Multi-objective optimization of equation of state molecular parameters: SAFT-VR Mie models for water

The determination of a suitable set of molecular interaction parameters for use with an equation of state (EoS) can be viewed as a multi-objective optimization (MOO) problem, where each objective quantifies the quality of the description for a particular type of thermodynamic property. We outline a methodology for the determination of a set of Pareto-optimal interaction parameters. The Pareto front is generated efficiently using a sandwich algorithm where one solves a sequence of weighted-sum scalarized single objective optimization problems. The algorithm presented can be used for any number of objective functions, allowing for the consideration of multiple thermodynamic property types as competing objectives in the MOO. The methodology is applied to the determination of suitable parameter sets for models of water within the SAFT-VR Mie framework. Three competing property targets are considered as objective functions: saturated-liquid density, vapour pressure and isobaric heat capacity. Two different types of molecular models are considered: spherical models of water, and non-spherical model of water. We analyse the two- and three-dimensional Pareto surfaces and parameter sets obtained for different property combinations in the MOO. The proposed methodology can be used to provide a rigorous comparison between different model types. Numerous Pareto-optimal parameter sets for SAFT-VR Mie water models are documented, and we recommend two new models (one spherical model and one non-spherical model) with an appropriate compromise between the competing objectives.