Fermentation processes by nature are complex, time-varying, and highly nonlinear. As dynamic systems their modeling and further high-quality control are a serious challenge. The conventional optimization methods cannot overcome the fermentation processes peculiarities and do not lead to a satisfying solution. As an alternative, genetic algorithms as a stochastic global optimization method can be applied. For the purpose of parameter identification of a fed-batch cultivation of S. cerevisiae altogether four kinds of simple and four kinds of multipopulation genetic algorithms have been considered. Each of them is characterized with a different sequence of implementation of main genetic operators, namely, selection, crossover, and mutation. The influence of the most important genetic algorithm parameters—generation gap, crossover, and mutation rates has—been investigated too. Among the considered genetic algorithm parameters, generation gap influences most significantly the algorithm convergence time, saving up to 40% of time without affecting the model accuracy. 1. Introduction Fermentation processes (FP) are preferred and widely used in different branches of industry. The modeling and control of FP pose serious challenges as FP are complex, nonlinear dynamic systems with interdependent and time-varying process parameters. An important step for adequate modeling of nonlinear models of FP is the choice of a certain optimization procedure for model parameter identification. Different metaheuristics methods have been applied to surmount the parameter estimation difficulties [1–3]. Since the conventional optimization methods cannot overcome the limitations of FP [4], genetic algorithms (GAs), as a stochastic global optimization method, are quite promising. Among a number of searching tools, the genetic algorithms are one of the methods based on biological evolution and inspired by Darwin’s theory of “survival of the fittest” [5]. GAs are directed random search techniques, based on the mechanics of natural selection and natural genetics. GAs find the global optimal solution in complex multidimensional search spaces simultaneously evaluating many points in the parameter space. They require only information concerning the quality of the solution and do not require linearity in the parameters. GAs have been successfully applied in a variety of areas to solve many engineering and optimization problems [6–8]. Properties such as noise tolerance and ease of interfacing and hybridization make GA a suitable method for the identification of parameters in fermentation
References
[1]
S. Fidanova, “An heuristic method for GPS surveying problem, computational science,” Lecture Notes in Computer Science, vol. 4490, no. 4, pp. 1084–1090, 2007.
[2]
F. Glover and G. A. Kochenberger, Handbook of Metaheuristiks, Kluwer Academic, Boston, Mass, USA, 2003.
[3]
G. R. Raidl, “A unified view on hybrid metaheuristics,” Lecture Notes in Computer Science, vol. 4030, pp. 1–12, 2006.
[4]
I. Hristozov, T. Pencheva, B. Iliev, and St. Tzonkov, “A Comparative analysis of genetic algorithms and conventional optimization procedures,” in Proceedings of the Scientific-Technical Union of Mechanical Engineering, V(3-25), pp. 187–192, 1998.
[5]
D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wiley Publishing Company, Massachusetts, Mass, USA, 1989.
[6]
G. E. Carrillo-Ureta, P. D. Roberts, and V. M. Becerra, “Genetic algorithms for optimal control of beer fermentation,” in Proceedings of the 2001 IEEE International Symposium on Intelligent Control (ISIC '01), pp. 391–396, Mexico City, Mexico, September 2001.
[7]
Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, Berlin, Heidelberg, Germany, 2nd edition, 1994.
[8]
J.-G. Na, Y. K. Chang, B. H. Chung, and H. C. Lim, “Adaptive optimization of fed-batch culture of yeast by using genetic algorithms,” Bioprocess and Biosystems Engineering, vol. 24, no. 5, pp. 299–308, 2001.
[9]
M. Angelova, S. Tzonkov, and T. Pencheva, “Genetic algorithms based parameter identification of Yeast Fed-Batch cultivation,” in Proceedings of the Conference on ”Numerical Methods and Applications”, vol. 6046 of Lecture Notes in Computer Science, pp. 224–231, 2011.
[10]
T. Pencheva, O. Roeva, and I. Hristozov, Functional State Approach to Fermentation Processes Modelling, Prof. Marin Drinov Academic Publishing House, Sofia, Bulgaria, 2006.
[11]
M. Ranganath, S. Renganathan, and C. Gokulnath, “Identification of bioprocesses using genetic algorithm,” Bioprocess Engineering, vol. 21, no. 2, pp. 123–127, 1999.
[12]
O. Roeva, Improvement of Genetic Algorithm Performance for Identification of Cultivation Process Models, Advanced Topics on Evolutionary Computing, Artificial Intelligence Series-WSEAS, 2008.
[13]
O. Roeva, “A modified genetic algorithm for a parameter identification of fermentation processes,” Biotechnology and Biotechnological Equipment, vol. 20, no. 1, pp. 202–209, 2006.
[14]
A. J. Chipperfield, P. Fleming, H. Pohlheim, and C. M. Fonseca, Genetic Algorithm Toolbox for Use with MATLAB, User’s Guide, Version 1.2, Department of Automatic Control and System Engineering, University of Sheffield, Sheffield, UK, 1994.
[15]
O. Cordon and F. Herrera, “Hybridizing genetic algorithms with sharing scheme and evolution strategies for designing approximate fuzzy rule-based systems,” Fuzzy Sets and Systems, vol. 118, no. 2, pp. 235–255, 2001.
[16]
R. J. Kuo, C. H. Chen, and Y. C. Hwang, “An intelligent stock trading decision support system through integration of genetic algorithm based fuzzy neural network and artificial neural network,” Fuzzy Sets and Systems, vol. 118, no. 1, pp. 21–45, 2001.
[17]
M. Obittko, “Genetic Algorithm,” 2005, http://cs.felk.cvut.cz/~xobitko/ga/main.html.
[18]
X.-C. Zhang, A. Visala, A. Halme, and P. Linco, “Functional state modelling approach for bioprosesses: local models for aerobic yeast growth processes,” Journal of Process Control, vol. 4, no. 3, pp. 127–134, 1994.
