Optimal Fed-Batch Culture for Penicillin G Production via a Hybrid Neural Model and a Real-Coded Genetic Algorithm

Copyright © IFAC Computer Applications in Biotechnology, Osaka, Japan, 1998

OPTIMAL FED-BATCH CULTURE FOR PENICILLIN G PRODUCTION VIA A HYBRID NEURAL MODEL AND A REALCODED GENETIC ALGORITHM

Ching-Ching Shih, Kewei Zuo, Wen-Teng Wu·

Department of Chemical Engineering National Tsing Hua University Hsinchu, Taiwan, R.o.C.

Abstract: Fed-batch culture has been commonly employed in fermentation process. The main concern of fed-batch culture is the feeding strategy for improving the fermentation performance. This work is to determine the optimal feeding for fed-batch culture in penicillin G production. 1;he optimization technique is based on a hybrid neural model and a real-coded genetic algorithm. The proposed technique is a general approach. Extension of the technique to other fed-batch fermentation process is suitable. Copyright © 1998 IFA C Keywords: Genetic algorithm; Neural network model; Optimization

recently (Bhat and McAvoy, 1990; Karim and Rivera, 1992; I, Wu and Liu. 1996). In the present study, a hybrid neural model is developed. The hybrid neural model is a set of differential equations with artificial neural networks to determine the parameters of the equations (psichogios and Ungar, 1992; Fu and Barford. 1996). The differential equations are formulated from the balance equations which provide better representation of the system dynamics than black box type of conventional neural networks models.

I . INTRODUCTION Fermentation processes are usually carried out using fed-batch culture. Constant feeding and discrete feeding with a given quantity are commonly employed in fermentation industries. Determination of a proper feeding strategy has been done by many investigators (yarnane and Shimizu. 1984; Wu et al.. 1985; Tholudur and Ramirez. 1996). Searching the feeding strategy is always based on a process model. Since modeling of a fermentation system is quite difficult. artificial neural networks are applied

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and specific substrate consumption rate (a) are given as

With the available system equations, optimization is then employed to detennine the optimal feeding strategy. In this study, the optimization technique is based on a rea1-coded genetic algorithm (Wright, 1991; Goldberg, 1991; Michielssen, et al., 1992). Using genetic algorithms for optimization has some advantages such as that determination of the optimal point is based on the search with population points instead of point by point search and it can be carried out using parallel calculation. The real-coded genetic algorithm has advantages over the binary coded genetic algorithm especially in the system with many parameters to be determined and high precision being required.

J..l

1C

Yxl s

fpls

cr=--+m s + - -

Cs

(5 )

(6)

and

f.J =f.Jsubsl - fxlsCfm(Cs)m s + fp(Cs)1! I f p1s ) (7 )

where

The fermentation system investigated is a fed-batch culture for penicillin G production. With the optimal feeding strategy, production of penicillin G has about 30% increase in comparison with that of the constant feeding method.

Cs J..lsubstr =J..lx KxCx + Cs f m (Cs)

=exp( -Cs I Em)

Jp (Cs) =exp( -Cs / Ep)

2. THE ALGORITHM

The objective of this work is to detennine an optimal feeding strategy in fed-batch culture for penicillin G production. A hybrid neural model is employed to represent the system. A rea1-coded genetic algorithm is then applied to detennine the optimal feeding strategy.

(8 )

( 9) ( 10 )

Cs is the substrate concentration ; Cx is the cell concentration ; pP is the specific production constant ; f.Jx is the maximum specific substrate to biomass conversion rate ; Em and Ep are parameters related to the endogenous fraction of maintenance and production, respectively ; k; is the inhibition constant ; Kp is the saturation constant ; Kx is the Contois saturation constant, and rn, is the maintenance constant.

2.1 The System The system equations are given as follows (Nicolal. et al. , 1991)

2.2 The Hybrid Neural Model

dS -=-oX+s F xF dt

( 1)

A hybrid neural model is developed from a set of material balance equations with a neural network estimator to determine the parameters of the equations. The model has the same form of the system equations of Eq.( 1 ) through Eq.( 4 ). The neural network estimator is applied to detennine the parameters of 0, Il and 7t. The input variables of the estimator are the state variables, S, X, P and V. The output variables are the parameters to be estimated, 0 , Il and 7t.The reason of using the hybrid neural model is that the hybrid model has a better representation of the system in comparison with that of the neural networks model which is not suitable for extrapolation prediction.

(2)

(3)

dV -=F dt

(4)

where S denotes the amount of substrate in the broth ; X is the amount of biomass ; SF is the substrate concentration of the feed stream ; P is the amount of product ; V is the working volume, and kh is the penicillin degradation constant. The relations of the specific growth rate (Il), specific production rate (7t),

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T$!ble 1 Mod~l narame~rs (Ni~l$!i et ill., 1991}

2.3 The Real-Coded Genelic Algorilhm

parameters values

Genetic algorithms have been successfully applied to solve the problems of process optimization. Using genetic algorithms has some advantages such as that the search of possible optimal point is carried out through some population points instead of point by point search and the search can be parallelly calculated. The real-coded genetic algorithm is similar to the binary-coded genetic algorithm. The procedure includes choosing the initial population, determining the fitness function, and applying crossover and mutation for reproduction. The real-coded genetic algorithm uses real parameter vectors as population members. In addition to the reproduction operators of crossover, the linear crossover is also employed (Wright, 1991).

units

fx/s

0.47

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1.2

gig

kIt

0.01

hr-I

ms

0.029

glg.hr

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0.00506

glg.hr

14

0.11

hr· I

Kx

0.006

gig

Kp

0.0001

gIL

Ki

0. 1

gIL

Em=Ep

gIL

3. RESULTS AND DISCUSSION For the real-coded genetic algorithm, the population size is 20; the crossover probability, Pc, is 0.3; the mutation probability, Pm, is 0.2; the linear crossover probability, Plc, is 0.2, and the maximum mutation size is 0.03.

The system equations are shown as Eq.( 1 ) through Eq.( 4 ). The simulation starts from the fed-batch culture. The initial conditions of the fed-batch culture are given as So=Og, Xo=1O.5g, Po=Og and Vo=7L. The total amount of substrate added is fixed to 1500g and the operating time is 120 hours. The substrate feeding rate, F, is less than 0.075Uhr and the substrate concentration in the feeding stream, SF, is 500gIL. The constrained equation gives

o~

By using the system equations, Eq.( 1 ) through Eq.( 4 ), and applying real-coded genetic algorithm for determining the optimal feeding strategy, the results are shown in Fig. 1. The final penicillin G obtained is 76.11g. If the fed-batch culture is carried out with constant feeding, F=0.025 LIhr (Nicolai et al., 1991), the penicillin G obtained is only 59.24g. The time course of the cultivation is also shown in Fig. 1. If the hybrid neural model is employed and the real-coded genetic algorithm is also applied for the optimization, the cultivation results are shown is Fig. 2. The final production of penicillin G is 77.62g which is a little higher than that of using the system equations. Fig. 3 shows the two feeding strategies. Although the feeding strategies are quite different, the production of penicillin G is almost the same.

F(I) ~ 0.075Uhr •

If

JsF· F(t)* t = 1500g. o

For training the hybrid neural model, five runs with constant feeding rates of F=0.025, 0.04, 0.055 and 0.075Llhr are carried out. The data are obtained by solving the system equations Eq.( 1 ) through Eq.( 4), with the parameters shown in Table 1. The neural networks have four layers including two hidden layer which have four and two neurons, respectively. There are four input neurons for S, X, P, and V, and three output neurons for 0.1.1 and 1t.

4. Conclusions

An optimal feeding strategy for fed-batch penicillin fermentation has been developed using a hybrid neural model and a real-coded genetic algorithm. In comparison with constant feeding for fed-batch culture, the optimal feeding strategy significantly improved the production of penicillin.

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If the experimental data are available, an hybrid neural model can be obtained from the data directly. Since the proposed approach is a general method, application of this optimization approach to other fed-batch fermentation processes is straightforward.

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Bhat, N. and T. 1. McAvony (1990). Use of neural nets for dynamic modeling and control of chemical process systems. Computer Chem. Engineering 14, 561-572 . Fu, P. C. and 1. P. Barford (1996). Computers Chem. Engineering 20, 951-958. Goldberg, D. E. (1991) . Real-coded genetic algorithms, virtual alphabets, and blocking. Complex Systems 5, 129-169. I, Y. P., W. T. Wu and Y. C. Liu (1996). The Chem. Eng. J. 61, 35-40. Karim, M. N. and S. L. Rivera (1992). Artificial neural networks in bioprocess state estimation. Biochem. Eng. Biotechnol. 46, 1-33. Michielssen, E., S. Ranjithen and R. Mittra (1992) . Optimal multi layer filter design using real coded genetic algorithm. lEE Proc. J. 139,

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Fig. I. Time courses of the fed-batch cultures. - - Optimal feeding based on the hybrid neural model.

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Nicolai, B. M., 1. F. Van Impe, P. A. Vanrolleghem and 1. Van de Walle (1991). A modified unstructured mathematical model for the penicillin G fed-batch fermentation. Biotechnol. Letters 13, 489-494. Psichogios, D. C. and L. H. Ungar (1992). A hybrid neural network - first principles approach to process modeling. AlChE Journal 38, 1499-

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Thoudur, A. and W. F. Ramirez (1996) . Optimization of fed-batch bioreactors using neural network parameter function models. Biotechnol. Prog. 12, 302-309. Wright, A. H. (1991). Foundation of genetiC algorithms (G. 1. E . Rawlins, (Ed.», 205-218. Morgan Kaufmann, San Mateo, CA. Wu, W. T., K. C. Chen and H. W. Chiou (1985) . Biotech. and Bioeng. 27, 756-760.

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REFERENCES

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