A reconsideration on the resolution of phase stability analysis using stochastic global optimization methods: Proposal of a reliable set of benchmark problems

Abstract

Phase stability analysis is an important thermodynamic calculation in the context of process systems engineering of multiphase units (e.g., separation systems, reactors). It implies the minimization of the Tangent plane distance function (TPDF), which has been recognized as a challenging global optimization problem. Despite the importance of this thermodynamic calculation, the characterization and classification of resolution complexity of phase stability problems that are commonly used to test and compare global optimization methods have not been addressed in literature. This paper reports the first step to propose a set of benchmark TPDF problems to assess and identify the advantages and limitations of stochastic optimization methods used in phase stability calculations. A detailed review of TPDF problem reported in literature was performed and the most representative ones were studied and classified in terms of their resolution complexity via the analysis of several performance metrics associated to both reliability and efficiency to find the global TPDF minimum. Differential Evolution, Simulated Annealing, Harmony Search, Tabu Search, Particle Swarm Optimization and Genetic Algorithm were selected as the metaheuristics to perform the global minimization of selected TPDF problems. 35 phase stability problems were classified in low, medium and high difficulty TPDF problems. Results showed that, although a wide variety of phase stability problems has been reported and used for phase stability calculations, a significant number of them corresponded to global optimization problems of easy resolution. Therefore, some authors have reported biased conclusions on the performance of stochastic optimization methods. A set of 23 TPDF was proposed as benchmark problems to obtain a reliable analysis of the numerical performance of metaheuristics employed in phase stability calculations. This benchmark set contains problems with different resolution difficulties and characteristics that are considered appropriate to study and assess new methods to resolve the global TPDF optimization, as well as to improve the existing methods. This paper highlights the relevance of a continuous development and improvement of stochastic global optimizers for solving, robustly and efficiently, the phase stability analysis in multicomponent systems. TPDF minimization can be still considered a challenging problem to be faced in the context of applied thermodynamics.