ISA Transactions. On-line evolutionary optimization of an industrial fed-batch yeast fermentation process

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1 ISA Transactions 48 (2009) Contents lists available at ScienceDirect ISA Transactions journal homepage: On-line evolutionary optimization of an industrial fed-batch yeast fermentation process Uğur Yüzgeç a,, Mustafa Türker b, Akif Hocalar b a Department of Electronic and Telecommunication Engineering, Kocaeli University, 41040, Kocaeli, Turkey b Pakmaya, PO. Box 149, 41001, Kocaeli, Turkey a r t i c l e i n f o a b s t r a c t Article history: Received 13 July 2007 Received in revised form 17 July 2008 Accepted 15 September 2008 Available online 11 October 2008 Keywords: Genetic algorithms Optimization Baker s yeast Fed-batch fermentation process This paper presents two genetic algorithms based on optimization methods to maximize biomass concentration, and to minimize ethanol formation. The objective function is maximized according to the values of feed flow rate, using genetic search approaches. Five case studies were carried out for different initial conditions, which strongly influence the optimal profiles of feed flow rate for the fermentation process. The ethanol and glucose disturbance effects were examined to stress the effectiveness of proposed approaches. The proposed genetic approaches were implemented for an industrial scale baker s yeast fermentor which produces Saccharomyces cerevisiae known as baker s yeast. The results show that optimal feed flow rate was obtained in a satisfactory and successful way for fed-batch fermentation process ISA. Published by Elsevier Ltd. All rights reserved. 1. Introduction The biotechnology industry, such as pharmaceutics, fermentation, agriculture and chemical processes, is rapidly developing. During the past few decades, process optimization, the key issue of industrial scale biotechnological production, has been used to maintain optimum operating conditions to increase product yields and to ensure product quality [1]. Control of a biochemical process is fairly difficult, due to the need for accurate control as a result of the sensitivity of micro-organisms, and the inability to fully influence internal environment of the cell [2]. In general, three operation modes are used in industrial fermentation processes: batch, fed-batch and continuous. Batch operations, such as some pharmaceutical productions [3,4], have not been commercially attractive and, in this type of operation, a substrate is added at the initial stage of the process, and final product is removed. In a continuous operation, such as the fermentation of milk in margarine production [5] and the biological purification of waste water [6], substrate is added and product is removed continuously. More economic is the fed-batch fermentation where the substrate, that is, feed rate profile is varied during the process and the final product is removed at the end of the process. Fed-batch operations may be operated in a variety of Corresponding author. Tel.: addresses: uyuzgec@kocaeli.edu.tr (U. Yüzgeç), mustafa@pakmaya.com.tr (M. Türker), akifh@pakmaya.com.tr (A. Hocalar). ways, by regulating the feed rate in a predetermined manner, or by using feedback control. The most commonly used are constantly fed, exponentially fed, and extended fed-batch [7]. Industrial scale processes are more complicated, and more difficult to control, due to the limitations in operating conditions. Therefore most fedbatch processes in industry are run by a human operator, according to personal experience, and as a result, the operation is not always uniform and optimal productivity is seldom obtained [8]. It is obvious that a model-based efficient approach is necessary to ensure uniform operation and maximum productivity with the lowest possible cost in fed-batch processes, without requiring a human operator. Optimizations of bioprocesses are performed, based on precise and robust mathematical models. In general, models of bioprocesses are described by a set of differential equations derived from mass balances. In this study, the mathematical model of industrial fed-batch fermentation process was derived from the model of Sonnleitner and Kappeli [9], which has large acceptance in describing the behaviour of yeast cultures. The control strategy of a fermentation process is to maximize the final product yield, and to minimize ethanol formation. Numerous studies have been reported concerning the control of fed-batch fermentation processes in the literature: Berber et al. [10] implemented a dynamic programming algorithm based optimization to fed-batch baker s yeast fermentor. The optimization results lead to the optimal feeding profile of substrates for the yeast fermentor. Hisbullah et al. [11] proposed several controllers for fermentation processes, namely, a fixedgain and a scheduled-gain PI controller, an adaptive neural /$ see front matter 2008 ISA. Published by Elsevier Ltd. All rights reserved. doi: /j.isatra

2 80 U. Yüzgeç et al. / ISA Transactions 48 (2009) Nomenclature β 1,2,3 weight factors µ specific growth rate (h 1 ) ε value of stop criteria A R cross-sectional area of fermentor (m 2 ) C i concentration of ith component (g L 1 ) F feed flow rate (L h 1 ) F a air feed rate (m 3 h 1 ) J objective function k L a o total volumetric mass transfer coefficient (h 1 ) K e saturation constant for ethanol (g L 1 ) K i inhibition constant (g L 1 ) K o saturation constant for oxygen (g L 1 ) K s saturation constant for substrate (glucose) (g L 1 ) L length of time interval (h) L c length of chromosome p c probability of crossover operator p m probability of mutation operator PS population size Q i specific consumption or production rate (g g 1 h 1 ) Q m glucose consumption rate for maintenance energy (g g 1 h 1 ) RQ respiratory quotient S o substrate concentration of feed (g L 1 ) t time (h) t d time delay (h) t f final time (h) V volume (L) V f volume of fermentor (L) Y i/j yield of component i on j (g g 1 ) Superscripts and subscripts * interface c carbon dioxide cr critic e ethanol lim limitation max maximum o oxygen ox oxidative pr production red reductive s substrate (glucose) up uptake x biomass network controller and a hybrid neural network-pi controller. Karakuzu et al. [12] developed two soft sensors, based on a neural network to estimate the specific grow rate and biomass concentration, and they proposed a control approach using neural soft sensors. Karakuzu et al. [13] designed a fuzzy substrate feeding controller, instead of the conventional controller for baker s yeast fermentation. Their paper shows that the proposed fuzzy controller provides higher productivity than a conventional controller. Peroni et al. [14] improved the simulation-based approximate dynamic programming method for optimal control of a fed-batch process and the optimal feed rate profile was determined by this simulation-based control strategy, under varying initial conditions. Zhang [15] presented a recurrent neurofuzzy network based modeling and optimal control for a fedbatch process. Although the product yield obtained by using the optimal control with recurrent neuro-fuzzy networks is lower than those predicted by the use of mechanistic models, the final concentrations of undesired species for this approach are also lower. Renard et al. [16] developed a robust control scheme, using minimal process knowledge and minimal measurement information, and developed controller applied to S. cerevisiae cultures in fermentation process. Visser et al. [17] proposed a cascade optimization scheme to implement such an optimal trajectory, despite disturbances and parametric uncertainty for penicillin fed-batch fermentation. Trelea et al. [18] presented a dynamic optimization sequential, using quadratic programming to obtain various desired final aroma profiles, and to reduce the total process time for a beer fermentation process. Their dynamic optimization consists of three control variables: temperature, top pressure and initial yeast concentration in the fermentor. The obtained aroma profiles remained within the tolerance limits, despite model uncertainty. If optimization problem has a nondifferentiable and complex structure, an analytical solution is obtained with difficulty using traditional search techniques, and moreover, sometimes a solution cannot be ever obtained. Whereas traditional search techniques use characteristics of the problem to determine the next sampling point (gradients, Hessians, linearity), instead of such assumptions, stochastic search techniques determine the next point, using stochastic decision rules [19,20]. For this reason, Genetic Algorithm (GA), which is one of the stochastic search methods, is considered to solve the optimization problem of fed-batch fermentation processes. GA are based on the principles of natural genetics and selection, such as crossover, mutation [20], and GA approaches are widely used as a tool in optimization [21,22], training process of artificial neural networks [23,24], data mining and classification [25,26]. A number of studies, including GA-based optimization for fed-batch fermentation processes, has been reported in the literature: Chen et al. [27] used GAs for optimizing the productivity of a seventh-order nonlinear model of fed-batch culture of hybridoma cells, and for identifying model parameters. Na and coworkers [28] proposed three genetic approaches to solve the optimization problem of a fed-batch process of yeast. By evaluating the performances of these genetic approaches for four initial conditions, the best alternative has been selected. Due to the large population size and long chromosome length, proposed approaches have a large computation time. Chen et al. [29] improved a modified genetic algorithm to determine the optimal feed rate profile. The obtained feed rate profile shows that the algorithm successfully solves the optimization problem. This paper deals with applying two evolutionary approaches to optimize a fed-batch fermentor for baker s yeast production on an industrial scale. The process kinetics which are adopted from the literature, and the reactor model are used to simulate the process dynamics, and to find the optimum feed flow rate profile during the process. Two optimization variants have been approached, all the time looking for biomass production maximization, by-product (ethanol) minimization, and a controlled yeast-growing rate. While the GA-I variant uses fixed-length feeding time-intervals during the batch, the GA-II considers a variable-length feeding intervals with initial/end-point constraints. Solutions obtained under various operating conditions are extensively discussed in terms of physical-meaning, economic efficiency, required computing time, and robustness when perturbations in statevariables occur during the process. Solutions are also checked with experimental data recorded from two industrial fermentors of different scales. The paper is organized as follows: Section 2 presents the mathematical equations associated with kinetic and dynamic model of fermentation processes. Besides, the definition of optimization problem is given and the both of proposed algorithms are explained in this section. Section 3 presents the details about the experimental part and the methods used in this work. In

3 Section 4, the performances of the proposed approaches are evaluated for five case studies with different initial conditions, and disturbance effects are examined to stress their robustness. At the end of this section, the optimization results of the proposed methods are given with experimental data for two fermentor types. The paper ends with concluding remarks. U. Yüzgeç et al. / ISA Transactions 48 (2009) Theory 2.1. The model of an industrial fed-batch yeast fermentation process The process model in this section consists of two parts: cell (kinetic) model and reactor (dynamic) model Kinetic model The kinetic model of yeast metabolism is based on the bottleneck hypothesis developed by Sonnleitner and Kappeli [9]. It assumes a limited oxygen capacity of yeast, leading to formation of ethanol under conditions of oxygen limitation and/or an excessive glucose concentration [10]. This model has been developed by Karakuzu et al. [30] with updated terms for the glucose uptake rate and oxidation capacity. The kinetic model comprises the following equations: C s ( ) Glucose uptake rate: Q s = Q s,max 1 e t/t d K s + C s K i Oxidation capacity: Q o,lim = Q o,max (2) K o + C o K i + C e Specific growth rate limit: Q s,lim = µ cr Y ox x/s ( ) Q s Oxidative glucose metabolism: Q s,ox = min Q s,lim Q o,lim /Y o/s Reductive glucose metabolism: Q s,red = Q s Q s,ox (5) ( ) ( ) Ce Ki Ethanol uptake rate: Q e,up = Q e,max (6) K e + C e K i + C e Oxidative ethanol metabolism: ( ) Q Q e,ox = e,up min ( ) (7) Qo,lim Q s,ox Y o/s Ye/o Ethanol production rate: Q e,pr = Q s,red Y e/s (8) Total specific growth rate: µ = Q s,ox Y ox x/s + Q s,redy red x/s + Q e,oxy x/e (9) Carbon dioxide production rate: Q c = Q s,ox Y ox c/s + Q s,redy red c/s + Q e,oxy c/e (10) Oxygen consumption rate: Q o = Q s,ox Y o/s + Q e,ox Y o/e (11) Respiratory Quotient: RQ = Q c /Q o. (12) Dynamic model The dynamic model is based on mass balance equations described by glucose, ethanol, oxygen and biomass concentrations. The model was constructed by completing the kinetics with substrate limitation and product inhibition: ( ) dc s = F dt V (S o C s ) dc o dt µ Y ox x/s + Q e,pr Y e/s C o + Q m (1) (3) (4) C x (13) ( = Q o C x + k L a o C ) o C F o V C o (14) Fig. 1. Profiles of feed flow rate and volume for all case. (F = F 0 e (α t) ). dc e = ( ) Q e,pr Q e,ox Cx F dt V C e (15) dc x = µ C x F dt V C x (16) dv dt = F (17) ( ) 0.25 Fa k L a o = 113 (18) A R where C s, C o, C e, C x represent concentrations of glucose, oxygen, ethanol and biomass, respectively. F a denotes air feed rate and A R denotes the cross-sectional area of the reactor (fermentor). The model parameters were obtained from the literature and experimental data as given in Table Optimization problem In general fermentation processes, it is desired that the biomass quantity (or other cellular products) should be maximized at the end of the process. Therefore, the objective function can be only consist of the biomass concentration. However, the amount of ethanol may increase as an undesired by-product during the fermentation, depending on the initial and operating conditions. Increasing the feed rate of the substrate to obtain the maximum final product causes an increase in the concentration of ethanol [10]. The amount and quality of the final product deteriorates due to the formation of ethanol at the end of the fermentation process. However, a decrease in the substrate feeding rate leads to a diminution in ethanol formation and the biomass growth rate, and to an insufficient use of the reactor capacity. The specific growth rate is another important parameter for fermentation. To obtain maximum final biomass, it is necessary that the growth rate is very close to the critical growth rate (µ cr ). Formation of ethanol increases once again when this critical value is passed. Considering all of these situations, optimization problem of fed-batch fermentation process consists in maximizing the concentration of biomass, while minimizing the concentration of ethanol as Eq. (19): ti maximize J (t i ) = β 1 C x (t i ) β 2 C e (t) dt F t [ i 1 ] 2 1 ti β 3 µ (t) dt µ cr (19) (t i t i 1 ) t i 1 subject to 0 t t f, F min F (t) F max. (20) β 1, β 2, β 3 represent weight factors and t i is time for ith iteration. The optimization problem given by Eqs. (19) and (20) comprises three parts: maximizing of the biomass concentration, minimizing of total ethanol formation, and obtaining the average substrate

4 82 U. Yüzgeç et al. / ISA Transactions 48 (2009) Table 1 Numeric values of the parameters in the fed-batch yeast fermentation model [9,10,30] Parameter Units Value Parameter Units Value Parameter Units Value K e g L Y e/o g g Q o,max g g 1 h K o g L Y e/s g g Q s,max g g 1 h K i g L Y x/e g g Q m g g 1 h K s g L Y ox c/s g g µ cr h Y ox x/s g g Y red c/s g g S o g L Y red x/s g g Y c/e g g C o g L Y o/s g g Q e,max g g 1 h A R m growth rate close to critical growth rate. The boundary conditions for the control variable, that is, maximum and minimum feed rate values are usually specified. Additionally, the operating conditions of the fermentation process are limited during the optimization procedure. The volume of the total biomass at the final time point must be lower than total volume of the fermentor (V (t) < V fer ). In this study, the total process time is separated into the calculation stages to solve the optimization problem. The optimization problem is solved for each stage, and this procedure is performed until the final process time is reached. Details of the solution algorithm of the optimization problem are given in the following section. Due to the fact that the structure of the objective function of fed-batch fermentation process is nondifferential and complex, an analytical solution is obtained with great difficulty using traditional search techniques, and moreover, sometimes a solution cannot ever be obtained. Stochastic search techniques reported better results, compared with traditional search techniques for solving this type of optimization problem. The advantage of stochastic search techniques is that it is not limited to the convexity, complexity and nonlinearity of an objective function, that is, it does not need any knowledge about the dynamics of the process [19]. This study introduces a novel search technique, based on a genetic algorithm (GA) to solve the optimization problem of fed-batch fermentation processes Determination of feed rate profile using GA To determine the optimum feed rate profile, which maximizes the objective function, the total fermentation time is divided into calculation stages. In this study, two approaches are used: first, the length of the time interval is considered as fixed, and then the optimal lengths of each time interval are determined by developing a second search strategy. The second strategy is given by Eq. (21): maximize F,L β 3 [ 1 L ti 1 +L J (t i 1 + L) = β 1 C x (t i 1 + L) β 2 C e (t) dt ti 1 +L t i 1 µ (t) dt µ cr t i 1 ] 2 β 4 L (21) where i is the iteration index, and L is the optimal length of each time interval. As can be noted from this equation, time interval term (β 4 L) was added to the objective function. A modified GA is used to solve the optimization problems in both search strategies. In the first search approach (GA I), each chromosome is considered as a binary string. The last bit of the chromosome denotes a value of the objective function called the fitness of the chromosome. The other bits represent the values of feed rate as binary code. The determination procedure of population size plays an important role for stochastic search methods. Goldberg [34] proposed that the population size (PS) can be defined as a function of the length of chromosome (L c ) as given by Eq. (22): PS = L c. (22) Table 2 GA parameters used for optimization Parameter name Parameter GA I GA II Population size (Eq. (21)) PS Length of chromosomes L c Crossover probability p c Mutation probability p m Stop criteria value ε 1e 6 1e 6 The roulette wheel procedure was preferred, because of satisfactory results in maximization problems. After a selection operation, both crossover and mutation genetic operators are considered, to obtain a new generation. Generally, the value of mutation probability is much smaller than the value of the crossover probability. GA is finished when the fitness for the best chromosome does not change significantly from iteration to iteration. The chromosome consists of three different parts for the second search approach (GA II): the first part denotes the feed rate value; the second part denotes the time interval value, and the last bit denote the value of fitness of chromosome. The parameters of GA I and GA II were chosen by a trial and error method and these parameters are given in Table 2. In numerical optimization methods using GA, fitness values are determined by an objective function at each generation step. For this reason, each individual of population which is generated by GA as a binary code is decoded, and these values are carried out to a fed-batch process as inputs. Solving optimization problem using GA takes a long time, due to running the process to calculate the fitness values of each individual in population. To overcome this excessive computing condition, the total fermentation time is divided into the subintervals, and the optimization problem is solved one by one for all of these calculation stages. Simultaneously, the chromosome length, which has an important effect on computation time of GA is short. One of the important conditions in an optimization method using GA is the initial population, which is generally determined by a random selection of a set of chromosomes. In the proposed algorithm structures, the solution set is divided by population size and each individual in a population is determined as a middle point, taken from equal parts of a solution set. By the proposed selection procedure of an initial population, the solution of the optimization problem is realized in a shorter time than classical optimization methods. Both search algorithms proposed in this work are explained below, as a sequence of calculations: GA I Algorithm: 1. The total process time between the start of the process (t = 0) and the end of the process (t = t f ) is separated into time intervals. The length of each time interval (L) is fixed. The length of chromosome to be used in GA is formed by the boundary values of the feed rate. 2. The solution set is divided into equal parts to establish each individual of an initial population. The initial chromosomes in the population are formed as a binary code of values taken at the middle points of these equal parts.

5 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 2. Profiles of biomass, glucose, ethanol and oxygen concentration for all cases. 3. The decoded values of each individual in the initial population are used as control variables of the model of the fermentation process. For the first iteration, the model is run from t 0 = 0 min to t 1 = L min and the output values, which are necessary for the objective function, are stored into the vectors (C x,c e, µ). The fitness values of each individual are calculated using the concentrations of biomass (C x ) at t 1 = L min, total ethanol consumption ( C e ) and average growth rate (µ). 4. The chromosome which has the best fitness value is recorded. Performing the roulette wheel procedure, the chromosomes having the maximum fitness values are selected, and in this way, the population has better individuals. 5. The new individuals in the population are created by performing the genetic operators (crossover and mutation). For this new generation, their fitness values are calculated by running the model from t 0 = 0 min to t 1 = L min as was done at Step 3. The best chromosome which has been previously recorded, is located into the new generation, instead of the chromosome which has the worst fitness value. 6. Repeat from Step 4 to Step 6 until a convergence criteria (ε) of the evaluation function is reached. 7. At the end of GA, the best individual is control variable (F) for the fermentation model. The model is run from t 0 = 0 min to t 1 = L min under this feed rate which is determined by GA. 8. For consecutive iterations, initial population is selected as first iteration and same procedures are repeated from Step 3 to Step 7. As can be noted from this algorithm that the model is run from t i 1 = (i 1) L min to t i = (i) L min to calculate the fitness values for ith iteration. At the last time stage from t f L to the final time t f, the optimum feed rate is determined by GA, and the model is run under this feed rate. GA II Algorithm: 1. The length of chromosome is formed by the boundary values of the feed rate and the length of the time interval. 2. The solution set is divided into equal parts to establish each individual of the initial population. The initial chromosomes in the population are formed as a binary code of values, taken at the middle point of these equal parts. The values of chromosomes in the population are stored in a vector with population size x, the length of chromosome.

6 84 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 3. The optimization result that is obtained by GA I: profiles of biomass, glucose, ethanol and oxygen concentration. 3. The fermentation model is run for each individual of the initial population. For all of the iteration, the fitness values are calculated by an objective function, using the model output values which are obtained for pairs of feed rate and length of time interval. 4. The best chromosome in the population is stored. The roulette wheel procedure is performed, and the chromosomes which have low fitness values are cleaned in the population. 5. Using the crossover and mutation operators, new individuals in population are generated. The fitness values of each individual in new generation are calculated with the help of the objective function as Step 3. The best chromosome stored previously is located into the new generation, instead of the worst chromosome. 6. Repeat from Step 4 to Step 6 until a convergence criteria (ε) of the evaluation function is reached. 7. At the end of GA, the best individual, that is, optimal feed rate and optimal length of time interval (L) are used as input of the fermentation model. The model is run from t 0 = 0 min to t 1 = L min under this optimal feed rate, which is determined by GA. 8. The same procedures are repeated from Step 3 to Step 7 for consecutive iterations. From t i 1 = (i 1) L min to t i = (i) L min, where the optimal length of time interval (L) is calculated by GA, the model is operated under the optimal feed rate (F) that is computed by GA for all of the iterations. Model output values are stored for each iteration, and for next iteration, these values are used as initial values of the model through an optimal time interval. 3. Materials and methods The fed-batch fermentation process was carried out in two industrial-scale bubble column bioreactors, with volumes of 100 m 3 and 25 m 3 using an industrial strain of S. cerevisiae. The 100 m 3 bioreactor was equipped with an external plate heat exchanger to remove metabolic heat. The fermentor inputs are substrate (molasses), air, ammonia, acid and anti-foam agent [31,32]. The carbon dioxide, oxygen (Servomex Gas Analyser, 1400 B4 SPX) and ethanol (Vogelbuch GS 2/3) concentrations are measured in the gas phase in the exhaust line. The fermentor with a 25 m 3 volume, is equipped with external half coils for cooling. The airflow rate is measured by a vortex flowmeter

7 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 4. Optimal profiles of feed flow rates determined by GA I for all cases. (EMCO, V-Bar 700) and molasses and ammonia flow rates are measured by electromagnetic flow meters (Krohne, IFM 090) [33]. Biomass concentration is not measured on-line, therefore it is determined by analyses in laboratory. In continuous experiments for fermentor with volume of 100 m 3, data were stored at every 15 min along the fermentation process. As for a small-scale fermentor, measurements were taken every 10 min. The Runge Kutta finite difference method was used for solutions of the first order ordinary differential equations in dynamic model. The sampling time was considered as 3.6 s, that is, proposed approaches perform for 1000 steps along one hour. The proposed genetic approaches were coded in Matlab r 6.5 and the programs were run on an Intel(R) Pentium(R) 4 microprocessor based 2.80 GHz with 512 MB RAM. For a mathematical model of the fermentation process, one main program (main_process_model.m) and three sub-programs (kinetic_model.m, dynamic_model.m, model_parameters.m) were written. To solve the optimization problem, two genetic search codes (GAI.m and GAII.m) were developed in this study. 4. Results and discussion For evaluating the performance of proposed GA structures, first, case studies were performed, and then disturbance effects were examined to stress their effectiveness. Finally, proposed optimization procedures were implemented for an industrial scale baker s yeast fermentor in this section Case studies To test the performance of both of the search algorithms, the five case studies having different initial conditions are considered. The five initial conditions are presented in Table 3. For Case I, initial biomass and glucose concentrations are considered as high values. Initial biomass concentration is appropriate, and initial glucose concentration is high for Case II. For Case III, initial biomass concentration is appropriate and initial glucose concentration is chosen as low value. Initial biomass concentration is low and initial glucose concentration is high for

8 86 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 5. Performance results of GA I for different values of length of time interval L, 0.5 h (dashed line), 1.0 h (solid line) and 1.5 h (bold solid line): (A) concentration of glucose, (B) ethanol, (C) biomass, (D) oxygen, (E) growth rate and (F) feed flow rate. As initial conditions of fermentation process, Case II was used. Table 3 Initial conditions for five case studies Initial conditions Case I Case II Case III Case IV Case V Biomass concentration (g biomass L 1 ) Glucose concentration (g glucose L 1 ) V(0) = L, S o = 325 g glucose L 1, t f = 16.5 h Case IV. For Case V, initial biomass and glucose concentration are considered as low values. The total time of the fermentation process was selected to be 16.5 h for the cases of GA I and GA II. The fixed length of time intervals in GA I was considered as 0.5 h, 1.0 h and 1.5 h. In GA II, the lengths of time intervals are determined by optimization procedures. The boundary values of the length of time interval were chosen to be from 0.5 h to 4.0 h. In both GA I and GA II, the first 12 bits from the beginning of the chromosome were assigned to represent information of the feed flow rate. The information of length of time interval was represented from 13 to 15 in bits of chromosome in GA II. The fitness values of the individuals in the population were stored in the last bit of the chromosomes for both of the algorithms. The mathematical model of fermentation process was run under these initial conditions for a profile of the feed flow rate (F = F 0 e (α t) ) shown in Fig. 1. In all cases, the total fermentation time (t f ) is 16.5 h, the volume of the fermentor (V fer ) is 100 m 3 and the concentration of feed (S o ) is 325 g glucose L 1. The results of the mathematical model, which are biomass, glucose, ethanol and oxygen concentrations are shown in Fig. 2 for all cases. The model results reveal that the ethanol formation depends on excessive glucose inside the fermentor, and the ethanol formation in Case I is lower than Case II due to a high biomass concentration in the initial conditions. In Case III, because of a low value of glucose concentration at the beginning of the fermentation, ethanol does not form during the process. In Case IV, ethanol formation increases, due to high value of initial glucose concentration and low value of initial biomass concentration. At the last case, in spite of the initial biomass and glucose concentration being considered as low values, it can be seen from figure that an excessive ethanol formation is observed, due to the use of a feed flow which contains high glucose (S o ). In optimization results obtained using genetic algorithms, Fig. 3 shows clearly the performance of GA I for all cases. It is to be noted from these results, that at the end of the fermentation process

9 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 6. The optimization result that is obtained by GA II: profiles of biomass, glucose, ethanol and oxygen concentration. for all of five cases, maximum biomass and minimum ethanol formation have been obtained by determining optimal profiles of feed flow rates under the condition that time intervals had a fixed length of 0.5 h. Indeed, the reduction in ethanol concentration is very satisfactory, for especially Case IV and Case V. Using GA I, the optimal profiles of feed flow rates are shown in Fig. 4 for all cases. The boundary condition of feed flow rate was chosen from 0 L h 1 to 4095 L h 1. It is clearly seen from the results in Fig. 4 that, as one might expect, the feed flow rate follows a trend which contains very low values at the points being of excessive ethanol formation. For different values of length of time interval, the performance of GA I is represented in Table 4. Here, four critical parameters are considered: biomass concentration at the end of the process, total ethanol concentration, average growth rate and total computing time of search algorithm. The simulation results obtained for three different values of length of time interval show that they have close profiles with each other. In general, the computing time is a very important point for all numeric search techniques from the point of view of implementation to an industrial scale process. The results which contain values of total computing time of GA I varies between 260 s and 450 s as less than the final time of process (16.5 h) and these results reveal that proposed algorithm can easily be used in optimization applications of industrial scale fermentation processes. It can be noted from Fig. 5 that profiles of output and input values of process follow the similar trends for different values of length of time interval. Comparing the optimization results of GA I with a fixed time interval length of 0.5 h and GA II, as given in Table 5, it is seen that they have close performances for initial case I, II and III. But especially, optimization results of GA II for the other two initial cases are less satisfactory than GA I as shown in Fig. 6. The total computing time required for solving the optimization problem using GA II is longer than the computing time of GA I. Finally, it can be clearly said that both of the proposed algorithm structures are rather appropriate for a real-time control application Disturbance case study During the fermentation process under different disturbance effects, the behaviors of proposed genetic algorithms were considered, and their attribute of robustness was introduced. For this purpose, two cases are considered as being taken note of

10 88 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 7. Optimization results of the fermentation process under the glucose disturbance of 15 g glucose l 1 h 1 between 2 h and 2.5 h using GA I. The concentration profiles with (A) off-line and (C) on-line optimization for initial condition of Case II, the concentration profiles with (B) off-line and (D) on-line optimization for initial condition of Case V. For initial conditions of (E) Case II and (F) Case V, feed flow rates determined by off-line (solid line) and on-line (bold solid line) optimization. Table 4 Performance of GA I for different values of length of time interval Case Biomass concentration at the final time (g biomass L 1 ) Total ethanol concentration (g ethanol L 1 ) Average growth rate (h 1 ) Total computing time of search algorithm (s) Length of time interval (L) Length of time interval (L) Length of time interval (L) Length of time interval (L) 0.5 h 1.0 h 1.5 h 0.5 h 1.0 h 1.5 h 0.5 h 1.0 h 1.5 h 0.5 h 1.0 h 1.5 h I II III IV V Table 5 Performances of GA I and GA II for five cases Case Biomass concentration at the final time (g biomass L 1 ) Total ethanol concentration (g ethanol L 1 ) Average growth rate (h 1 ) Total computing time of search algorithm (s) GA I GA II GA I GA II GA I GA II GA I GA II I II III IV V

11 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 8. Optimization results of fermentation process under an ethanol disturbance of 10 g ethanol l 1 h 1 between 2 h and 2.25 h using GA I. The concentration profiles with (A) off-line and (C) on-line optimization for initial condition of Case II, the concentration profiles with (B) off-line and (D) on-line optimization for initial condition of Case V. For initial conditions of (E) Case II and (F) Case V, feed flow rates determined by off-line (solid line) and on-line (bold solid line) optimization. disturbance problems in real industrial fermentation processes: the ethanol disturbance of 10 g ethanol L 1 h 1 between 2 h and 2.25 h and the glucose disturbance of 15 g glucose L 1 h 1 between 2 h and 2.5 h. At first, the profile of the feed flow rate and values of the length of the time interval were determined by the proposed algorithms for no disturbance, and then during the fermentation process; concentration profiles are obtained under these disturbance cases. At a second step, using both GA I and GA II, evolutionary optimizations are performed under the same disturbance cases. Fig. 7 shows that the concentration profiles by off-line and on-line optimization using a GA I-based approach under the glucose disturbance for initial conditions of Case II and Case V. It can be seen from Fig. 7(A) that, due to the effect of the glucose disturbance of 15 g glucose L 1 h 1 from 2 h and 2.5 h, at first the glucose concentration increases to 1.56 g glucose L 1 between 2 h and 2.5 h and then again decreases from 2.5 h to 3 h and goes to close zero until the end of the process. At this disturbance case, excessive glucose formation in the fermentor is not spent in oxidative metabolism and therefore reductive glucose metabolism is performed as given in Eq. (5). As a result of the reductive glucose metabolism, the ethanol production rate (Eq. (8)) increases, beginning from 2 h. The reductive glucose metabolism keeps on until the end of the fermentation process, due to the profile of feed flow rate which is determined by GA I for no disturbance. At the end of the process, a biomass concentration of g biomass L 1 and ethanol concentration of g ethanol L 1 are obtained for off-line optimization. Noting from Fig. 7(C) that on-line optimization results show that the biomass concentration increases at final time and excessive ethanol formation decreases during fermentation, by determining the optimum feed rate, using a GA I approach. The biomass concentration is obtained as g biomass L 1 at the final time and the maximum value of ethanol formation is 1.36 g ethanol L 1 during the process. It can be clearly seen from Fig. 7(E) that, as one might expect, the optimum feed flow rate profile reduces from 1200 L h 1 to 0 L h 1 in the time interval of the glucose disturbance. The disturbance effect is shown far too much in off-line optimization due to the characteristics of Case V which has initial biomass and glucose concentration of low values as shown in Fig. 7(B). The final biomass concentration of g biomass L 1, and the final ethanol concentration of g ethanol L 1 are obtained by off-line optimization under the glucose disturbance. In results of on-line optimization using GA I, as shown from Fig. 7(D), at the end of the fermentation process,

12 90 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 9. For the initial condition of Case II, the concentration profiles with (A) off-line and (C) on-line optimization using GA II under the ethanol disturbance of 10 g ethanol l 1 h 1 between 2 h and 2.25 h, the concentration profiles with (B) off-line and (D) on-line optimization using GA II under the glucose disturbance of 15 g glucose l 1 h 1 between 2 h and 2.5 h and feed flow rates determined by off-line (solid line) and on-line (bold solid line) optimization for both disturbances. the biomass concentration of g biomass L 1 is found, and maximum ethanol formation is close to 2.65 g ethanol L 1 during process. Fig. 7(F) shows a comparison of profiles of feed flow rate by evolutionary optimization under no disturbance and glucose disturbance. It is noted from this comparison, that the profile of feed flow rate determined by on-line optimization flows below than that by off-line optimization. Fig. 8 shows that the performance of GA I under an ethanol disturbance of 10 g ethanol L 1 h 1 from 2 h to 2.25 h. For initial condition of Case II, the results of off-line optimization as given in Fig. 8(A), present that the final biomass concentration is g biomass L 1 and the final ethanol concentration is g ethanol L 1. Introducing the ethanol disturbance, excessive ethanol formation appears in the fermentor as being under the case of glucose disturbance and thus reductive glucose metabolism occurs. Fig. 8(C) shows that on-line optimization performance using GA I is better than the off-line optimization results for the ethanol disturbance. Noting from Fig. 8(C) that the formation of ethanol is blocked, and at the final time, the biomass concentration of g biomass L 1 and maximum ethanol formation of 2.08 g ethanol L 1 are obtained by GA I. Fig. 8(E) shows a comparison of the optimum profile of the feed flow rate determined by on-line optimization using GA I, and the profile of feed flow rate determined by GA I for no disturbance. The profile of feed flow rate follows to lower values than results by off-line from 2 h to 4 h. In the same way, Fig. 8(B) and Fig. 8(D) represent that the off-line and on-line optimization performances under the ethanol disturbance for initial condition of Case V. The final biomass concentration of 8.29 g biomass L 1 and the final ethanol concentration of g ethanol L 1 are obtained for off-line optimization under the ethanol disturbance, whereas on-line optimization results present that the final value of biomass goes up to g biomass L 1 and maximum ethanol formation is limited to approximately 2.75 g ethanol L 1. Both of the profiles of feed flow rate for no disturbance and for ethanol disturbance are displayed in Fig. 8(F). To limit excessive formation of ethanol, the profile of feed flow rate varies between 0 L h 1 and 120 L h 1 and in the last stage of the process, the feed profile increases, beginning from 12 h to the end. Fig. 9 represents the performance of GA II for both of the disturbance cases. As observed from the Fig. 9(A) and (B), the final biomass concentration (32.02 g biomass L 1 for an ethanol disturbance and g biomass L 1 for glucose disturbance) decreases and all through the process, excessive ethanol (34.95 g

13 U. Yüzgeç et al. / ISA Transactions 48 (2009) Fig. 10. Comparison of optimization results and experimental data for fermentor with volume of 100 m 3. (A) Biomass concentration and (B) feed flow rate. ethanol L 1 and g ethanol L 1 ) forms for the disturbance cases. It is apparent from Fig. 9(C) and (D) that the excessive ethanol formation is limited, and the final product is obtained as close to an acceptable value by the GA II approach. GA II gives the same profiles for both of disturbances as shown in Fig. 9(E). It can be seen from this figure that the value of the feed flow rate is decreased from 1000 L h 1 to 0 L h 1 by on-line optimization in the interval where the disturbance occurs. In this way, excessive ethanol formation is obstructed due to the disturbance. Finally, all of the disturbance studies show that the performances of GA I and GA II are quite successful and satisfactory for applications of the fermentation process Experimental study In order to evaluate the performance of the proposed genetic search approaches, on-line evolutionary optimization has been performed for an industrial fed-batch fermentation process. The various experimental data obtained from two fermentors with volumes of 100 m 3 and 25 m 3, were used in the performance test of the GA I and GA II. In brief, two experimental data sets were provided. Fig. 10 displays that the comparison of profiles of biomass concentration and feed flow rate for GA I, GA II and first data set taken from the fermentor of 100 m 3. It can be seen from this figure, that the biomass concentration calculated by the proposed genetic search approaches are quite close to experimental data. The profiles of feed flow rate determined by GA I and GA II, look like stairs due to the limitation in the number of the time intervals. Note from Fig. 10(B) that there is good agreement between results obtained by proposed approaches and experimental data. For small-scale fermentor, as shown in Fig. 11(A), the biomass concentration of model by optimization using proposed approaches follows the actual process fairly well. The boundary value of feed flow rate is considered from 0 L h 1 to 4095 L h 1 for both fermentors. Fig. 11(B) shows that profiles of feed flow rate, which are calculated by both of the proposed genetic search approaches and measured from small-scale fermentor. The ethanol formation was obtained close to reasonable values for all of the optimization procedures using GA I and GA II. It is shown overall in experimental results, that the proposed evolutionary search approaches have the potential to improve the performance of fed-batch fermentation processes. Fig. 11. Comparison of optimization results and experimental data for fermentor with volume of 25 m 3. (A) Biomass concentration and (B) feed flow rate. 5. Conclusions This paper presents evolutionary search approaches for the optimization of fed-batch fermentation process. The strategy developed provides for maximizing the biomass concentration at the end of the process, and minimizing ethanol formation during the process. Optimization results obtained by the proposed approaches (GA I and GA II) show that the maximum biomass production is obtained with minimum ethanol formation. In other words, these approaches give nearly optimal performance for different initial conditions, which influence the optimal feed flow rate profiles in the baker s yeast fermentation process. It is demonstrated from ethanol and glucose disturbance cases, that the proposed approaches are robust and successful. It is noted from experimental results that GA I and GA II predict optimal feed rate profiles fairly well. The short computing time encourages that the proposed approaches easily adapt to industrial scale processes in real time. The performance using GA I is more successful than that using GA II. In general, the proposed approaches are designed for the optimization problem associated with ethanol and biomass regulation in baker s yeast fed-batch processes. However, the proposed approaches can be extended to other important optimization problems in fed-batch fermentation, such as the regulation of the dissolved oxygen concentration or a limiting substrate concentration. Consequently, the evolutionary search approaches developed in this study appear to be an effective method for solving nonlinear industrial dynamic optimization problems as fermentation process. As an outcome of this study, the effects of disturbances and uncertainties in the model can be reduced in on-line optimal control of industrial process. Acknowledgments The authors would like to thank the Editors and Reviewers for their constructive, valuable and informative comments. References [1] Schmidt FR. Optimization and scale up of industrial fermentation processes. Applied Microbiology and Biotechnology 2005;68: [2] Rani KY, Rao VSR. Control of fermenters A review. Bioprocess Engineering 1999;21:77 88.

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