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Springer Handbook of Computational Intelligence pp 1159–1171Cite as

Solving Phase Equilibrium Problems by Means of Avoidance-Based Multiobjectivization

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Abstract

Phase-equilibrium problems are good examples for real-world engineering optimization problems with a certain characteristic. Despite their low dimensionality, finding the desired optima is difficult as their basins of attraction are small and surrounded by the much larger basin of the global optimum, which unfortunately resembles a physically impossible and therefore unwanted solution. We tackle such problems by means of a multiobjectivization-assisted multimodal optimization algorithm which explicitly uses problem knowledge concerning where the sought solutions are not in order to find the desired ones. The method is successfully applied to three phase-equilibrium problems and shall be suitable also for tackling difficult multimodal optimization problems from other domains.

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Abbreviations

CEA:

cellular evolutionary algorithm

CMA:

covariance matrix adaptation

DE:

differential evolution

EA:

evolutionary algorithm

EC:

evolutionary computation

EMOA:

evolutionary multiobjective algorithm

ES:

evolution strategy

GA:

genetic algorithm

GP:

genetic programming

LLE:

liquid–liquid equilibrium

MMA:

multimemetic algorithm

MOAMO:

multiobjectivization-assisted multimodal optimization

NSGA:

nondominated sorting genetic algorithm

PC-SAFT:

perturbed chain statistical associating fluid theory

SMS-EMOA:

S-metric selection evolutionary multiobjective algorithm

TS:

tabu search

References

  1. A.A. Törn, A. Žilinskas (Eds.): Global Optimization, Lecture Notes in Computer Science, Vol. 350 (Springer, Berlin, Heidelberg 1989)

    MATH  Google Scholar 

  2. D.H. Wolpert, W.G. Macready: No free lunch theorems for optimization, IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)

    Article  Google Scholar 

  3. D. Beasley, D.R. Bull, R.R. Martin: A sequential niche technique for multimodal function optimization, Evol. Comput. 1(2), 101–125 (1993)

    Article  Google Scholar 

  4. A.E. Eiben, J.E. Smith: Introduction to Evolutionary Computing (Springer, Berlin, Heidelberg 2003)

    Book  MATH  Google Scholar 

  5. K.A. De Jong: An Analysis of the Behavior of a Class of Genetic Adaptive Systems, Ph.D. Thesis (University of Michigan, Ann Arbor 1975)

    Google Scholar 

  6. D.E. Goldberg, J. Richardson: Genetic algorithms with sharing for multimodal function optimization, Proc. Second Int. Conf. Genet. Algorithm. Their Appl. (1987) pp. 41–49

    Google Scholar 

  7. M. Jelasity: UEGO, an abstract niching technique for global optimization, Lect. Notes Comput. Sci. 1498, 378–387 (1998)

    Article  Google Scholar 

  8. A. Pétrowski: A clearing procedure as a niching method for genetic algorithms, Proc. 1996 IEEE Int. Conf. Evol. Comput. (1996) pp. 798–803

    Chapter  Google Scholar 

  9. J.-P. Li, M.E. Balazs, G.T. Parks, P.J. Clarkson: A species conserving genetic algorithm for multimodal function optimization, Evol. Comput. 10(3), 207–234 (2002)

    Article  Google Scholar 

  10. F. Streichert, G. Stein, H. Ulmer, A. Zell: A clustering based niching method for evolutionary algorithms, Proc. Genet. Evol. Comput. (2003) pp. 644–645

    Google Scholar 

  11. M. Tomassini: Spatially Structured Evolutionary Algorithms Artificial Evolution in Space and Time (Springer, Berlin, Heidelberg 2005)

    MATH  Google Scholar 

  12. M. Preuss: Niching prospects, bioinspired optimization methods and their applications, BIOMA 2006 (2006) pp. 25–34

    Google Scholar 

  13. F. Oppacher, M. Wineberg: The shifting balance genetic algorithm: Improving the GA in a dynamic environment, Proc. Genet. Evol. Comput. Conf. (1999) pp. 504–510

    Google Scholar 

  14. M. Preuss, G. Rudolph, F. Tumakaka: Solving multimodal problems via multiobjective techniques with application to phase equilibrium detection, IEEE Cong. Evol. Comput. (CEC 2007) (2007) pp. 2703–2710

    Chapter  Google Scholar 

  15. E.G. de Azevedo, J.M. Prausnitz, R.N. Lichtenthaler: Molecular Thermodynamics of Fluid Phase Equilibria (Prentice Hall, Englewood Cliffs 1986)

    Google Scholar 

  16. J. Gross, G. Sadowski: Perturbed-chain saft: An equation of state based on a perturbation theory for chain molecules, Ind. Eng. Chem. Res. 40(4), 1244–1260 (2001)

    Article  Google Scholar 

  17. M. Kleiner, F. Tumakaka, G. Sadowski, H. Latz, M. Buback: Phase equilibria in polydisperse and associating copolymer solutions: Poly(ethene-co- (meth)acrylic acid)--monomer mixtures, Fluid Ph. Equilib. 241(1/2), 113–123 (2006)

    Article  Google Scholar 

  18. S. Behme: Thermodynamik von Polymersystemen bei hohen Drücken, Ph.D. Thesis (Technische Universität, Berlin 2000)

    Google Scholar 

  19. G.P. Rangaiah: Evaluation of genetic algorithms and simulated annealing for phase equilibrium and stability problems, Fluid Ph. Equilib. 187/188, 83–109 (2001)

    Article  Google Scholar 

  20. M. Srinivas, G.P. Rangaiah: A study of differential evolution and tabu search for benchmark, phase equilibrium and phase stability problems, Comput. Chem. Eng. 31(7), 760–772 (2007)

    Article  Google Scholar 

  21. L. Gao, N.W. Loney: New hybrid neural network model for prediction of phase equilibrium in a two-phase extraction system, Ind. Eng. Chem. Res. 41(1), 112–119 (2002)

    Article  Google Scholar 

  22. X. He, X. Zhanga, S. Zhanga, J. Liub, C. Lia: Prediction of phase equilibrium properties for complicated macromolecular systems by HGALM neural networks, Fluid Ph. Equilib. 238(1), 52–57 (2005)

    Article  Google Scholar 

  23. Y.S. Teh, G.P. Rangaiah: Tabu search for global optimization of continuous functions with application to phase equilibrium calculations, Comput. Chem. Eng. 27(11), 1665–1679 (2003)

    Article  Google Scholar 

  24. M. Srinivas, G.P. Rangaiah: Implementation and evaluation of random tunneling algorithm for chemical engineering applications, Comput. Chem. Eng. 30(9), 1400–1415 (2006)

    Article  Google Scholar 

  25. M. Srinivas, G.P. Rangaiah: Differential evolution with tabu list for global optimization and its application to phase equilibrium and parameter estimation problems, Ind. Eng. Chem. Res. 46(10), 3410–3421 (2007)

    Article  Google Scholar 

  26. C.G.E. Boender, A.H.G. Rinnooy Kan, G.T. Timmer, L. Stougie: A stochastic method for global optimization, Math. Program. 22(1), 125–140 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Balogh, T. Csendes, R.P. Stateva: Application of a stochastic method to the solution of the phase stability problem: cubic equations of state, Fluid Ph. Equilib. 212(1/2), 257–267 (2003)

    Article  Google Scholar 

  28. T. Csendes, L. Pál, J.O.H. Sendín, J.R. Banga: The global optimization method revisited, Optim. Lett. 2(4), 445–454 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Hooke, T.A. Jeeves: Direct search solution of numerical and statistical problems, J. ACM 8, 212–229 (1961)

    Article  MATH  Google Scholar 

  30. N. Hansen, A. Ostermeier: Completely derandomized self-adaptation in evolution strategies, Evol. Comput. 9(2), 159–195 (2001)

    Article  Google Scholar 

  31. J.C. Nash: Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd edn. (Adam Hilger, Bristol 1990)

    MATH  Google Scholar 

  32. J.D. Knowles, R.A. Watson, D.W. Corne: Reducing local optima in single-objective problems by multi-objectivization, Lect. Notes Comput. Sci. 1993, 269–283 (2001)

    Article  MathSciNet  Google Scholar 

  33. J. Handl, S. Lovell, J. Knowles: Multiobjectivization by decomposition of scalar cost functions, Lect. Notes Comput. Sci. 5199, 31–40 (2008)

    Article  Google Scholar 

  34. J. Handl, S. Lovell, J. Knowles: Investigations into the effect of multiobjectivization in protein structure prediction, Lect. Notes Comput. Sci. 5199, 702–711 (2008)

    Article  Google Scholar 

  35. V. Cutello, G. Narzisi, G. Nicosia: Computational studies of peptide and protein structure prediction problems via multiobjective evolutionary algorithms. In: Multiobjective Problem Solving from Nature. From Concepts to Applications, ed. by J. Knowles, D. Corne, K. Deb (Springer, Berlin, Heidelberg 2008) pp. 93–114

    Chapter  Google Scholar 

  36. D. Brockhoff, T. Friedrich, N. Hebbinghaus, C. Klein, F. Neumann, E. Zitzler: Do additional objectives make a problem harder?, Proc. 9th Annu. Conf. Genet. Evol. Comput. (2007) pp. 765–772

    Google Scholar 

  37. H.A. Abbass, K. Deb: Searching under multi-evolutionary pressures, Lect. Notes Comput. Sci. 2632, 391–404 (2003)

    Article  MATH  Google Scholar 

  38. A. Toffolo, E. Benini: Genetic diversity as an objective in multi-objective evolutionary algorithms, Evol. Comput. 11(2), 151–167 (2003)

    Article  Google Scholar 

  39. L.T. Bui, J. Branke, H.A. Abbass: Diversity as a selection pressure in dynamic environments, Proc. 2005 Conf. Genet. Evol. Comput. (2005) pp. 1557–1558

    Google Scholar 

  40. K. Deb, A. Saha: Multimodal optimization using a bi-objective evolutionary algorithm, Evol. Comput. 20(1), 27–62 (2012)

    Article  Google Scholar 

  41. M. Emmerich, N. Beume, B. Naujoks: An EMO algorithm using the hypervolume measure as selection criterion, Lect. Notes Comput. Sci. 3410, 62–76 (2005)

    Article  MATH  Google Scholar 

  42. N. Beume, B. Naujoks, M. Emmerich: SMS-EMOA: Multiobjective selection based on dominated hypervolume, Eur. J. Oper. Res. 181(3), 1653–1669 (2007)

    Article  MATH  Google Scholar 

  43. K. Deb: Multi-Objective Optimization Using Evolutionary Algorithms (Wiley, New York 2001)

    MATH  Google Scholar 

  44. T.E. Daubert, R.P. Danner: Data Compilation Tables of Properties of Pure Compounds, Design Institute for Physical Property Data (American Institute of Chemical Engineers, New York 1985)

    Google Scholar 

  45. J. Gross, G. Sadowski: Application of the perturbed-chain saft equation of state to associating systems, Ind. Eng. Chem. Res. 41(22), 5510–5515 (2002)

    Article  Google Scholar 

  46. M. Kleiner, G. Sadowski: Modeling of polar systems using PC-SAFT: An approach to account for induced-association interactions, J. Phys. Chem. C 111(43), 15544–15553 (2007)

    Article  Google Scholar 

  47. G.A. Chubarov, S.M. Danov, G.V. Brovkina, T.V. Kupriyanov: Equilibrium in system methanol methyl methacrylate water, J. Appl. Chem. USSR 51(2), 434–437 (1978)

    Google Scholar 

  48. J. Kooi: The system methylmethacrylate – methanol – water, J. R. Neth. Chem. Soc. 68(1), 34–42 (1949)

    Google Scholar 

  49. S.M. Danov, T.N. Obmelyukhina, G.A. Chubarov, A.L. Balashov, A.A. Dolgopolov: Investigation and calculations of liquid-vapor-equilibrium in binary methyl-methacrylate impurity systems, J. Appl. Chem. USSR 63(3), 566–568 (1990)

    Google Scholar 

  50. J. Fu, K. Wang, Y. Hu: Studies on the vapor-liquid equilibrium and vapor-liquid-liquid equilibrium for a methanol-methyl methacrylate-water ternary system (II) Ternary system, J. Chem. Ind. Eng. (China) 4(1), 14–25 (1988)

    Google Scholar 

  51. A.C.G. Marigliano, M.B.G. de Doz, H.N. Solimo: Influence of temperature on the liquid-liquid equilibria containing two pairs of partially miscible liquids - water + furfural + 1-butanol ternary system, Fluid Ph. Equilib. 153(2), 279–292 (1998)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Inst. Wirtschaftsinformatik, WWU Münster, Leonardo-Campus 3, 48149, Münster, Germany

    Mike Preuss

  2. Fak. Informatik, Technische Universität Dortmund, Otto-Hahn-Str. 14, 44227, Dortmund, Germany

    Simon Wessing & Günter Rudolph

  3. Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Emil-Figge-Str. 70, 44227, Dortmund, Germany

    Gabriele Sadowski

Authors
  1. Mike Preuss
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  2. Simon Wessing
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  3. Günter Rudolph
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  4. Gabriele Sadowski
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Corresponding author

Correspondence to Mike Preuss .

Editor information

Editors and Affiliations

  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

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Preuss, M., Wessing, S., Rudolph, G., Sadowski, G. (2015). Solving Phase Equilibrium Problems by Means of Avoidance-Based Multiobjectivization. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_58

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  • DOI: https://doi.org/10.1007/978-3-662-43505-2_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43504-5

  • Online ISBN: 978-3-662-43505-2

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