Performance analysis of stopping criteria of population-based metaheuristics for global optimization in phase equilibrium calculations and modeling

Abstract

This paper investigates the numerical behavior of several stochastic optimization methods in phase equilibrium modeling and calculations using different stopping (also known as termination and convergence) criteria. Several optimization methods, namely, Ant Colony Optimization, Particle Swarm Optimization, Differential Evolution and Harmony Search, and some of their variants, were used to compare the capabilities and limitations of different stopping criteria in phase stability problems, phase equilibrium calculations, reactive phase equilibrium calculations and parameter estimation for local composition models. The termination conditions included improvement-, movement- and distribution-type stopping rules that track the values of objective function and/or decision variables. Drawbacks and implications of tested stopping criteria were analyzed, and results showed that the selection of the stopping condition is a key factor for reliable thermodynamic calculations via global optimization using these metaheuristics. In particular, improvement-type criteria based on the tracking of the objective function values are recommended for identifying the convergence of stochastic methods in solving new phase equilibrium problems, where the global optimum is unknown.