  We consider a homogenization problem for magnetic Ginzburg-Landau functional
in domains with large number of small holes. For sufficiently strong magnetic
field, a large number of vortices is formed and they are pinned by the holes.
We establish a scaling relation between sizes of holes and the magnitude of the
external magnetic field when pinned vortices are multiple and their homogenized
density is described by a hierarchy of variational problems. This stands in
sharp contrast with homogeneous superconductors, where all vortices are known
to be simple. The proof is based on $\Gamma$-convergence approach which is
applied to a coupled continuum/discrete variational problem: continuum in the
induced magnetic field and discrete in the unknown finite (quantized) values of
multiplicity of vortices pinned by holes.
