On the Thermodynamics of Global Optimization

TL;DR

This paper explores how thermodynamic principles from statistical mechanics can improve global optimization algorithms, especially in complex energy landscapes with multiple funnels, by analyzing the effects of PES transformations on overcoming local minima.

Contribution

It introduces a thermodynamic perspective to explain the success of a specific optimization method in navigating complex potential energy surfaces with multiple funnels.

Findings

PES transformations broaden thermodynamic transitions.

Global minima become more accessible at certain temperatures.

Overcoming free energy barriers is key to successful optimization.

Abstract

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.