Weighted-ensemble simulated annealing: Faster optimization on hierarchical energy surfaces

A method, weighted-ensemble annealing, is proposed for finding the global minima of complicated functions, such as those found in biological problems. This method performs simulated annealing using multiple system copies; it automatically adjusts the distribution of copies and the allocation of computer resources as the cooling proceeds. This readjustment procedure is designed to take advantage of the hierarchical structure of the energy landscape of biomolecules and other systems. This method is applied to a fractal-like function with energy barriers of many sizes and a large entropy barrier. It is shown that using an optimal number of system copies results in a success rate for finding the global minimum, which is an order of magnitude higher than the success rate from traditional single-copy annealing, using the same total number of function evaluations.