A study of differential evolution and tabu search for benchmark, phase equilibrium and phase stability problems

Abstract Phase equilibrium calculations (PEC) and phase stability (PS) problems play a crucial role in the simulation, design and optimization of separation processes such as distillation and extraction. The former involve the global minimization of Gibbs free energy function whereas the latter requires the global minimization of tangent plane distance function (TPDF). In this work, two promising global optimization techniques: differential evolution (DE) and tabu search (TS) have been evaluated and compared, for the first time, for benchmark, PEC and PS problems. A local optimization technique is used at the end of both TS and DE to improve the accuracy of the final solution. Benchmark problems involve 2–20 variables with a few to hundreds of local minima whereas PEC and PS problems consist of multiple components with comparable minima. PEC involves both vapor–liquid, liquid–liquid and vapor–liquid–liquid equilibria with popular thermodynamic models. The results show that DE is more reliable but computationally less efficient compared to TS for benchmark, PEC and PS problems tested.

[1]  Selmer M. Johnson,et al.  Chemical Equilibrium in Complex Mixtures , 1958 .

[2]  Kenneth R. Hall,et al.  An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases , 2003 .

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

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

[5]  I. Grossmann,et al.  Computation of phase and chemical equilibria , 1981 .

[6]  S. Gómez,et al.  Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method , 2002 .

[7]  B. Lin,et al.  Tabu search algorithm for chemical process optimization , 2004, Comput. Chem. Eng..

[8]  Zafer Bingul.  A New PID Tuning Technique Using Differential Evolution for Unstable and Integrating Processes with Time Delay , 2004, ICONIP.

[9]  G. P. Rangaiah,et al.  A Study of Equation-Solving and Gibbs Free Energy Minimization Methods for Phase Equilibrium Calculations , 2002 .

[10]  B. Kinghorn,et al.  Differential evolution - an easy and efficient evolutionary algorithm for model optimisation , 2005 .

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

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[13]  M. Stadtherr,et al.  Validated Computing Approach for High-Pressure Chemical and Multiphase Equilibrium , 2004 .

[14]  Carmen G. Moles,et al.  Parameter estimation in biochemical pathways: a comparison of global optimization methods. , 2003, Genome research.

[15]  C. Floudas,et al.  GLOPEQ: A new computational tool for the phase and chemical equilibrium problem , 1997 .

[16]  B. Lin,et al.  Solving heat exchanger network synthesis problems with Tabu Search , 2004, Comput. Chem. Eng..

[17]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

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

[19]  Sadiq M. Sait,et al.  Evolutionary algorithms, simulated annealing, and Tabu search: a comparative study , 1998, Optics & Photonics.

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

[21]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[22]  N. Hu.  Tabu search method with random moves for globally optimal design , 1992 .

[23]  Warren D. Seider,et al.  Computation of phase and chemical equilibrium: Part II. Phase‐splitting , 1979 .

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

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

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

[27]  M. Stadtherr,et al.  Reliable Phase Stability Analysis for Excess Gibbs Energy Models , 2000 .

[28]  Xueguang Shao,et al.  A fast annealing evolutionary algorithm for global optimization , 2002, J. Comput. Chem..