Application of the simplex simulated annealing technique to nonlinear parameter optimization for the SAFT-VR equation of state

Abstract

A non-equilibrium simplex simulated annealing algorithm is applied as a global optimization method to parameter optimization for an equation of state based on the generalized statistical associating fluid theory incorporating potentials of variable range. The parameters are determined by optimizing the calculated phase behaviour of a number of pure solvents, such as water and alcohols, and aqueous electrolyte solutions. The optimized parameters obtained via the simulated annealing algorithm are compared to those obtained using the simplex method and, for the electrolyte solutions, a gradient-based quasi-Newton method. In the case of the pure solvents, the lowest values of the objective function have been obtained using the simulated annealing technique in six out of the seven studied systems, while for the electrolyte solutions the method results in the lowest values in nine systems out of 11; in the other systems the local methods have resulted in lower values of the objective function. It is observed that both for the solvents and the solutions considered the parameters obtained using the annealing technique are theoretically justifiable, follow physically meaningful trends, and can more easily be generalized; such results provide a measure of confidence that the annealing method does converge to the global minimum in the majority of the studied systems. For pure solvents a simple generalization of parameters leads to accurate predictions for other solvents in the same homologous series. In the case of the electrolyte systems correlations among parameters obtained via simulated annealing can be qualitatively identified, and a simple correlation is proposed which simplifies the molecular models. This is generally not the case for the two local minimization methods considered which, except for a few specific cases, lead to parameters showing no general trends, despite the calculated phase behaviour being almost identical.