Direct Sequential Based Firefly Algorithm for the \(\alpha \)-Pinene Isomerization Problem

  • Ana Maria A. C. Rocha
  • Marisa C. Martins
  • M. Fernanda P. Costa
  • Edite M. G. P. Fernandes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9786)


The problem herein addressed is a parameter estimation problem of the \(\alpha \)-pinene process. The state variables of this bioengineering process satisfy a set of differential equations and depend on a set of unknown parameters. A dynamic system based parameter estimation problem aiming to estimate the model parameter values in a way that the predicted state variables best fit the experimentally observed state values is used. A numerical direct method, known as direct sequential procedure, is implemented giving rise to a finite bound constrained nonlinear optimization problem, which is solved by the metaheuristic firefly algorithm (FA). A Matlab™ programming environment is developed with the mathematical model and the computational application of the method. The results produced by FA, when compared to those of the fmincon function and other metaheuristics, are competitive.


\(\alpha \)-pinene isomerization Parameter estimation Direct sequential procedure Firefly algorithm 



The authors wish to thank two anonymous referees for their comments and suggestions. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundação para a Ciência e Tecnologia, within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.


  1. 1.
    Banga, J.R., Balsa-Canto, E., Moles, C.G., Alonso, A.A.: Improving food processing using modern optimization methods. Trends Food Sci. Tech. 14(4), 131–144 (2003)CrossRefGoogle Scholar
  2. 2.
    Grossmann, I.E. (ed.): Global Optimization in Engineering Design, Nonconvex Optimization and Its Applications, vol. 9. Springer Science & Business Media (1996)Google Scholar
  3. 3.
    Vanrolleghem, P.A., Dochain, D.: Bioprocess model identification. In: Van Impe, J.F.M., Vanrolleghem, P.A., Iserentant, D.M. (eds.) Advanced Instrumentation, Data Interpretation, and Control of Biotechnological Processes, pp. 251–318. Kluwer Academic Publ. (1998)Google Scholar
  4. 4.
    Rodríguez-Fernández, M.: Modelado e Identificación de Bioprocesos. Ph.D. thesis, University of Vigo, Spain (2006)Google Scholar
  5. 5.
    Rodriguez-Fernandez, M., Mendes, P., Banga, J.R.: A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Biosystems 83(2–3), 248–265 (2006)CrossRefGoogle Scholar
  6. 6.
    Gill, P.E., Murray, W., Saunders, M.A., Wright, M.H.: Constrained nonlinear programming. In: Handbooks in Operations Research and Management Science, vol. 1, Optimization, pp. 171–210 (1989)Google Scholar
  7. 7.
    Banga, J.R., Balsa-Canto, E., Moles, C.G., Alonso, A.A.: Dynamic optimization of bioreactors: a review. Proc.-Indian National Sci. Acad. Part A 69(3/4), 257–266 (2003)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Esposito, W.R., Floudas, C.A.: Global optimization for the parameter estimation of differential-algebraic systems. Ind. Eng. Chem. Res. 39(5), 1291–1310 (2000)CrossRefGoogle Scholar
  9. 9.
    Moles, C.G., Mendes, P., Banga, J.R.: Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res. 13(11), 2467–2474 (2003)CrossRefGoogle Scholar
  10. 10.
    Moles, C.G., Gutierrez, G., Alonso, A.A., Banga, J.R.: Integrated process design and control via global optimization: a wastewater treatment plant case study. Chem. Eng. Res. Des. 81(5), 507–517 (2003)CrossRefGoogle Scholar
  11. 11.
    Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, vol. 1, pp. 39–43, New York, NY (1995)Google Scholar
  12. 12.
    Yang, X.-S.: Firefly algorithms for multimodal optimization. In: Watanabe, O., Zeugmann, T. (eds.) SAGA 2009. LNCS, vol. 5792, pp. 169–178. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Lin, Y., Stadtherr, M.A.: Deterministic global optimization for parameter estimation of dynamic systems. Ind. Eng. Chem. Res. 45(25), 8438–8448 (2006)CrossRefGoogle Scholar
  14. 14.
    Miro, A., Pozo, C., Guillén-Gosálbez, G., Egea, J.A., Jiménez, L.: Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems. BMC Bioinf. 13, 90 (2012)CrossRefGoogle Scholar
  15. 15.
    Polisetty, P.K., Voit, E.O., Gatzke, E.P.: Identification of metabolic system parameters using global optimization methods. Theor. Biol. Med. Model. 3, 4 (2006)CrossRefGoogle Scholar
  16. 16.
    Balsa-Canto, E., Peifer, M., Banga, J.R., Timmer, J., Fleck, C.: Hybrid optimization method with general switching strategy for parameter estimation. BMC Syst. Biol. 2, 26 (2008)CrossRefGoogle Scholar
  17. 17.
    Box, G., Hunter, W., MacGregor, J., Erjavec, J.: Some problems associated with the analysis of multiresponse data. Technometrics 15(1), 33–51 (1973)CrossRefzbMATHGoogle Scholar
  18. 18.
    Rodriguez-Fernandez, M., Egea, J.A., Banga, J.R.: Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinf. 7, 483 (2006)CrossRefGoogle Scholar
  19. 19.
    Fuguitt, R.E., Hawkins, J.E.: Rate of the thermal isomerization of \(\alpha \)-pinene in the liquid phase. J. Am. Chem. Soc. 69(2), 319–322 (1947)CrossRefGoogle Scholar
  20. 20.
    Hunter, W., McGregor, J.: The estimation of common parameters from several responses: Some actual examples. Unpublished Report, Department of Statistics. University of Winsconsin (1967)Google Scholar
  21. 21.
    Srinivasan, B., Palanki, S., Bonvin, D.: Dynamic optimization of batch processes: I. Characterization of the nominal solution. Comput. Chem. Eng. 27(1), 1–26 (2003)CrossRefGoogle Scholar
  22. 22.
    Banga, J.R., Balsa-Canto, E., Moles, C.G., Alonso, A.A.: Dynamic optimization of bioprocesses: efficient and robust numerical strategies. J. Biotechnol. 117, 407–419 (2005)CrossRefGoogle Scholar
  23. 23.
    Schlegel, M., Marquardt, W.: Direct sequential dynamic optimization with automatic switching structure detection. In: Shah, S.L., MacGregor, J. (eds.) Dynamics and Control of Process Systems 2004 (DYCOPS-7), vol. 1, pp. 419–424. Elsevier IFAC Publ. (2005)Google Scholar
  24. 24.
    Biegler, L.T.: Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes. MOS-SIAM Series on Optimization (2010)Google Scholar
  25. 25.
    Zhigljavsky, A., \(\breve{Z}\)ilinskas, A.: Stochastic Global Optimization. Springer Optimization and its Applications. Springer, New York (2008)Google Scholar
  26. 26.
    Floudas, C.A., Akrotirianakis, I.G., Caratzoulas, S., Meyer, C.A., Kallrath, J.: Global optimization in the 21st century: advances and challenges. Comput. Chem. Eng. 29, 1185–1202 (2005)CrossRefGoogle Scholar
  27. 27.
    Tsai, K.-Y., Wang, F.-S.: Evolutionary optimization with data collocation for reverse engineering of biological networks. Bioinformatics 21(7), 1180–1188 (2005)CrossRefGoogle Scholar
  28. 28.
    Goldberg, D.E., Korb, B., Deb, K.: Messy genetic algorithms: motivation, analysis, and first results. Complex Syst. 3(5), 493–530 (1989)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Holland, J.H.: Genetic algorithms. Sci. Am. 267(1), 66–72 (1992)CrossRefGoogle Scholar
  30. 30.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Santa Fe Institute Studies on the Sciences of Complexity, Oxford University Press (1999)Google Scholar
  31. 31.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann Publishers Inc., San Francisco (2001)Google Scholar
  32. 32.
    Millonas, M.M.: Swarms, phase transitions, and collective intelligence. In: Langton, C.G. (ed.) Artificial Life III, vol. XVII, pp. 417–445. Addison-Wesley, Reading (1994)Google Scholar
  33. 33.
    Yang, X.-S.: Nature-Inspired Metaheuristic Algorithms, 2nd edn. Luniver Press, Bristol (2010)Google Scholar
  34. 34.
    Yang, X.-S.: Biology-derived algorithms in engineering optimization. In: Olariu, S., Zomaya, A.Y. (eds.) Handbook of Bioinspired Algorithms and Applications, pp. 589–600. Chapman & Hall, Boca Raton (2005)Google Scholar
  35. 35.
    Yang, X.-S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspired Comput. 2(2), 78–84 (2010)CrossRefGoogle Scholar
  36. 36.
    Egea, J.A., Rodríguez-Fernández, M., Banga, J.R., Marti, R.: Scatter search for chemical and bioprocess optimization. J. Glob. Optim. 37(3), 481–503 (2007)CrossRefzbMATHGoogle Scholar
  37. 37.
    Rocha, A.M.A.C., Silva, A., Rocha, J.G.: A new competitive implementation of the electromagnetism-like algorithm for global optimization. In: Gervasi, O., Murgante, B., Misra, S., Gavrilova, M.L., Rocha, A.M.A.C., Torre, C., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2015. LNCS, vol. 9156, pp. 506–521. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  38. 38.
    Dolan, E.D., Moré, J.J., Munson, T.S.: Benchmarking Optimization Software with COPS 3.0. Argonne National Laboratory Technical report ANL/MCS-TM-273 (2004)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ana Maria A. C. Rocha
    • 1
  • Marisa C. Martins
    • 1
  • M. Fernanda P. Costa
    • 2
  • Edite M. G. P. Fernandes
    • 1
  1. 1.Algoritmi Research CentreUniversity of MinhoBragaPortugal
  2. 2.Centre of MathematicsUniversity of MinhoGuimarãesPortugal

Personalised recommendations