  Optimal packing of spheres in $\mathbb R^d$ is studied by optimization of the
energy $E$ (effective conductivity) of composites with ideally conducting
spherical inclusions. It is demonstrated that the minimum of $E$ over locations
of spheres is attained at the optimal packing. The energy is estimated in the
framework of structural approximations. This method yields upper bounds and
sometimes exact values for the maximal concentrations of spheres in $\mathbb
R^d$. A constructive algorithm for the optimal locations of spheres associated
to the classes of the Delaunay graphs is constructed.
