Optimal weights in serial generalized-ensemble simulations

In serial generalized-ensemble simulations, the sampling of a collective coordinate of a system is enhanced through non-Boltzmann weighting schemes. A popular version of such methods is certainly the simulated tempering technique, which is based on a random walk in temperature ensembles to explore the phase space more thoroughly. The most critical aspect of serial generalized-ensemble methods with respect to their parallel counterparts, such as replica exchange, is the difficulty of weight determination. Here we propose an adaptive approach to update the weights on the fly during the simulation. The algorithm is based on generalized forms of the Bennett acceptance ratio and of the free energy perturbation. It does not require intensive communication between processors and, therefore, is prone to be used in distributed computing environments with modest computational cost. We illustrate the method in a series of molecular dynamics simulations of a model system and compare its performances to two recent approaches, one based on adaptive Bayesian-weighted histogram analysis and the other based on initial estimates of weight factors obtained by potential energy averages.