Packing congruent spheres into a multi-connected polyhedral domain

In this paper, we have considered a problem of packing the maximal number of congruent spheres into a multi‐connected polyhedral domain. A mathematical model of the problem has been formulated on the basis of Φ functions. This paper proposes a special way of constructing starting points. To find local maxima, a modification of the Zoutendijk method of feasible directions and a strategy of active inequalities are used. We developed a special approach to search for an approximation to a global maximum. A number of numerical examples are also provided.