Multicriteria optimization of molecular force fields by Pareto approach

Molecular force fields are widely used for simulating thermodynamic properties of fluids. In developing such force fields, usually some of their parameters are adjusted to experimental data sets, which are often of different type. The adjustment is commonly carried out by minimizing a single objective function which represents the deviations between the model and the data. In the present work, a different approach is explored. Individual objective functions are defined for each data set and a multicriteria optimization task is solved. It is explicitly acknowledged that the different objectives are usually conflicting. The multicriteria optimization problem is solved by determining the Pareto set. By definition this set includes all solutions for which no further improvement in one objective can be achieved without having to accept a decline in at least one other objective and, hence, contains best compromises. The user can then choose out of these solutions one which is particularly suited for his application. The procedure is illustrated using the parameterization of the Lennard-Jones model for argon and methane as examples. Six different objective functions are included in the optimization. They represent the deviations between the model and the following properties at boiling conditions over a wide temperature range: (a) liquid density, (b) vapor pressure, (c) enthalpy of vaporization, (d) liquid shear viscosity, (e) liquid thermal conductivity, and (f) surface tension. First single objective fits are carried out for all properties. Then Pareto sets are determined for two triples of objectives namely, (a, b, c) on one side and (d, e, f) on the other side. An unexpected topology of the Pareto set is observed and explained. Then the full Pareto set for all six properties is determined and all results are compared. They show that good results can be achieved with the simple Lennard-Jones model for the two studied fluids, even when the goal is to simultaneously describe many different thermodynamic properties. The work also illustrates the benefits of using Pareto optimization for developing force fields, and, more generally thermodynamic models.