  Theoretical design of global optimization algorithms can profitably utilize
recent statistical mechanical treatments of potential energy surfaces (PES's).
Here we analyze the basin-hopping algorithm to explain its success in locating
the global minima of Lennard-Jones (LJ) clusters, even those such as \LJ{38}
for which the PES has a multiple-funnel topography, where trapping in local
minima with different morphologies is expected. We find that a key factor in
overcoming trapping is the transformation applied to the PES which broadens the
thermodynamic transitions. The global minimum then has a significant
probability of occupation at temperatures where the free energy barriers
between funnels are surmountable.
