Simulated Annealing with Coarse Graining and Distributed Computing

Abstract

EON is a software package that uses distributed computing, systematic coarse graining and bookkeeping of minima and first order saddle points too speed up adaptive kinetic Monte Carlo simulations. It can be used to optimize continuously differentiable functions of a large number of variables. The approach is based on finding minima of the cost function by traversing low-lying, first-order saddle points from one minimum to another. A sequence of minima is thus generated in a path through regions of low values of the cost function with the possibility of ‘temperature’ controlled acceptance of higher lying saddle points. Searches of first order saddle points are carried out using distributed computing and the minimum-mode following method. Coarse graining which involves merging local minima into composite states and the recognition of previous search paths and saddle points are used to accelerate the exploration of the cost function. In addition to obtaining an estimate of the global minimum, a simulation using this approach gives information about the shape of the cost function in the regions explored. Example applications to the simulated annealing of a cluster of water molecules on a platinum metal surface and grain boundary in copper are presented.