Optimization of fermentation media for exopolysaccharide production from Lactobacillus plantarum using artificial intelligence-based techniques

Process Biochemistry 41 (2006) 1842–1848 www.elsevier.com/locate/procbio

Optimization of fermentation media for exopolysaccharide production from Lactobacillus plantarum using artificial intelligence-based techniques K.M. Desai a, S.K. Akolkar a, Y.P. Badhe b, S.S. Tambe b, S.S. Lele a,* a

Food Engineering and Technology Department, Institute of Chemical Technology, University of Mumbai, Matunga, Mumbai 400019, India b Chemical Engineering and Process Development Division, National Chemical Laboratory, Dr. Homi Bhabha Road, Pune 411008, India Received 21 August 2005; received in revised form 27 March 2006; accepted 31 March 2006

Abstract A Lactobacillus strain was isolated from the fermented Eleusine coracana. This strain was characterized as Lactobacillus plantarum and was found to produce an exopolysaccharide (EPS) in quantitative amounts. The objective of the present paper is to determine optimum media composition and inoculum volume for the stated fermentative production of the EPS. A hybrid methodology comprising the Plackett–Burman (PB) design method, artificial neural networks (ANN) and genetic algorithms (GA) was utilized. Specifically, the PB, ANN and GA formalisms were used for identifying influential media components, modeling non-linear process and optimizing the process, respectively. More specifically, the PB method was used to determine those media components, which significantly influence the EPS yield. By ignoring the less influential media components, the dimensionality of the input space of the process model could be reduced significantly. Out of the five media components only three were found influential namely, lactose, casein hydrolysate and triammonium citrate. Next, an ANN-based process model was developed for approximating the non-linear relationship between the fermentation operating variables and the EPS yield. The average % error and correlation coefficient for the developed ANN model were 4.8 and 0.999, respectively. The input parameters of ANN model were subsequently optimized using the GA formalism for obtaining maximum EPS yield in batch fermentation. The optimized media composition has predicted the yield of 7.01 g/l. The GA-optimized solution comprising media composition and inoculum volume was verified experimentally and it comes out be 7.14 g/l. # 2006 Elsevier Ltd. All rights reserved. Keywords: Artificial neural network; Genetic algorithm; Exopolysaccharide; Fermentation; Lactobacillus plantarum; Media optimization; Plackett–Burman

1. Introduction A variety of polysaccharides are produced by plants, algae and bacteria. Among these, the cellulose, pectin, starch (plant origin), agar, carrageenan, alginate (from algae) and gums like dextran, gellan, pullunan and xanthan (from bacteria), are used commercially as food additives and also in pharmaceuticals. Polysaccharides possess gelling, stabilizing and thickening properties [1]. Some microorganisms such as the lactic acid producers are known to synthesize exopolysaccharides (EPS) that have health stimulating properties such as immunity

Abbreviations: ANN, artificial neural network; EBP, error back propagation; EPS, exopolysaccharide; GA, genetic algorithm; MLP, multi-layer perceptron; PB, Plackett–Burman * Corresponding author. E-mail address: [email protected] (S.S. Lele). 1359-5113/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2006.03.037

stimulation [2,3], anti-ulcer activity [4] and cholesterol reduction [5]. Further, these EPS are generally recognized as safe (GRAS status) and hence biotechnologists are constantly in search of newer strains possessing a high EPS productivity. In this study, optimization of media and inoculum volume has been carried out for an enhanced exopolysaccharide production by fermentation of Lactobacillus plantarum isolated from the fermented Eleusine coracana (ragi). To achieve high product yields in a fermentation process, it is a prerequisite to design an optimal production medium and a set of optimal process operating conditions. The most widely used optimization method, single factor at a time, does not account for the combined effect of all the influential factors since other factors are maintained arbitrarily at a constant level. Further, this method is time consuming and requires a large number of experiments to determine the optimum levels of the production medium. The limitations of the single factor optimization

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method can be overcome by developing a non-linear multivariate process model and using this model for optimization. In the last decade, artificial neural networks (ANNs) have emerged as an attractive tool for developing non-linear empirical models especially in situations wherein the development of phenomenological or conventional empirical models becomes impractical or cumbersome. The most widely utilized ANN paradigm is the multi-layered perceptron (MLP) that approximates non-linear relationships existing between multiple causal (input) process variables and the corresponding dependent (output) variables [6]. Once an ANN-based process model with fairly good generalization capability is constructed, its input space can be optimized appropriately to secure the optimal values of process variables. The ANN models being exclusively data-based, it cannot be guaranteed to be smooth. Hence, the conventionally used gradient-based optimization methods cannot be used efficiently for optimizing the input space of an ANN model. Thus, it becomes necessary to explore alternative non-linear optimization formalisms. In recent years, genetic algorithms (GAs) [7–9], which are artificial intelligence-based stochastic non-linear optimization formalisms, have been used with a great success in solving problems involving very large search spaces (see e.g., [10,11]). The GAs follows the theory of population evolution in natural systems. Specifically, GAs are based on the principles of ‘‘survival-of-the-fittest’’ and ‘‘random exchange of memory during genetic propagation’’, which are followed by the biologically evolving species. The principal features, advantages and procedural details of GAs that are described in [12– 14], make the GAs an ideal technique to solve diverse optimization problems in biochemical engineering [15,16]. The specific example of initial media optimization using GA can be cited in Bapat and Wangikar [17]. The newly isolated strain was found to be an excellent producer of EPS in MRS medium. Since MRS media is specifically used for lactobacilli isolation, it was imperative to design suitable production media. Thus, the objective of the present paper is to obtain an optimal media composition and inoculum size for the fermentative production of the EPS. An optimal media composition and inoculum size has been achieved in following three steps: (i) Placket–Burman (PB) has been used select the most influential media components [18], (ii) an ANN model has been developed using the influential process variables as model inputs and the EPS yield as the model output, and (iii) the input space of the ANN model is optimized using the GA formalism with a view of maximizing the EPS yield. 2. Materials and methods

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2.2. Medium The MRS medium was used for the isolation of the Lactobacillus strain. For the production of EPS, the existing MRS medium was modified; the modified media was containing, lactose, casine hydrolysate, triammonium citrate, beef extract and proteose peptone (in given quantity); along with sodium acetate: 1 g/ l, Mg-sulfate: 1 g/l, manganese sulfate: 0.5 g/l, and calcium chloride: 0.25 g/l. This medium was autoclaved at 110 8C for 10 min; lactose was autoclaved separately.

2.3. Fermentation conditions The batch fermentations were carried in a 250 ml shake flask for 24 h at 150 rpm and 35 8C. The pH of the fermentation medium was adjusted to 6.5
0.3 with the addition of 1N NaOH/1N HCl. Flasks at the end of fermentation were analyzed for EPS production.

2.4. Analysis The cells were separated by centrifugation (10,000 rpm, 10 8C, 15 min) and the crude EPS was precipitated from the broth at 4 8C by the addition of two volumes of cold ethanol (95%). The resulting precipitate was collected by centrifugation and re-dissolved in water. The crude EPS solution was dialyzed at 4 8C to estimate the yield [18].

2.5. Computational techniques Plackett–Burman model computations were performed using commercial software Minitab 13.3. For ANN and GA, in-house software developed in National Chemical Laboratory (India) on C++ platform was used.

3. Theory of computational methods 3.1. Plackett–Burman statistical technique In modeling problems involving multiple inputs, it becomes difficult to ascertain those inputs, which are most influential in determining the model output. The Plackett–Burman design aims to select the most important variables in the system [19]. The PB method allows evaluation of Nˆ  1 variables by Nˆ number of experiments (Nˆ must be a multiple of four). Each variable is represented at two levels, namely, ‘‘high’’ and ‘‘low’’. These levels define the upper and lower limits of the range covered by each variable. In addition to the variables of real interest, the PB design considers insignificant dummy variables, whose number should be one-third of all variables. The dummy variables, which are not assigned any values, introduce some redundancy required by the statistical procedure. Incorporation of the dummy variables into an experiment allows an estimation of the variance (experimental error) of an effect. In the PB design, experiments are performed at various combinations of high and low values of the process variables and analyzed for their effect on the process [20].

2.1. Bacterial strain

3.2. ANN-based modeling Lactobacilli strain was isolated from the Indian fermented food ragi (E. coracana). This isolate was characterized as L. plantarum using biochemical tests [19]. Upon screening for the EPS production, the isolate was found to produce high quantities of EPS. The molecular weight of EPS was determined by centrifugal dialysis and viscometric measurement. The product composition, in the present study (glucose:rhaminose::3:1) remains unchanged.

The MLP, which is the most widely used ANN paradigm for non-linear modeling, consists of three layers of nodes. The layers described as input, hidden and output layers, comprise, L, M and N number of processing nodes (neurons), respectively.

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There also exists an additional node, known as the bias (with its input fixed at +1) in the input and hidden layers of an MLP network. All the nodes in a layer are connected to each node in the subsequent layer with weighted connections. The MLP network is a non-linear function mapping device that determines the N-dimensional non-linear function vector, f, where f: X ! Y. Here, X is a set of P number of L-dimensional input vectors (X = {xp}; p = 1, 2, . . ., P, and x = [x1, x2, . . ., xl, . . ., xL]T), and Y is the set of the corresponding output vectors (Y = {yp}; p = 1, 2, . . ., P), where y = [y1, y2, . . ., yN]T. The precise form of f is determined by: (i) network topology, (ii) choice of the activation function used for computing the outputs of the hidden and output nodes and (iii) network weight matrices, WH and WO (these refer to the weights on connections between input and hidden nodes, and hidden and output nodes, respectively). Thus, the non-linear mapping executed by the MLP can be expressed as:

The GA-based search for an optimal solution (decision) vector, x*, begins with a randomly initialized population of probable (candidates) solutions. The solutions, coded in the form of binary or real-valued strings (chromosomes) are then evaluated to measure their fitness in fulfilling the optimization objective. Next, a main loop of operations consisting of: (i) selection of better (fitter) parent chromosomes to create a mating pool, (ii) crossover, i.e., the production of offspring solutions by pair-wise crossing-over of the contents between pairs of fitter parent chromosomes and, (iii) mutating elements of the offspring strings, is executed. An implementation of this loop produces a new population of candidate solutions, which then compared with the current population, usually performs better at fulfilling the optimization objective. The best string that evolves after repeating the above-described loop till convergence forms the solution to the optimization problem.

y ¼ f ðx; WÞ

4. Results and discussion

(1)

The most widely used formalism for the training of the network is the error-back-propagation (EBP) algorithm [21]. The details of training an optimal MLP model possessing good prediction and generalization abilities are described for instance in Bishop [22], Tambe and Kulkarni [23], Freeman and Skapura [24]. The EBP training algorithm makes use of two adjustable parameters namely, the learning rate (h) (0 < h  1), and momentum coefficient (a) (0 < a  1). The magnitudes of both these parameters are optimized heuristically along with the number of hidden layer neurons, M. 3.3. GA-based optimization of input parameters in the ANN model Once a generation capable ANN-based process model with good prediction accuracy is developed, a genetic algorithm can be used to optimize its input space (x) representing process variables, with a view of maximizing the process performance. The underlying optimization objective is defined as: find optimal decision variable vector, x ¼ the L-dimensional     T x1 ; x2 ; . . . ; xl ; . . . ; xL , such that it maximizes the objective function, f(x*, W).

4.1. Selection of influential media components for process modeling The fermentation media for the EPS process comprised following five components: lactose, casein hydrolysate, beef extract, proteose peptone and triammonium citrate. Among these media components, the ones which significantly affect the EPS yield significantly were chosen using the PB. A total of seven variables comprising five media components and two dummy variables, were screened in eight experiments. These experiments were performed at different combinations of the high and low values of each variable (see Table 1) and the results of the PB design calculations along with the corresponding variable-specific F-scores are given in Table 2. It is seen from the table that the mean square of the experimental error for the dummy variables is 0.0183 ((0.0276 + 0.0091)/2). It is also observed from the F-score values that the influence of beef extract and proteose peptone on the EPS yield is insignificant when compared to that of the lactose, casein hydrolysate and triammonium citrate. This indicates that among the five variables representing concentrations of the five media components, the concentrations of

Table 1 Plackett–Burman design for seven variablesa Trial Variables Lactose (g/l) Casein hydrolysate (g/l) Beef extract (g/l) Protease peptone (g/l) E (dummy) Tri-ammonium citrate (g/l) G (dummy) 1 2 3 4 5 6 7 8

H L L H L H H L a

H H L L H L H L

H H H L L H L L

L H H H L L H L

H L H H H L L L

L H L H H H L L

H L H L H H H L

EPS yield (g/l) 0.75 2.80 0.84 0.4 2.61 0.5 0.81 0.96

Lactose at low (L) level of 1 (g/l) and at high (H) level of 3 (g/l); casein hydrolysate at low (L) level of 1 (g/l) and at high (H) level of 3 (g/l); beef extract at low (L) level of 1 (g/l) and at high (H) level of 3 (g/l); protease peptone at low (L) level of 1 (g/l) and at high (H) level of 3 (g/l); E is dummy variable; triammonium citrate at low (L) level of 1 (g/l) and at high (H) level of 3 (g/l); G is dummy variable.

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Table 2 Statistical calculations for Plackett–Burman design Quantity

Lactose

yi+ yi Syi+–Syi

3.21 7.21 4.0 2

M.S.D. F-score

109.289

Casein hydrolysate

Beef extract

Proteose peptone

Dummy variable I

6.97 2.7 4.27

4.89 4.78 0.11

4.85 4.82 0.03

4.6 5.07 0.47

2.279

0.0015

0.00

0.0276

124.541

0.0819

0.00

1.508

Tri-ammonium citrate

Dummy variable II

6.31 3.36 2.95

4.7 4.97 0.27

1.087

0.0091

59.39

0.497

lactose, casein hydrolysate and triammonium citrate are the most influential.

noticed, the MLP-based model had fitted the experimental data with an excellent accuracy.

4.2. ANN-based modeling of EPS fermentation

4.3. GA-based optimization of the MLP model

The MLP network has four input nodes (L = 4) for representing the four influential process variables (concentrations of lactose, casein hydrolysate and triammonium citrate, and inoculum size) and one output node (N = 1) representing the EPS yield (g/l) at the end of a batch. The process data for MLP-based modeling was generated by carrying out a number of fermentation runs by varying the input conditions. Specially, a total of 54 experiments were conducted and the corresponding data is tabulated in Table 3. For ANN-based modeling, the process data comprising 54 patterns (example set) each representing a pair of model inputs (fermentation conditions) and a single output (EPS concentration), was partitioned into a training set (44 patterns) and a test set (10 patterns). While the training set was utilized for adjusting the weights (W) of the MLP model during its training, the test set was used for gauging the network’s generalization performance after each training iteration. The weights resulting in the least test set RMSE magnitude were chosen as the optimum weights. In the network training procedure, the logistic sigmoid activation function was used for computing the outputs of the hidden and output nodes. While developing an optimal MLP model, the effect of varying number of hidden nodes and the EBP algorithm specific parameters (learning rate, h, and momentum coefficient, a) on the training and test set RMSE was rigorously studied. It was observed that an MLP architecture with four hidden nodes resulted in the least value for the test set RMSE, i.e., Etst = 0.179. The values of h and a, which resulted in the minimum Etst were 0.8 and 0.05, respectively; and the corresponding RMSE value for the training set (Etrn) was 0.102. The average error (%) between the desired and modelpredicted EPS concentrations for the training and test set data were 4.3 and 6.8, respectively; the values of coefficient of correlation (CC) between the model-predicted and desired EPS concentrations pertaining to the training set (CCtrn) and the test set (CCtst) were 0.997 and 0.992, respectively. The small and comparable magnitudes of the RMSE and average prediction error (%), and the high and comparable values of CC, for both the training and test set outputs suggest that the MLP-based model possesses good approximation and generalization characteristics. A comparison of the network-predicted and desired values of the EPS yield is depicted in Fig. 1. As can be

The objective of the GA-based process optimization was to obtain the optimal values (x*) of influential fermentation operating variables in a manner such that the EPS concentration is maximized. Since the MLP model represents the non-linear relationship between the four fermentation variables and EPS concentration, the same can be used to define the corresponding single objective optimization problem as stated below: Maximize y ¼ f ðx; WÞ;

xLl  xl  xU l ;

l ¼ 1; 2; . . . ; L (2)

where f represents the objective function (ANN model); y refers to the EPS yield; the L-dimensional decision vector, x, denotes the fermentation operating conditions (L = 4) and xLl and xU l , respectively, represent the lower and upper bounds on xl. The values of GA-specific parameters used in the optimization simulations were: lchr (chromosome length) = 40, Npop (population size) = 40, pcr (crossover probability) = 0.9, pmut (mutation probability) = 0.01, and Ngmax (number of generations over which GA evolved) = 500. For evaluating the fitness score of a candidate solution in a population, first the four-dimensional solution vector was applied to the MLP model and the model output (EPS yield) was evaluated. Next, the fitness score of the solution was evaluated using following equation, ej ¼ 1 

1 j yˆ pred

;

j ¼ 1; 2; . . . ; Npop

(3)

where ej denotes the fitness score of the jth candidate solution j and yˆ pred refers to the MLP model-predicted EPS yield when jth solution is used as the model input. During GA-implementation, the search for the optimal solutions was restricted to the following ranges of the four process operating variables: (1) lactose concentration (g/l) (x1): [2.0, 25.0], (2) triammonium citrate concentration (g/l) (x2): [0.0, 0.4], (3) casein hydrolysate concentration (g/l) (x3): [2.0, 8.0], and (4) inoculum percentage (x4): [1.0, 4.0]. These ranges are the same over which the process operating variables were varied for collecting the experimental data listed in Table 3. In the case of a non-linear objective function, it is possible that the optimization algorithm obtains a locally optimal

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Table 3 Fermentation data used in ANN modeling Exp. no.

Lactose (g/l)

Triammonium citrate (g/l)

Casein hydrolysate (g/l)

Inoculum size (vol%)

EPS (g/l)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

8 8 25 8 25 25 20 4 25 25 8 20 10 4 25 4 8 8 4 4 25 4 25 8 8 8 4 20 8 8 8 4 25 40 2 8 8 20 25 4 4 20 4 25 4 20 20 4 4 4 25 4 20 25

0 0.2 0 0.2 0.2 0.2 0.2 0.2 0.2 0 0 0.1 0.2 0 0.2 0 0.2 0.2 0.2 0.2 0 0 0 0 0 0 0 0.3 0.2 0 0.2 0.2 0 0.2 0.2 0.2 0.2 0.2 0 0 0.2 0.2 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0 0.4 0

2 8 4 2 2 8 8 4 4 8 4 5 4 4 4 2 4 8 2 4 4 4 8 2 4 8 8 5 4 4 2 8 4 4 4 8 4 4 2 8 8 1 2 2 2 5 3 8 4 4 2 8 5 8

1.5 3.5 1.5 2 2 2 1 1.5 2 1.5 1.5 1 1 1.5 1.5 2 1.5 1.5 1.5 1 2 2 3.5 2 3.5 3.5 2 1 3.5 2 1.5 2 3.5 1 1 2 1 1 3.5 1.5 3.5 1 3.5 2 3.5 1 1 1.5 2 3.5 3.5 3.5 1 2

2.29
0.41 3.43
0.12 5.16
0.73 2.38
0.62 4.51
0.37 5.32
0.12 1.64
0.18 1.54
0.04 5.20
0.24 5.66
0.76 2.80
0.01 1.80
0.50 1.35
0.64 1.43
0.15 5.22
0.57 0.98
0.58 2.91
0.32 3.79
0.53 1.08
0.42 0.80
0.51 5.40
0.12 1.59
0.34 5.13
0.30 2.59
0.59 2.87
0.47 3.78
0.52 2.21
0.71 1.90
0.44 2.68
0.42 2.65
0.45 2.51
0.66 1.99
0.07 5.04
0.16 1.88
0.05 0.65
0.46 3.55
0.40 1.20
0.05 1.70
0.18 4.61
0.73 2.26
0.48 2.17
0.39 0.80
0.69 1.02
0.34 4.90
0.57 1.11
0.21 1.95
0.26 1.40
0.13 1.98
0.79 1.60
0.73 2.53
0.28 5.04
0.69 2.25
0.12 1.86
0.26 5.64
0.66

Table 4 GA-optimized solutions and EPS yield GA-optimized solution

Lactose (x1 )

Triammonium citrate (x2 )

Casein hydrolysate (x3 )

Inoculum size (x4 )

GA-optimized EPS yield (y)

Experimental yield of EPS

1 2 3

39.949 39.997 40.0

0.116 0.137 0.139

7.524 7.947 7.969

1.906 1.943 1.943

7.026 6.981 6.933

7.14 7.11 7.14

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obtained in the verification experiment was 7.14 (g/l), which is in close agreement with the GA-optimized EPS yield of 7.0 g/l. This L. plantarum strain when isolated and characterized was found to produce 2.0 g/l EPS. The utilization of the PB–ANN– GA hybrid formalism has resulted in the EPS yield of 7.45 g/l. From the experimental data given in Table 3, it is noted that the maximum yield of EPS obtained in different trial experiments was 5.7 g/l, which was increased by approximately 25%. It is thus seen that the usage of a combination of statistical and artificial intelligence-based modeling and optimization methods could improve the EPS yield significantly. 5. Conclusion

Fig. 1. Parity plot of EPS yield.

solution instead of the globally optimal one. Thus, for an objective function maximization problem, a thorough exploration of the solution space is necessary to secure a solution that corresponds to the tallest local or the global maximum [6]. Accordingly, in the present study the GA-based optimization simulations were repeated by using each time a different randomly initialized population of the candidate solutions. Dissimilar initial populations ensure that each time the GA begins its search for the optimal solution from a different search sub-space, which helps in locating the tallest local or the global maximum on the objective function surface. Accordingly, the three best solutions obtained after conducting numerous (50) GA-trials are given in Table 4. It was also observed that despite beginning the search in a different search space, the GA converged to similar optimal solutions. This indicates that the GA has indeed captured the solution corresponding to the tallest local or global maximum on the objective function surface. From the GA-optimized solutions listed in Table 4. It can be seen that the best set of fermentation conditions (solution I) is expected to result in the EPS yield of 7.0 (g/l). GA is run for total 500 generations, but the best solution is obtained at 4th generation. Fig. 2 depicts the nature of convergence. This result was verified by carrying out a fermentation run using the GA-specified optimum conditions. The EPS yield

In the present study, optimum media composition and inoculum volume have been developed for the production of EPS using L. plantarum by means of artificial intelligencebased modeling and optimization methods. Plackett–Burman statistical design technique was found to be a useful for identifying the most influential components of the system. The ANN model was constructed on the basis of data from 54 fermentation experiments. This ANN model was found to possess excellent prediction accuracy and generalization ability. The GA-optimized best solution when verified experimentally resulted in the EPS yield of 7.14 (g/l), which is in close agreement with the GA-predicted EPS yield of 7.01 (g/l). The experimentally verified EPS yield value 25% higher than the maximum yield obtained during the experiments used for developing the ANN model. It can thus be seen that the usage of ANN-GA hybrid methodology has resulted in a significant improvement in the EPS yield. The approach presented in this paper is sufficiently general and thus can also be employed for modeling and optimization of other bioprocesses. Acknowledgements We are thankful to the University Grants Commission for the financial support. The authors also acknowledge CSIR for Yogesh Badhe’s fellowship. Appendix A. Nomenclature CCtrn, CCtst Etrn, Etst lchr L M Nˆ N

Fig. 2. The progressive performance of genetic algorithm generations till optimum solution is obtained.

Nd Ngmax

correlation coefficient for the training set and test set, respectively RMSE value for the training set and test set, respectively length of the chromosome number of processing nodes in the input layer of MLP network number of processing nodes in the hidden layers of MLP network number of experiments in PB design number of processing nodes in the output layer of MLP network Number of dummy variables in PB design maximum number of generations in GA

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Npop pcr pmut P Veff WH, WO

x x* xp, yp X yi+ yi yin ; yˆ in j yˆ pred

Y

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number of candidate solutions in a GA population probability of crossover probability of mutation number of input-output patterns Variance of effect in PB design weights on connections between input and hidden nodes, and hidden and output nodes, respectively input variable GA-optimized solution vector pth input and output vector, respectively input vector of ANN model yield of EPS at high level concentration of a given media component yield of EPS at low level concentration of a given media component desired and ANN predicted output for ith input vector ANN predicted yield when jth solution is applied to the ANN model as input output vector of ANN model

Greek letters h learning rate in EBP algorithm a momentum coefficient in EBP algorithm

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