THERMODYNAMICS OF GLOBAL OPTIMIZATION

Theoretical design of global optimization algorithms can profitably ut ilize recent statistical mechanical treatments of potential energy sur faces (PES's). Here we analyze a particular method to explain its succ ess in locating global minima on surfaces with a multiple-funnel struc ture, where trapping in local minima with different morphologies is ex pected. We find that a key factor in overcoming trapping is the transf ormation applied to the PES which broadens the thermodynamic transitio ns. The global minimum then has a significant probability of occupatio n at temperatures where the free energy barriers between funnels are s urmountable.