On the capabilities and limitations of harmony search for parameter estimation in vapor–liquid equilibrium modeling

Abstract

The modeling of vapor–liquid equilibrium data using local composition models is an interesting and challenging global optimization problem in the context of chemical engineering and applied thermodynamics. Until now, several deterministic and stochastic global optimization strategies have been used for modeling vapor–liquid equilibrium (VLE) data. Stochastic optimization methods may offer several advantages for solving global optimization problems and, until now, some meta-heuristics have been tested for modeling phase equilibrium data. However, these optimization strategies usually show a robust performance but, in some challenging problems, they may fail to locate the global optimum. In particular, Harmony Search (HS) is a direct-search method with attractive characteristics for its use in phase equilibrium modeling and calculations. However, to the best of our knowledge, this stochastic optimization strategy has not been used to perform this type of thermodynamic calculations. This study introduces the HS method for solving the non-linear parameter estimation problem involved in the modeling of VLE data. Specifically, the performance of this meta-heuristic has been tested and analyzed using several sets of binary VLE data with local composition models and both the classical approach of the least squares regression and the error-in-variable formulation. Results of this study are used to identify the capabilities and limitations of HS for VLE data modeling. In summary, HS is a promising meta-heuristic for processing these phase equilibrium data using the classical least square formulation and may offer a better performance than those obtained using current stochastic methods such as Genetic Algorithm or Particle Swarm Optimization. However, the reliability of the traditional HS is poor for VLE parameter estimation using the error-in-variable formulation. Finally, this paper discusses and analyzes alternatives to improve the performance of HS in VLE data modeling especially for the error-in-variable approach. Results indicate that the HS variants called the Improved Harmony Search and the Global-Best Harmony Search offer a better performance for solving EIV parameter estimation problems.