Population Size Influence on the Genetic and Ant Algorithms Performance in Case of Cultivation Process Modeling

  • Olympia Roeva
  • Stefka Fidanova
  • Marcin Paprzycki
Part of the Studies in Computational Intelligence book series (SCI, volume 580)


In this paper, an investigation of the influence of the population size on the Genetic Algorithm (GA) and Ant Colony Optimization (ACO) performance for a model parameter identification problem, is considered. The mathematical model of an E. coli fed-batch cultivation process is studied. The three model parameters—maximum specific growth rate (\(\mu _{max}\)), saturation constant (\(k_{S}\)) and yield coefficient (\(Y_{S/X}\)) are estimated using different population sizes. Population sizes between 5 and 200 chromosomes and 5 and 100 ants in the population are tested with constant number of generations. In order to obtain meaningful information about the influence of the population size a considerable number of independent runs of the GA are performed. The observed results show that the optimal population size is 100 chromosomes for GA and 70 ants for ACO for 200 generations. In this case accurate model parameters values are obtained in reasonable computational time. Further increase of the population size, above 100 chromosomes for GA and 70 ants for ACO, does not improve the solution accuracy. Moreover, the computational time is increased significantly.


Ant colony optimization Genetic algorithm Least square distance Hausdorff distance 



Work presented here is a part of the Poland-Bulgarian collaborative Grant “Parallel and distributed computing practices” and by European Commission project ACOMIN.


  1. 1.
    Akpinar, S., Bayhan, G.M.: A hybrid genetic algorithm for mixed model assembly line balancing problem with parallel workstations and zoning constraints. Eng. Appl. Artif. Intell. 24(3), 449–457 (2011)CrossRefGoogle Scholar
  2. 2.
    Alander, J.T.: On optimal population size of genetic algorithms. In: Proceedings of the IEEE Computer Systems and Software Engineering, p. 6569 (1992)Google Scholar
  3. 3.
    Al-Duwaish, H.N.: A genetic approach to the identification of linear dynamical systems with static nonlinearities. Int. J. Syst. Sci. 31(3), 307–313 (2000)CrossRefGoogle Scholar
  4. 4.
    Arndt, M., Hitzmann, B.: Feed Forward/feedback Control of Glucose Concentration during Cultivation of Escherichia coli. In: 8th IFAC Int, Conference on Comparative Applications in Biotechnology, pp. 425–429, Canada (2001)Google Scholar
  5. 5.
    Bartz-Beielstein, T.: Experimental Research in Evolutionary Computation: The New Experimentalism. Natural Computing Series. Springer, Berlin (2006)Google Scholar
  6. 6.
    Bastin, G., Dochain, D.: On-Line Estimation and Adaptive Control of Bioreactors. Elsevier, Amsterdam (1991)Google Scholar
  7. 7.
    Benjamin, K.K., Ammanuel, A.N., David, A., Benjamin, Y.K.: Genetic algorithm using for a batch fermentation process identification. J. Appl. Sci. 8(12), 2272–2278 (2008)CrossRefGoogle Scholar
  8. 8.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, New York (1999)MATHGoogle Scholar
  9. 9.
    Clune, J., Goings, S., Punch, B., Goodman, E.: Investigations in meta-gas: panaceas or pipe dreams. In: GECCO 05 Proceedings, pp. 235–241 (2005)Google Scholar
  10. 10.
    Contiero, J., Beatty, C., Kumari, S., DeSanti, C.L., Strohl, W.L.: WolfeA.: Effects of mutations in acetate metabolism on high-cell-density growth of Escherichia coli. J. Ind. Microbiol. Biotechnol. 24, 421–430 (2000)CrossRefGoogle Scholar
  11. 11.
    da Silva, M.F.J., Perez, J.M.S., Pulido, J.A.G., Rodriguez, M.A.V.: AlineaGA—A genetic algorithm with local search optimization for multiple sequence alignment. Appl. Intell. 32, 164–172 (2010)CrossRefGoogle Scholar
  12. 12.
    Diaz-Gomez, P.A., Hougen, D. F.: Initial population for genetic algorithms. In: Hamid R. Arabnia., Jack Y. Yang., Mary Qu Yang. (eds.) A Metric Approacs, Proceedings of the International Conference on Genetic and Evolutionary Methods, GEM 2007, pp. 43–49. Las Vegas, Nevada, USA (2007)Google Scholar
  13. 13.
    Dorigo, M., Stutzle, T.: Ant Colony Optimization. MIT Press, London (2004)Google Scholar
  14. 14.
    Eiben Á, E., Hinterding, R., Michalewicz, Z.: Parameter control in evolutionary algorithms. IEEE Trans. Evol. Comput. 3(2), 124–141 (1999)CrossRefGoogle Scholar
  15. 15.
    Fidanova, S.: Simulated annealing: A monte carlo method for gps surveying. Comput. Sci. Lect. Notes Comput. Sci. 3991, 1009–1012 (2006)CrossRefGoogle Scholar
  16. 16.
    Goldberg, D.E.: Genetic Algorithms in Search. Optimization and Machine Learning. Addison Wesley Longman, London (2006)Google Scholar
  17. 17.
    Holland, J.H.: Adaptation in Natural and Artificial Systems, 2nd edn. MIT Press, Cambridge (1992)Google Scholar
  18. 18.
    Koumousis, V.K., Katsaras, C.P.: A sawtooth genetic algorithm combining the effects of variable population size and reinitialization to enhance performance. IEEE Trans. Evol. Comput. 10(1), 19–28 (2006)CrossRefGoogle Scholar
  19. 19.
    Levisauskas, D., Galvanauskas, V., Henrich, S., Wilhelm, K., Volk, N., Lubbert, A.: Model-based optimization of viral capsid protein production in fed-batch culture of recombinant Escherichia coli. Bioprocess Biosyst. Eng. 25, 255–262 (2003)CrossRefGoogle Scholar
  20. 20.
    Lobo, F.G., Goldberg, D.E.: The parameterless genetic algorithm in practice. Inf. Sci. Inform. Comput. Sci. 167(1–4), 217–232 (2004)MATHGoogle Scholar
  21. 21.
    Lobo, F.G., Lima, C.F.: A review of adaptive population sizing schemes in genetic algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 228–234 (2005)Google Scholar
  22. 22.
    Nowotniak, R., Kucharski, J.: GPU-based Tuning of Quantum-Inspired Genetic Algorithm for a Combinatorial Optimization Problem. In: Proceedings of the XIV International Conference System Modeling and Control, ISSN 978–83-927875-1-8 (2011)Google Scholar
  23. 23.
    Paplinski, J.P.: The genetic algorithm with simplex crossover for identification of time delays, Intelligent, Information Systems, pp. 337–346 (2010)Google Scholar
  24. 24.
    Kumar, S.M., Jain, R., Anantharaman, N., Dharmalingam, V., Sheriffa-Begum, K.M.M.: Genetic algorithm based PID controller tuning for a model bioreactor. J. Indian Chem. Eng., 50(3), 214–226 (2008)Google Scholar
  25. 25.
    Reeves, C.R.: Using genetic algorithms with small populations. In: Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 92–99. San Francisco (1993)Google Scholar
  26. 26.
    Roeva, O.: Improvement of genetic algorithm performance for identification of cultivation process models. In: Advanced Topics on Evolutionary Computing. Artificial Intelligence Series-WSEAS, pp. 34–39 (2008)Google Scholar
  27. 27.
    Roeva, O., Slavov, T.S.: Fed-batch Cultivation Control based on Genetic Algorithm PID Controller Tuning. Lecture Notes on Computer Science. Springer, Berlin (2011)Google Scholar
  28. 28.
    Roeva, Fidanova, S.: A comparison of genetic algorithms and ant colony optimization for modeling of E. coli cultivation process. In: Real-World Application of Genetic Algorithms, pp. 261–282. In Tech. (2012)Google Scholar
  29. 29.
    Saremi, A., ElMekkawy, T.Y., Wang, G.G.: Tuning the parameters of a memetic algorithm to solve vehicle routing problem with backhauls using design of experiments. Int. J. Oper. Res. 4(4), 206–219 (2007)MATHGoogle Scholar
  30. 30.
    Piszcz, A., Soule, T.: Genetic programming: optimal population sizes for varying complexity problems. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 953–954 (2006)Google Scholar
  31. 31.
    Zelic, B., Vasic-Racki, D., Wandrey, C., Takors, R.: Modeling of the pyruvate production with Escherichia coli in a fed-batch bioreactor. Bioprocess Biosyst. Eng. 26, 249–258 (2004)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Olympia Roeva
    • 1
  • Stefka Fidanova
    • 2
  • Marcin Paprzycki
    • 3
  1. 1.Institute of Biophysics and Biomedical EngineeringBulgarian Academy of ScienceSofiaBulgaria
  2. 2.Institute of Information and Communication TechnologiesBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Systems Research InstitutePolish Academy of Sciences, Warsaw and Management AcademyWarsawPoland

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