Meta-Optimization of Evolutionary Strategies for Empirical Potential Development:  Application to Aqueous Silicate Systems

The use of evolutionary strategy optimizations in fitting empirical potentials against first-principles data is considered. Empirical potentials can involve a large number of interdependent quantities, the number varying with the complexity of the potential, and the optimization of these presents a challenging numerical problem. Evolutionary strategies are a general class of optimization methods that mimic natural selection by stochastically evolving a population of trial solutions according to rules that select for high values of some fitness function. In this work we apply a variety of evolutionary optimization methods to a representative “parametrization problem” in order to determine which such methods are well-suited to such applications. Prior work on the design of evolutionary strategies has generally focused on finding the extrema of relatively simple mathematical functions, and the findings of such studies may not be transferable to chemical applications of very high dimensionality. The test problem consists of parametrization of the Feuston-Garofalini all-atom potential developed for simulation of silicic acid oligomerization in aqueous solution (Feuston, B. P.; Garofalini, S. H. J. Phys. Chem. 1990, 94, 5351). “Meta-optimization” of the evolutionary method is first considered by fitting this potential against itself, using a wide variety of population sizes, recombination algorithms, mutation-size control methods, and selection methods. Simulated annealing is also considered as an alternative approach. Optimal choices of population size, recombination operator, mutation size control approach, and selection method are discussed, as well as the quantity of data required for the parametrization. It is clear from comparisons of multiple independent optimizations that, even when fitting this potential against itself, there are a considerable number of local extrema in the fitness function. Evolutionary methods are found to be competitive with simulated annealing and are more easily parallelized. Finally, the potential is reparametrized against reference data taken from a Car−Parrinello Molecular Dynamics trajectory of several relevant silicate species in aqueous solution, again using several variant algorithms.