- Email: [email protected]
Prediction Model for True Metabolizable Energy of Feather Meal and Poultry Offal Meal Using Group Method of Data Handling-Type Neural Network
Prediction Model for True Metabolizable Energy of Feather Meal and Poultry Offal Meal Using Group Method of Data Handling-Type Neural Network H. Ahmadi,*1 A. Golian,* M. Mottaghitalab,† and N. Nariman-Zadeh‡ *Center of Excellence in the Animal Science Department, Ferdowsi University of Mashhad, Mashhad, Iran 91775-1163; †Department of Animal Science, University of Guilan, Rasht, Iran 41635-1314; and ‡Department of Mechanical Engineering, University of Guilan, Rasht, Iran 41635-3756 ABSTRACT A group method of data handling-type neural network (GMDH-type NN) with an evolutionary method of genetic algorithm was used to predict the TMEn of feather meal (FM) and poultry offal meal (POM) based on their CP, ether extract, and ash content. Thirty-seven data lines consisting of 15 FM and 22 POM samples were collected from literature and used to train a GMDH-type NN model. A genetic algorithm was deployed to design the whole architecture of the GMDH-type NN. The accuracy of the model was
examined by R2 value, adjusted R2, mean square error, residual standard deviation, mean absolute percentage error, and bias. The developed model could accurately predict the TMEn of FM or POM samples from their chemical composition. The R2 for the GMDH-type NN model had a higher accuracy of prediction than 2 models reported previously. This study revealed that the novel modeling of GMDH-type NN with method of genetic algorithm can be used to predict the TMEn of poultry by-products.
Key words: feather meal, poultry offal meal, metabolizable energy, neural network model 2008 Poultry Science 87:1909–1912 doi:10.3382/ps.2007-00507
INTRODUCTION Once the nutrient requirements of the animals were established, a correct balanced diet can be formulated if the accurate nutrient composition of feedstuffs is known. The feather meal (FM) and poultry offal meal (POM) are widely used in broiler diets, and the accurate information on their energy content are of importance to renderers and the nutritionists (Dale and Batal, 2002). It is reported that the energy content of feedstuffs, especially FM and POM in terms of TMEn, strongly depends on their chemical composition. The nutritionists are interested in using a model that can precisely predict the TMEn value of animal by-products. The researchers have tried to develop a TMEn prediction model for the FM and POM samples (Dale, 1992; Dale et al., 1993). All the previously TMEn prediction models reported for poultry by-product meals were based on the regression analysis methods using their CP, ether extract (EE), and ash content. Alternatively, a soft-computing method of artificial neural network (ANN) seemed to be more appropriate for the TMEn prediction of a feedstuff. An ANN is a set of non©2008 Poultry Science Association Inc. Received December 17, 2007. Accepted May 19, 2008. 1 Corresponding author: [email protected]
linear equations that predicts output variable(s) from input variable(s) in a flexible way using layers of linear regressions and S-shaped functions. There is no need to provide an a priori model when using an ANN. It is potentially advantageous in modeling the biological processes often characterized as highly nonlinear (Dayhoff and DeLeo, 2001). The ANN functions are applied to many fields to model and predict the behaviors of unknown systems, very complex systems, or both based on given input-output values (Dayhoff and DeLeo, 2001). One submodel of ANN is a group method of data handling-type neural network (GMDH-type NN). It is a self-organizing approach by which gradually more complex models are generated from their performance evaluation and a set of multi-input, single output data pairs (Lemke and Mueller, 2003). The GMDH was first developed by Ivakhnenko (1971) as a multivariate analysis method for modeling and identification of complex systems. The main idea of GMDH is to build an analytical function in a feed-forward network based on a quadratic node transfer function whose coefficients obtained by using a regression technique (Farlow, 1984). Recently, the use of such self-organizing networks has led to a successful application of the GMDH-type algorithm in a broad range of areas in engineering, science, and economics (Amanifard et al., 2008). In the poultry field, Ahmadi et al. (2007) demonstrated that the GM-
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Table 1. The observed TMEn values and composition of feather and poultry offal samples used to train and validate group method of data handling-type neural network model for the TMEn prediction1 Inputs Item Training set Feather meal
Poultry offal meal
Mean ± SD Validation set Feather meal Poultry offal meal
Mean ± SD 1
Data lines
Crude protein (%)
Crude fat (%)
Crude ash (%)
Observed TMEn (kcal/kg)
Predicted TMEn (kcal/kg)
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
90.00 88.00 84.84 87.58 90.11 85.16 87.79 96.32 96.63 87.05 91.89 87.16 52.50 73.48 52.61 71.30 58.15 54.13 53.04 51.52 52.07 52.61 52.83 51.63 51.20 54.89 51.96 59.67 64.67 60.65 69.71 ± 17.32
6.63 12.42 12.63 8.11 7.37 9.68 8.84 2.95 1.89 9.16 5.79 10.32 33.15 19.89 34.89 25.98 37.83 38.26 39.57 39.67 37.93 35.54 40.98 36.74 38.48 38.70 39.67 27.17 31.09 29.57 24.03 ± 14.20
2.53 2.32 2.21 2.63 2.32 3.26 2.32 2.32 3.05 2.63 2.11 3.26 15.76 5.65 12.39 3.04 6.41 7.39 6.96 8.80 7.72 7.72 7.17 6.09 7.28 6.09 6.41 11.09 5.22 6.85 5.63 ± 3.37
3,491 4,206 3,933 3,699 3,377 3,621 3,741 3,255 3,269 3,794 3,367 3,731 4,240 3,941 4,707 4,632 5,275 5,436 5,151 5,596 5,328 5,309 5,593 4,886 5,139 5,187 5,201 4,570 5,105 4,864 4,455 ± 791
3,511 3,926 3,881 3,608 3,555 3,688 3,648 3,273 3,206 3,662 3,461 3,739 4,560 4,230 4,874 4,752 5,412 5,226 5,304 5,264 5,184 5,159 5,438 5,187 5,222 5,305 5,277 4,496 4,999 4,748 4,460 ± 776
31 32 33 34 35 36 37
89.05 85.79 87.05 62.07 51.74 51.96 58.04 69.39 ± 17.15
6.74 8.32 10.74 30.76 39.13 42.83 32.07 24.37 ± 15.35
2.74 2.32 2.32 6.52 10.43 6.74 10.65 5.96 ± 3.65
3,523 3,768 3,764 4,900 5,034 5,703 4,876 4,510 ± 823
3,522 3,690 3,766 4,834 5,207 5,598 4,783 4,486 ± 821
All data were adjusted to 100% dry matter basis.
DH-type NN model could provide an effective means of describing the data patterns in broiler performance prediction based on their dietary nutrients. The purpose of this study was to examine the validity of GMDH-type NN with a genetic algorithm method to predict the TMEn of feather meal and poultry offal meal based on their chemical analysis.
MATERIALS AND METHODS Data Source Thirty-seven raw data lines consisting of 15 FM and 22 POM samples were used to train a GMDH-type NN. The FM and POM data were those reported by Dale (1992) and Dale et al. (1993), respectively. Each data line consisted of CP, EE, and ash percentages and a measured TMEn for an individual sample (Table 1). Similar procedures were used to determine the chemi-
cal composition and the TMEn of meal samples (Dale, 1992; Dale et al., 1993).
Model Development A detailed description of a GMDH-type NN terminology, development, application, and examples of using this approach were reported by several researchers (Farlow, 1984; Mueller and Lemke, 2000; Lemke and Mueller, 2003; Nariman-Zadeh et al., 2005). The parameters of interest in this multi-input, single-output system that influenced the TMEn were CP, EE, and ash content of the samples. The raw data were divided into 2 parts of training and validation sets. Thirty input-output data lines (12 from FM and 18 from POM samples) were randomly selected and used to train the GMDH-type NN model as a training set. The validation set consisted of the 7 remaining data lines (3 from FM and 4 from POM samples), which were used to validate
NEURAL NETWORK MODEL FOR METABOLIZABLE ENERGY PREDICTION
1911
Table 2. Statistics and information on group method of data handling-type neural network model for TMEn prediction (training vs. validation values) Statistics1 R2 Adjusted R2 MSE Residual mean RSD MAPE Bias Number of hidden layers Number of hidden neurons
Neural network training
Neural network validation
0.96 0.95 26,821 −5.10 166.49 3.04 −5.10
0.99 0.99 8,629 24.09 96.91 1.53 24.09
2 4
1 MSE = mean square error; RSD = residual standard deviation; MAPE = mean absolute percentage error; hidden neurons = number of hidden neurons produced by the genetic algorithm to fit the group method of data handling-type neural network model.
the prediction of the evolved neural network during the training processes. The data set was imported into a GEvoM for GMDH-type NN training (GEvoM, 2008). Two hidden layers were considered for prediction of the TMEn model. A population of 15 individual values with a crossover probability of 0.7, mutation probability of 0.07, and 300 generations was used to genetically design the neural network (Yao, 1999). It appeared that no further improvement could be achieved for this population size. A quantitative verifying fit for the predictive model was made using error measurement indices commonly used to evaluate forecasting models. The goodness of
fit or accuracy of the model was determined by R2 value, adjusted R2, mean square error, residual standard deviation, mean absolute percentage error, and bias (Oberstone, 1990).
RESULTS AND DISCUSSION The optimal structure of the evolved 2-hidden-layer GMDH-type NN was produced from the genetic algorithm (GA) for modeling the TMEn was found with 4 hidden neurons. These neurons were the output of the GA to fit the GMDH-type NN model. The constructed model was characterized by a superb response for all
Figure 1. The comparison of observed and model predicted TMEn values obtained from training (1 to 12 and 13 to 30 are feather and offal samples, respectively) and validation (31 to 33 and 34 to 37 are feather and offal samples, respectively) sets.
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input variables from the training data set. It appeared that the percentage of CP, EE, and ash had a strong effect on the TMEn prediction. The corresponding polynomial equations used to develop the TMEn model were as follows: Y1 = −20,942.48 + 483.67 CP + 525.44 EE − 2.43 CP2
− 2.33 EE2 − 4.60 CP.EE
[1]
Y2 = 2,485.45 + 74.66 CP + 563.71 Ash − 0.67 CP2
− 15.27 Ash2 − 6.60 CP.Ash
[2]
Y3 = 0.00041 + 0.01223 CP + 1.005 Y1 + 0.00316 CP2
+ 0.0000002 Y12 − 0.000145 CP.Y1
[3]
Y4 = 0.00061 + 0.00539 EE + 1.292 Y2 + 0.205 EE2
− 0.00009 Y22 + 0.00325 EE.Y2
[4]
TMEn = 0.00024 + 0.66044 Y3 + 0.33404 Y4
+ 0.00266 Y32 + 0.00265 Y42 − 0.00531 Y3.Y4
[5]
The TMEn values predicted by the GMDH-type NN model is shown in Table 1. The observed and predicted values of TMEn from the training and validation sets are shown in Figure 1. The comparison of observed and predicted TMEn describes the behavior of the GMDHtype NN model from investigating inputs. The results revealed a very good agreement between the observed and predicted TMEn values (for training or validation). The GMDH-type NN model could accurately predict the TMEn of the validation data set that was not used during the training processes. The statistical tests (in terms of R2, adjusted R2, mean square error, residual standard deviation, and mean absolute percentage error) indicated that there was a relatively better prediction of TMEn for the validation as compared with the training values (Table 2). Dale (1992) proposed a linear equation to predict the TMEn of FM samples with one variable of EE (R2 = 0.81). Dale et al. (1993) developed several prediction equations for estimating the TMEn of POM samples with 1 (EE), 2 (EE and ash), or 3 input (EE, ash, and CP) variables, or a combination of these. They suggested that the most accurate prediction equation was obtained with 3 input variables (R2 of 0.81). We proposed neural network model with 3 variables and a combination of 30 data lines of FM and POM samples to compare the results of this study with those of Dale (1992) and Dale et al. (1993). The goodness of fit in terms of R2 corresponding to GMDH-type NN model showed a higher accuracy of prediction than
equations (0.96 vs. 0.81) reported by Dale (1992) and Dale et al. (1993). The results of this study revealed that the novel modeling of GMDH-type NN with an evolutionary method of GA can be used to predict the TMEn of FM and POM samples based on their CP, EE, and ash content. The advantage of using the GMDH-type NN to predict an output from the input variables is that there is no need to preselect a model or base the model entirely on the fit of the data. It is concluded that the GMDH-type NN may be used to accurately estimate the nutritive value of poultry meals from their corresponding chemical composition.
REFERENCES Ahmadi, H., M. Mottaghitalab, and N. Nariman-Zadeh. 2007. Group method of data handling-type neural network prediction of broiler performance based on dietary metabolizable energy, methionine, and lysine. J. Appl. Poult. Res. 16:494–501. Amanifard, N., N. Nariman-Zadeh, M. Borji, A. Khalkhali, and A. Habibdoust. 2008. Modelling and pareto optimization of heat transfer and flow coefficients in microchannels using GMDH type neural networks and genetic algorithms. Energy Convers. Manage. 2:311–325. Dale, N. 1992. True metabolizable energy of feather meal. J. Appl. Poult. Res. 1:331–334. Dale, N., and A. Batal. 2002. Feedstuffs Ingredient Analysis Table. Miller Publishing Co., Minnetonka, MN. Dale, N., B. Fancher, M. Zumbado, and A. Viuacres. 1993. Metabolizable energy content of poultry offal meal. J. Appl. Poult. Res. 2:40–42. Dayhoff, J. E., and J. M. DeLeo. 2001. Artificial neural networks: Opening the black box. Cancer 91(Suppl. 8):1615– 1635. Farlow, S. J. 1984. Self-organizing methods in modeling. GMDH type algorithms. Marcel Dekker Inc., New York, NY. GEvoM. 2008. GMDH-type neural network designed by an evolutionary method of modelling. http://research.guilan. ac.ir/gevom/ Accessed Jan. 20, 2008. Ivakhnenko, A. G. 1971. Polynomial theory of complex systems. IEEE Trans. Syst. Man Cybern. 4:364–378. Lemke, F., and J. A. Mueller. 2003. Medical data analysis using self-organizing data mining technologies. Syst. Anal. Model. Simul. 10:1399–1408. Mueller, J. A., and F. Lemke. 2000. Self-organising data mining: An intelligent approach to extract knowledge from data. Hamburg Pub. Libri., Germany. Nariman-Zadeh, N., A. Darvizeh, A. Jamali, and A. Moieni. 2005. Evolutionary design of generalized polynomial neural networks for modelling and prediction of explosive forming process. J. Mater. Process. Technol. 164– 165:1561–1571. Oberstone, J. 1990. Management Science-Concepts, Insights, and Applications. West Publ. Co., New York, NY. Yao, X. 1999. Evolving artificial neural networks. Proc. IEEE 9:1423–1447.
examined by R2 value, adjusted R2, mean square error, residual standard deviation, mean absolute percentage error, and bias. The developed model could accurately predict the TMEn of FM or POM samples from their chemical composition. The R2 for the GMDH-type NN model had a higher accuracy of prediction than 2 models reported previously. This study revealed that the novel modeling of GMDH-type NN with method of genetic algorithm can be used to predict the TMEn of poultry by-products.
Key words: feather meal, poultry offal meal, metabolizable energy, neural network model 2008 Poultry Science 87:1909–1912 doi:10.3382/ps.2007-00507
INTRODUCTION Once the nutrient requirements of the animals were established, a correct balanced diet can be formulated if the accurate nutrient composition of feedstuffs is known. The feather meal (FM) and poultry offal meal (POM) are widely used in broiler diets, and the accurate information on their energy content are of importance to renderers and the nutritionists (Dale and Batal, 2002). It is reported that the energy content of feedstuffs, especially FM and POM in terms of TMEn, strongly depends on their chemical composition. The nutritionists are interested in using a model that can precisely predict the TMEn value of animal by-products. The researchers have tried to develop a TMEn prediction model for the FM and POM samples (Dale, 1992; Dale et al., 1993). All the previously TMEn prediction models reported for poultry by-product meals were based on the regression analysis methods using their CP, ether extract (EE), and ash content. Alternatively, a soft-computing method of artificial neural network (ANN) seemed to be more appropriate for the TMEn prediction of a feedstuff. An ANN is a set of non©2008 Poultry Science Association Inc. Received December 17, 2007. Accepted May 19, 2008. 1 Corresponding author: [email protected]
linear equations that predicts output variable(s) from input variable(s) in a flexible way using layers of linear regressions and S-shaped functions. There is no need to provide an a priori model when using an ANN. It is potentially advantageous in modeling the biological processes often characterized as highly nonlinear (Dayhoff and DeLeo, 2001). The ANN functions are applied to many fields to model and predict the behaviors of unknown systems, very complex systems, or both based on given input-output values (Dayhoff and DeLeo, 2001). One submodel of ANN is a group method of data handling-type neural network (GMDH-type NN). It is a self-organizing approach by which gradually more complex models are generated from their performance evaluation and a set of multi-input, single output data pairs (Lemke and Mueller, 2003). The GMDH was first developed by Ivakhnenko (1971) as a multivariate analysis method for modeling and identification of complex systems. The main idea of GMDH is to build an analytical function in a feed-forward network based on a quadratic node transfer function whose coefficients obtained by using a regression technique (Farlow, 1984). Recently, the use of such self-organizing networks has led to a successful application of the GMDH-type algorithm in a broad range of areas in engineering, science, and economics (Amanifard et al., 2008). In the poultry field, Ahmadi et al. (2007) demonstrated that the GM-
1909
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Ahmadi et al.
Table 1. The observed TMEn values and composition of feather and poultry offal samples used to train and validate group method of data handling-type neural network model for the TMEn prediction1 Inputs Item Training set Feather meal
Poultry offal meal
Mean ± SD Validation set Feather meal Poultry offal meal
Mean ± SD 1
Data lines
Crude protein (%)
Crude fat (%)
Crude ash (%)
Observed TMEn (kcal/kg)
Predicted TMEn (kcal/kg)
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
90.00 88.00 84.84 87.58 90.11 85.16 87.79 96.32 96.63 87.05 91.89 87.16 52.50 73.48 52.61 71.30 58.15 54.13 53.04 51.52 52.07 52.61 52.83 51.63 51.20 54.89 51.96 59.67 64.67 60.65 69.71 ± 17.32
6.63 12.42 12.63 8.11 7.37 9.68 8.84 2.95 1.89 9.16 5.79 10.32 33.15 19.89 34.89 25.98 37.83 38.26 39.57 39.67 37.93 35.54 40.98 36.74 38.48 38.70 39.67 27.17 31.09 29.57 24.03 ± 14.20
2.53 2.32 2.21 2.63 2.32 3.26 2.32 2.32 3.05 2.63 2.11 3.26 15.76 5.65 12.39 3.04 6.41 7.39 6.96 8.80 7.72 7.72 7.17 6.09 7.28 6.09 6.41 11.09 5.22 6.85 5.63 ± 3.37
3,491 4,206 3,933 3,699 3,377 3,621 3,741 3,255 3,269 3,794 3,367 3,731 4,240 3,941 4,707 4,632 5,275 5,436 5,151 5,596 5,328 5,309 5,593 4,886 5,139 5,187 5,201 4,570 5,105 4,864 4,455 ± 791
3,511 3,926 3,881 3,608 3,555 3,688 3,648 3,273 3,206 3,662 3,461 3,739 4,560 4,230 4,874 4,752 5,412 5,226 5,304 5,264 5,184 5,159 5,438 5,187 5,222 5,305 5,277 4,496 4,999 4,748 4,460 ± 776
31 32 33 34 35 36 37
89.05 85.79 87.05 62.07 51.74 51.96 58.04 69.39 ± 17.15
6.74 8.32 10.74 30.76 39.13 42.83 32.07 24.37 ± 15.35
2.74 2.32 2.32 6.52 10.43 6.74 10.65 5.96 ± 3.65
3,523 3,768 3,764 4,900 5,034 5,703 4,876 4,510 ± 823
3,522 3,690 3,766 4,834 5,207 5,598 4,783 4,486 ± 821
All data were adjusted to 100% dry matter basis.
DH-type NN model could provide an effective means of describing the data patterns in broiler performance prediction based on their dietary nutrients. The purpose of this study was to examine the validity of GMDH-type NN with a genetic algorithm method to predict the TMEn of feather meal and poultry offal meal based on their chemical analysis.
MATERIALS AND METHODS Data Source Thirty-seven raw data lines consisting of 15 FM and 22 POM samples were used to train a GMDH-type NN. The FM and POM data were those reported by Dale (1992) and Dale et al. (1993), respectively. Each data line consisted of CP, EE, and ash percentages and a measured TMEn for an individual sample (Table 1). Similar procedures were used to determine the chemi-
cal composition and the TMEn of meal samples (Dale, 1992; Dale et al., 1993).
Model Development A detailed description of a GMDH-type NN terminology, development, application, and examples of using this approach were reported by several researchers (Farlow, 1984; Mueller and Lemke, 2000; Lemke and Mueller, 2003; Nariman-Zadeh et al., 2005). The parameters of interest in this multi-input, single-output system that influenced the TMEn were CP, EE, and ash content of the samples. The raw data were divided into 2 parts of training and validation sets. Thirty input-output data lines (12 from FM and 18 from POM samples) were randomly selected and used to train the GMDH-type NN model as a training set. The validation set consisted of the 7 remaining data lines (3 from FM and 4 from POM samples), which were used to validate
NEURAL NETWORK MODEL FOR METABOLIZABLE ENERGY PREDICTION
1911
Table 2. Statistics and information on group method of data handling-type neural network model for TMEn prediction (training vs. validation values) Statistics1 R2 Adjusted R2 MSE Residual mean RSD MAPE Bias Number of hidden layers Number of hidden neurons
Neural network training
Neural network validation
0.96 0.95 26,821 −5.10 166.49 3.04 −5.10
0.99 0.99 8,629 24.09 96.91 1.53 24.09
2 4
1 MSE = mean square error; RSD = residual standard deviation; MAPE = mean absolute percentage error; hidden neurons = number of hidden neurons produced by the genetic algorithm to fit the group method of data handling-type neural network model.
the prediction of the evolved neural network during the training processes. The data set was imported into a GEvoM for GMDH-type NN training (GEvoM, 2008). Two hidden layers were considered for prediction of the TMEn model. A population of 15 individual values with a crossover probability of 0.7, mutation probability of 0.07, and 300 generations was used to genetically design the neural network (Yao, 1999). It appeared that no further improvement could be achieved for this population size. A quantitative verifying fit for the predictive model was made using error measurement indices commonly used to evaluate forecasting models. The goodness of
fit or accuracy of the model was determined by R2 value, adjusted R2, mean square error, residual standard deviation, mean absolute percentage error, and bias (Oberstone, 1990).
RESULTS AND DISCUSSION The optimal structure of the evolved 2-hidden-layer GMDH-type NN was produced from the genetic algorithm (GA) for modeling the TMEn was found with 4 hidden neurons. These neurons were the output of the GA to fit the GMDH-type NN model. The constructed model was characterized by a superb response for all
Figure 1. The comparison of observed and model predicted TMEn values obtained from training (1 to 12 and 13 to 30 are feather and offal samples, respectively) and validation (31 to 33 and 34 to 37 are feather and offal samples, respectively) sets.
1912
Ahmadi et al.
input variables from the training data set. It appeared that the percentage of CP, EE, and ash had a strong effect on the TMEn prediction. The corresponding polynomial equations used to develop the TMEn model were as follows: Y1 = −20,942.48 + 483.67 CP + 525.44 EE − 2.43 CP2
− 2.33 EE2 − 4.60 CP.EE
[1]
Y2 = 2,485.45 + 74.66 CP + 563.71 Ash − 0.67 CP2
− 15.27 Ash2 − 6.60 CP.Ash
[2]
Y3 = 0.00041 + 0.01223 CP + 1.005 Y1 + 0.00316 CP2
+ 0.0000002 Y12 − 0.000145 CP.Y1
[3]
Y4 = 0.00061 + 0.00539 EE + 1.292 Y2 + 0.205 EE2
− 0.00009 Y22 + 0.00325 EE.Y2
[4]
TMEn = 0.00024 + 0.66044 Y3 + 0.33404 Y4
+ 0.00266 Y32 + 0.00265 Y42 − 0.00531 Y3.Y4
[5]
The TMEn values predicted by the GMDH-type NN model is shown in Table 1. The observed and predicted values of TMEn from the training and validation sets are shown in Figure 1. The comparison of observed and predicted TMEn describes the behavior of the GMDHtype NN model from investigating inputs. The results revealed a very good agreement between the observed and predicted TMEn values (for training or validation). The GMDH-type NN model could accurately predict the TMEn of the validation data set that was not used during the training processes. The statistical tests (in terms of R2, adjusted R2, mean square error, residual standard deviation, and mean absolute percentage error) indicated that there was a relatively better prediction of TMEn for the validation as compared with the training values (Table 2). Dale (1992) proposed a linear equation to predict the TMEn of FM samples with one variable of EE (R2 = 0.81). Dale et al. (1993) developed several prediction equations for estimating the TMEn of POM samples with 1 (EE), 2 (EE and ash), or 3 input (EE, ash, and CP) variables, or a combination of these. They suggested that the most accurate prediction equation was obtained with 3 input variables (R2 of 0.81). We proposed neural network model with 3 variables and a combination of 30 data lines of FM and POM samples to compare the results of this study with those of Dale (1992) and Dale et al. (1993). The goodness of fit in terms of R2 corresponding to GMDH-type NN model showed a higher accuracy of prediction than
equations (0.96 vs. 0.81) reported by Dale (1992) and Dale et al. (1993). The results of this study revealed that the novel modeling of GMDH-type NN with an evolutionary method of GA can be used to predict the TMEn of FM and POM samples based on their CP, EE, and ash content. The advantage of using the GMDH-type NN to predict an output from the input variables is that there is no need to preselect a model or base the model entirely on the fit of the data. It is concluded that the GMDH-type NN may be used to accurately estimate the nutritive value of poultry meals from their corresponding chemical composition.
REFERENCES Ahmadi, H., M. Mottaghitalab, and N. Nariman-Zadeh. 2007. Group method of data handling-type neural network prediction of broiler performance based on dietary metabolizable energy, methionine, and lysine. J. Appl. Poult. Res. 16:494–501. Amanifard, N., N. Nariman-Zadeh, M. Borji, A. Khalkhali, and A. Habibdoust. 2008. Modelling and pareto optimization of heat transfer and flow coefficients in microchannels using GMDH type neural networks and genetic algorithms. Energy Convers. Manage. 2:311–325. Dale, N. 1992. True metabolizable energy of feather meal. J. Appl. Poult. Res. 1:331–334. Dale, N., and A. Batal. 2002. Feedstuffs Ingredient Analysis Table. Miller Publishing Co., Minnetonka, MN. Dale, N., B. Fancher, M. Zumbado, and A. Viuacres. 1993. Metabolizable energy content of poultry offal meal. J. Appl. Poult. Res. 2:40–42. Dayhoff, J. E., and J. M. DeLeo. 2001. Artificial neural networks: Opening the black box. Cancer 91(Suppl. 8):1615– 1635. Farlow, S. J. 1984. Self-organizing methods in modeling. GMDH type algorithms. Marcel Dekker Inc., New York, NY. GEvoM. 2008. GMDH-type neural network designed by an evolutionary method of modelling. http://research.guilan. ac.ir/gevom/ Accessed Jan. 20, 2008. Ivakhnenko, A. G. 1971. Polynomial theory of complex systems. IEEE Trans. Syst. Man Cybern. 4:364–378. Lemke, F., and J. A. Mueller. 2003. Medical data analysis using self-organizing data mining technologies. Syst. Anal. Model. Simul. 10:1399–1408. Mueller, J. A., and F. Lemke. 2000. Self-organising data mining: An intelligent approach to extract knowledge from data. Hamburg Pub. Libri., Germany. Nariman-Zadeh, N., A. Darvizeh, A. Jamali, and A. Moieni. 2005. Evolutionary design of generalized polynomial neural networks for modelling and prediction of explosive forming process. J. Mater. Process. Technol. 164– 165:1561–1571. Oberstone, J. 1990. Management Science-Concepts, Insights, and Applications. West Publ. Co., New York, NY. Yao, X. 1999. Evolving artificial neural networks. Proc. IEEE 9:1423–1447.