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.

相稳定性分析是多相单元（例如分离系统、反应器）过程系统工程环境中的重要热力学计算。它意味着切线平面距离函数 ( TPDF )的最小化，这已被公认为具有挑战性的全局优化问题。尽管这种热力学计算很重要，但通常用于测试和比较全局优化方法的相稳定性问题的分辨率复杂性的表征和分类尚未在文献中得到解决。本文报告第一步提出一套基准TPDF评估和识别相稳定性计算中使用的随机优化方法的优点和局限性的问题。对文献中报告的TPDF问题进行了详细审查，并通过分析与可靠性和效率相关的几个性能指标来研究和分类最具代表性的问题，以找到全局TPDF最小值。差分进化、模拟退火、和谐搜索、禁忌搜索、粒子群优化和遗传算法被选为元启发式来执行选定的TPDF问题的全局最小化。35个相位稳定性问题分为低、中、高难度TPDF问题。结果表明，虽然已经报道了各种各样的相稳定性问题并用于相稳定性计算，但其中很大一部分对应于易于解决的全局优化问题。因此，一些作者报告了关于随机优化方法性能的有偏见的结论。提出了一组 23 个TPDF作为基准问题，以获得对相稳定性计算中使用的元启发式数值性能的可靠分析。该基准集包含具有不同解决难度和特征的问题，这些问题被认为适合研究和评估解决全局TPDF 的新方法优化，以及改进现有方法。本文强调了随机全局优化器的持续开发和改进对于稳健有效地解决多组分系统中的相稳定性分析的相关性。TPDF最小化仍然被认为是应用热力学背景下面临的一个具有挑战性的问题。