Performance of Stochastic Global Optimization Methods in the Calculation of Phase Stability Analyses for Nonreactive and Reactive Mixtures

In this paper, we perform a comparative study of four stochastic optimization methods for calculating the phase stability of reactive and nonreactive mixtures. We have compared the algorithms: simulated annealing, very fast simulated annealing, a modified version of direct search simulated annealing, and stochastic differential equations. We test the numerical performance and reliability of these methods using several stability problems. From our results, the simulated annealing algorithm appears to be the most reliable method for minimization of the tangent plane distance function for both reactive and nonreactive mixtures.

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  D. Peng,et al.  A New Two-Constant Equation of State , 1976 .

[3]  R. Reid,et al.  The Properties of Gases and Liquids , 1977 .

[4]  L. E. Baker,et al.  Gibbs energy analysis of phase equilibria , 1982 .

[5]  M. Michelsen The isothermal flash problem. Part I. Stability , 1982 .

[6]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[7]  Parisi,et al.  SIGMA - A Stochastic-Integration Global Minimization Algorithm. , 1985 .

[8]  Sandro Ridella,et al.  Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithmCorrigenda for this article is available here , 1987, TOMS.

[9]  H. Renon,et al.  The isothermal flash problem: New methods for phase split calculations , 1987 .

[10]  Francesco Zirilli,et al.  A global optimization algorithm using stochastic differential equations , 1988, TOMS.

[11]  Wayne S. DeSarbo,et al.  A simulated annealing methodology for clusterwise linear regression , 1989 .

[12]  William L. Goffe,et al.  SIMANN: FORTRAN module to perform Global Optimization of Statistical Functions with Simulated Annealing , 1992 .

[13]  Michael F. Doherty,et al.  Theory of phase equilibria in multireaction systems , 1995 .

[14]  M. Doherty,et al.  Vapor-liquid phase equilibrium in systems with multiple chemical reactions , 1995 .

[15]  Christodoulos A. Floudas,et al.  Global optimization for the phase stability problem , 1995 .

[16]  Mrinal K. Sen,et al.  Global Optimization Methods in Geophysical Inversion , 1995 .

[17]  W. Seider,et al.  Homotopy-continuation method for stability analysis in the global minimization of the Gibbs free energy , 1995 .

[18]  Global Stability Analysis and Calculation of Liquid−Liquid Equilibrium in Multicomponent Mixtures† , 1996 .

[19]  M. Doherty,et al.  Thermodynamic behavior of reactive azeotropes , 1997 .

[20]  M. Stadtherr,et al.  Enhanced Interval Analysis for Phase Stability: Cubic Equation of State Models , 1998 .

[21]  Xu Zhihong,et al.  Lipschitz optimization for phase stability analysis: application to Soave–Redlich–Kwong equation of state , 1999 .

[22]  Shashi Prakash Sharma,et al.  Global Optimisation of Time Domain Electromagnetic Data Using Very Fast Simulated Annealing , 1999 .

[23]  Yushan Zhu,et al.  A reliable prediction of the global phase stability for liquid-liquid equilibrium through the simulated annealing algorithm: Application to NRTL and UNIQUAC equations , 1999 .

[24]  S. Wasylkiewicz,et al.  Global phase stability analysis for heterogeneous reactive mixtures and calculation of reactive liquid–liquid and vapor–liquid–liquid equilibria , 2000 .

[25]  Yushan Zhu,et al.  Global stability analysis and phase equilibrium calculations at high pressures using the enhanced simulated annealing algorithm , 2000 .

[26]  S. T. Harding,et al.  Phase stability with cubic equations of state: Global optimization approach , 2000 .

[27]  Patrick Siarry,et al.  Tabu Search applied to global optimization , 2000, Eur. J. Oper. Res..

[28]  G. P. Rangaiah Evaluation of genetic algorithms and simulated annealing for phase equilibrium and stability problems , 2001 .

[29]  Yushan Zhu,et al.  Calculation of chemical and phase equilibrium based on stability analysis by QBB algorithm: application to NRTL equation , 2001 .

[30]  R. P. Marques,et al.  Modeling and analysis of the isothermal flash problem and its calculation with the simulated annealing algorithm , 2001 .

[31]  C.A. Roa-Sepulveda,et al.  A solution to the optimal power flow using simulated annealing , 2001, 2001 IEEE Porto Power Tech Proceedings (Cat. No.01EX502).

[32]  Masao Fukushima,et al.  Hybrid simulated annealing and direct search method for nonlinear unconstrained global optimization , 2002, Optim. Methods Softw..

[33]  S. Gómez,et al.  Phase stability analysis with cubic equations of state by using a global optimization method , 2002 .

[34]  M. Montaz Ali,et al.  A direct search variant of the simulated annealing algorithm for optimization involving continuous variables , 2002, Comput. Oper. Res..

[35]  Erik Appel Jensen,et al.  Determination of discrete relaxation spectra using Simulated Annealing , 2002 .

[36]  Gade Pandu Rangaiah,et al.  Tabu search for global optimization of continuous functions with application to phase equilibrium calculations , 2003, Comput. Chem. Eng..

[37]  T. Csendes,et al.  Application of a stochastic method to the solution of the phase stability problem: cubic equations of state , 2003 .

[38]  Vaidyanathan Jayaraman,et al.  Production , Manufacturing and Logistics A simulated annealing methodology to distribution network design and management , 2002 .

[39]  Mark A. Stadtherr,et al.  Reliable phase stability analysis for asymmetric models , 2005 .