Euclidean metric and a special non-Euclidean metric. It is required to maximize the radius of the balls for a given number of balls of each type and a known ratio of radii. We propose a omputational algorithm based on a combination of the billiard modeling method and the optical-geometric approach employing the fundamental physical principles of Fermat and Huygens. The results of numerical experiments are discussed.