  We introduce a global optimization approach for binary clusters that for a
given cluster size is able to directly search for the structure and composition
that has the greatest stability. We apply this approach to binary Lennard-Jones
clusters, where the strength of the interactions between the two atom types is
the same, but where the atoms have different sizes. We map out how the most
stable structure depends on the cluster size and the atomic size ratio for
clusters with up to 100 atoms and up to 30% difference in atom size. A
substantial portion of this parameter space is occupied by structures that are
polytetrahedral, both those that are polyicosahedral and those that involve
disclination lines. Such structures involve substantial strains for
one-component Lennard-Jones clusters, but can be stabilized by the
different-sized atoms in the binary clusters. These structures often have a
`core-shell' geometry, where the larger atoms are on the surface, and the
smaller atoms are in the core.
