  Theoretical design of global optimization algorithms can profitably utilize
recent statistical mechanical treatments of potential energy surfaces (PES's).
Here we analyze a particular method to explain its success in locating global
minima on surfaces with a multiple-funnel structure, 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.
