- Email: [email protected]
Group Method of Data Handling-Type Neural Network Prediction of Broiler Performance Based on Dietary Metabolizable Energy, Methionine, and Lysine
©2007 Poultry Science Association, Inc.
Group Method of Data Handling-Type Neural Network Prediction of Broiler Performance Based on Dietary Metabolizable Energy, Methionine, and Lysine
*Department of Animal Science, Faculty of Agriculture, University of Guilan, PO Box 41635-1314, Rasht, Iran; and †Department of Mechanical Engineering, Faculty of Engineering, University of Guilan, PO Box 41635-3756, Rasht, Iran
Primary Audience: Poultry Scientists, Poultry Nutrition Experts SUMMARY Artificial neural networks have been shown to be powerful tools for system modeling. One submodel of artificial neural networks is the group method of data handling-type neural networks (GMDH-type NN). The use of such self-organizing networks leads to successful application in a broad range of areas. However, in some fields, such as poultry science, the use of GMDH-type NN is still scarce. Broiler nutrition is recognized as a biological system consisting of a complex set of interconnected variables. Knowledge of an adequate description of variables, such as broiler ME and amino acid requirements, can help in establishing specific feeding programs, defining optimal performance, and reducing production costs. In this way, a genetic algorithm is deployed in a new approach to design the whole architecture of the GMDH-type NN (i.e., the number of neurons in each hidden layer and the configuration of their connectivities). This study addressed the question of whether GMDH-type NN could be used to estimate broiler performance (outputs) based on specified variables—inputs (level of dietary ME, Met, and Lys)—on a broiler farm. Results suggest that GMDH-type NN provide an effective means of efficiently recognizing the patterns in data and accurately predicting a performance index based on investigating inputs, and also can be used to optimize broiler performance based on nutritional factors. Key words: broiler performance index, nutritional factor, modeling, neural network 2007 J. Appl. Poult. Res. 16:494–501 doi:10.3382/japr.2006-00074
DESCRIPTION OF PROBLEM In broiler chicken production, cereal grains and oilseeds, such as corn and soybean meal, make up the majority of the dietary ingredients and account for a large portion of ME, protein, and amino acids (AA) [1]. When considering the effects of nutrition on broiler performance, 1
Corresponding author: [email protected]
several nutrients may influence the breast meat yield, feed:gain ratio, and number of days required to produce the market BW; among them, ME and AA, such as Lys and Met, are more important [2, 3]. In terms of AA, whatever system is used to describe the essential AA requirements for broiler chickens, predicting the performance to be used in deciding the most advan-
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
H. Ahmadi,* M. Mottaghitalab,*1 and N. Nariman-Zadeh†
AHMADI ET AL.: NEURAL NETWORKS AND BROILER PERFORMANCE
495
Table 1. Samples (10 sets) of data used to develop the group method of data handling-type neural network model for the performance index (PI) Input Met
Lys
Output (PI)
0 to 21 d
2,995 2,700 2,864 3,000 2,895 2,775 3,200 2,995 2,995 3,000
0.52 0.6 0.59 0.5 0.58 0.77 0.63 0.44 0.52 0.52
1.18 1.28 1.2 1.23 1.22 1.44 1.16 1.17 1.18 1.17
19.8 14.1 12.3 15.71 15.15 11.53 11.06 17.87 19.8 18.52
21 to 42 d
3,100 2,890 2,824 3,090 2,836 3,000 3,100 3,200 2,800 2,767
0.38 0.51 0.54 0.49 0.46 0.36 0.53 0.38 0.50 0.53
1.07 1.11 1.15 1.02 1.13 0.98 1.09 1 1.12 1
20.36 18.3 17.46 20.4 16.3 18.86 20.2 18.12 15.81 15.7
42 d to final day
3,100 2,887 3,200 2,921 2,880 3,100 3,150 2,905 2,995 2,887
0.38 0.57 0.31 0.377 0.4 0.38 0.29 0.51 0.4 0.57
1.07 1.05 0.85 0.78 0.83 1.07 0.85 0.83 0.84 1.05
20.36 19.45 17.25 16.1 15 20.6 18 15.44 19.54 15.5
tageous dietary AA patterns in practical and useful terms is still difficult, even when the digestibility or availability of AA is specified [1, 4]. This difficulty is partly due to the nonlinearity of growth responses related to changes in dietary AA concentrations [2, 5]. A more useful method is to model the system, which in turn requires an explicit mathematical inputoutput relationship. Such explicit mathematical modeling is, however, very difficult and is not readily tractable in poorly understood systems. Alternatively, soft-computing methods, which concern computation in an imprecise environment, have gained significant attention. One of the soft-computing methods is artificial neural networks (ANN), which have shown great ability in solving complex nonlinear system identification and control problems. Artificial neural
networks are applied in many fields to model and predict the behaviors of unknown systems, very complex systems, or both based on given input-output data. Several studies have been conducted to examine the potential for use of ANN in poultry science, such as in the prediction of ascites in broilers [6, 7], the comparison of logistic and linear regression models for predicting pulmonary hypertension syndrome [8], the estimation of production variables of broilers breeders in the production phase [9], and the comparison of Gompertz and neural network models of broiler growth [10]. One submodel of ANN is group method of data handling-type neural networks (GMDHtype NN), which is a self-organizing approach by which gradually more complicated models are generated based on the evaluation of their
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
ME, kcal/kg
Growth
JAPR: Research Report (15.5 ± 5.5) (18.9 ± 2.1) (18.2 ± 2) (1.245 ± 0.128) (1.096 ± 0.076) (0.903 ± 0.085) (0.614 ± 0.097) (0.519 ± 0.067) (0.384 ± 0.088)
MATERIALS AND METHODS Database
0 to 21 d 21 to 42 d 42 d to final day
2,700–3,200 2,760–3,200 2,852–3,200
(2,911 ± 81) (2,950 ± 91) (3,205 ± 113)
0.4–0.7 0.35–0.68 0.3–0.55
Met ME, kcal/kg Growth
Input, maximum-minimum (mean ± SD)
0.91–1.44 0.97–1.25 0.74–1.1
Lys
10.8–19.9 15.47–22.5 15.1–22
Output [PI, maximumminimum (mean ± SD)]
performance on a set of multi-input, singleoutput data pairs. The GMDH was firstly developed by Ivakhnenko [11] as a multivariate analysis method for modeling and identification of complex systems. Group method of data handling-type neural networks were used to circumvent the difficulty of having prior knowledge of the mathematical model of the process being considered. In other words, GMDH can be used to model complex systems without having specific knowledge of the systems. The main idea of GMDH is to build an analytical function in a feed-forward network based on a quadratic node transfer function [12] whose coefficients are obtained by using a regression technique. In recent years, however, the use of such self-organizing networks has led to successful application of the GMDH-type algorithm in a broad range of areas in engineering, science, and economics. This study was conducted to address whether GMDH-type NN could be used to estimate broiler performance (outputs) based on specified variables—inputs (level of dietary ME, Met, and Lys)—on a broiler farm.
Data were collected from 10 commercial broiler farms from a single genetic line (Lohmann) [13] during the period between March 2003 and April 2005. Over this period, 10 flocks produced 52 data sets (input-output data). The collected data consisted of ME (kcal/kg), Met (% of DM), and Lys (% of DM) as the input variables and data related to the FCR, length of production (days), mortality, and live weight, which are required to calculate a performance index (PI) as the system output. The PI is calculated by using the formula PI = L × LW × 10/FCR × t, where L is livability (%), LW is live weight (kg), FCR is the feed conversion ratio, and t is age in days. Data were collected from 3 separate growth periods, at 0 to 21 d, 21 to 42 d, and 42 d to the final day old, referred to as growth periods 1, 2 and 3, respectively. Diets were formulated
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
Table 2. Ranges of data patterns (input-output) from the database used to develop the group method of data handling-type neural network model for the performance index (PI)
496
AHMADI ET AL.: NEURAL NETWORKS AND BROILER PERFORMANCE
497
based on corn and soybean meal (as the energy and protein-AA source, respectively) and supplemented with fishmeal to establish an appropriate balance between the ration and bird re-
quirements. Forty-two data lines (training set) and 10 data lines (validation set) were randomly extracted from the database to train and calibrate the GMDH-type NN. Tables 1 and 2 show
Figure 2. Neural network model-predicted performance index (PI) in comparison with actual data in growth period 2 (21 to 42 d) for the training (42 input-output data) and validation sets (10 unforeseen input-output data).
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
Figure 1. Neural network model-predicted performance index (PI) in comparison with actual data in growth period 1 (0 to 21 d) for the training (42 input-output data) and validation sets (10 unforeseen input-output data).
JAPR: Research Report
498 samples as well as ranges of data patterns (input-output) collected from 3 growth periods to develop the GMDH-type NN model for a PI. Model Development
n
MAD =
⎢
⎢
∑ ⎢⎢yi − yˆi ⎢⎢ i=1
n
;
2) the mean absolute percentage error (MAPE), computed as − yˆi) ⎢ ⎢ yi ⎢ × 100; and n
⎢ (yi
MAPE =
∑ ⎢⎢
3) the MS error (MSE), computed as n
MSE =
⎢
⎢2
∑ ⎢⎢yˆi − yi ⎢⎢ i=1
n
,
where yi equals the actual value, yˆi equals the predicted value, and n equals the number of observations (42 for training and 10 for validation).
RESULTS AND DISCUSSION The optimal structures of the evolved 2hidden-layer GMDH-type NN that were suggested by GA for PI modeling were found with 2, 4, and 4 hidden neurons for growth periods 1, 2, and 3, respectively. In the first period, the structure obtained appeared with the GA, which was less complex than in the second and third periods, in which the GA suggested 2 hidden neurons to fit the network. All models constructed from this data set were characterized by a superb response for all input variables from the learning set. The partial descriptions of the GMDH-type NN were found with 2 hidden layers and 2 hidden neurons for growth period 1 (which are shown as polynomial equations [1] to [3]), whereas it appeared with 2 hidden layers and 4 hidden neurons for growth periods 2 (polynomial equations [4] to [8]) and 3 (polynomial equations [9] to [13]). In fact, these equations revealed the quantitative relation between input (ME, Met, and Lys) and output (PI) variables under investigation. The corresponding polynomial equation representations of such a model for growth period 1 were obtained as follows
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
A detailed description of GMDH-type NN terminology, development, and application is beyond the scope of this paper. Suggested references include Nariman-Zadeh et al. [14, 15]. The GMDH-type NN models were developed with GMDH-type NN designed by an evolutionary method of modeling (GEvoM) [16], which is a program based on GMDH-type NN that generates polynomial neural networks to model either simulation or experimental data of any kind. Such a neural network identification process, in turn, needs some optimization methods to find the best network architecture. In this way, genetic algorithms (GA) are deployed in a new approach to design the whole architecture of the GMDH-type NN, that is, the number of neurons in each hidden layer and their configuration of connectivities, in combination with singular value decomposition to find the optimal set of appropriate coefficients of quadratic expressions to model a broiler PI. The parameters of interest in this multi-input, single-output system that affect the broiler PI are dietary ME (kcal/kg), Met (%), and Lys (%). Forty-two input-output actual data lines obtained from 3 rearing periods were used to train the GMDHtype NN models. The validation sets, which consisted of 10 unpredictable input-output data lines during the training process, were used merely for validation to show the prediction ability of such evolved neural networks during the training process. Databases were imported into GEvoM for GMDH-type NN training. Two hidden layers were considered for each model. To genetically design such neural networks, a population of 10 individuals with a crossover probability of 0.7, mutation probability of 0.07, and 600 generations was used; it appeared that no further improvement could be achieved for such a population size. All procedures were applied for 3 growth periods as 3 separate models, and all results were recorded. A quantitative examination of the fit of the predictive models was made by using error measurement indices, which are commonly used to evaluate forecasting models [17]. The accuracy of the models
was determined by using the 1) mean absolute deviation (MAD), computed as
AHMADI ET AL.: NEURAL NETWORKS AND BROILER PERFORMANCE
499
Y1 = −0.0000000549 − 0.0000801ME + 0.000000185Met + 0.0000017ME2 + 0.00000024Met2 + 0.00058MEMet, Y2 = −156.37 + 17.4Y1 + 52.54Lys − 0.59Y12 − 32.5Lys2 + 16.57Y1Lys, and PI = 322.7 − 38.84Y1 − 35.96Y2 + 0.28Y12 − 0.819Y22 + 1.89Y1Y2.
and [1]
And polynomial equations for growth period 3 were developed as
[3]
Y1 = 0.0000019 + 0.00295ME + 0.0000022Lys − 0.00000023ME2 + 0.0000024Lys2 + 0.0041MELys,
[9]
Y2 = 0.0000038 + 0.0058ME + 0.00000087Met − 0.000000066ME2 − 0.00000021Met2 + 0.0009MEMet,
[10]
Y1 = −0.000004 − 0.0059ME + 0.00000074Met + 0.00000339ME2 [4] + 0.000002Met2 + 0.0049MEMet,
Y3 = −92.2 + 11.4Y1 − 32.8Met − 0.32Y12 − 46.4Met2 + 4.1Y1Met, Y4 = −161.8 + 13.27Y1 + 4.52Y2 − 0.57Y12 − 0.329Y22 + 0.47Y1Y2,
[8]
[2]
Polynomial equations for growth period 2 were
Y2 = −0.00000011 − 0.00016ME + 0.0000004Lys + 0.00000179ME2 + 0.0000001Lys2 + 0.0013MELys,
PI = 10.79 − 16.78Y3 + 16.63Y4 + 7.91Y32 − 6.92Y42 − 14.81Y3Y4.
[5]
[6]
[7]
Y3 = −19.7 + 48.28Y1 − 517Lys − 2.57Y12 − 241Lys2 + 52Y1Lys,
[11]
Y4 = −406.9 − 624Met + 58.47Y2 + 117Met2 − 1.87Y22 [12] + 291.1MetY2, and PI = 190 − 5.11Y3 − 15.82Y4 [13] 2 2 − 0.24Y3 + 0.064Y4 + 0.8Y3Y4.
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
Figure 3. Neural network model-predicted performance index (PI) in comparison with actual data in growth period 3 (42 to final d) for the training (42 input-output data) and validation sets (10 unforeseen input-output data).
JAPR: Research Report
500
Table 3. Model statistics and information for the group method of data handling-type neural network model for predicting the broiler performance index Growth 0 to 21 d
21 to 42 d
42 d to final day
Neural training
Neural validation
Neural training
Neural validation
Neural training
Neural validation
R2 MSE RMSE MAD MAPE
0.9914 2.0485 1.4313 1.0014 6.8376
0.9948 1.3527 1.1631 1.008 6.1470
0.9943 1.9800 1.4071 1.0781 5.7539
0.9925 2.8773 1.6963 1.2742 6.7014
0.99559 1.4710 1.2128 0.9896 5.5665
0.9861 4.8941 2.2123 1.5531 9.1159
Number of hidden layers Hidden neurons
2 2
2 4
2 4
1 MSE = MS error (standard deviation); RMSE = root MS error; MAD = mean absolute deviation; MAPE = mean absolute percentage error; hidden neurons = number of hidden neurons suggested by the genetic algorithm to fit the group method of data handling-type neural network models.
As described earlier, the validation of results was tested by using 10 sets of data (validation sets) that were extracted from the database. The neural networks were trained with only 42 sets, and 10 sets were omitted. After the training process, the predicted values of neural networks were compared with those of actual values (the remaining 10 sets). The findings are demonstrated in Figures 1, 2, and 3. Results (training and validation values) showed very good agreement with actual and predicted PI with GMDH-type NN for 3 growth periods. Comparisons showed the behavior of such neural network models in predicting PI. These results suggest that the levels of 3 chosen variables demonstrated strong effects
on the broiler PI, which is similar to the results reported in other studies, for example, for AA balance, dietary energy, and protein level [18], effect of energy [19], and response to Met [20]. Table 3 summarizes the statistical results for the training and validation sets of GMDHtype NN models. These results indicate forecasting error measurements based on differences between the model and actual values. By considering these training data, the lowest MSE, MAD, and MAPE, and the highest R2 were calculated for growth period 3. For validation data, however, the lowest MSE, MAD, and MAPE, and the highest R2 were observed for growth period 1.
CONCLUSIONS AND APPLICATIONS 1. Knowledge of an adequate description of broiler ME and AA requirements can help in establishing specific feeding programs, defining optimal performance, and reducing production costs. 2. Calculated statistics indicate that GMDH-type NN provide an effective means of efficiently recognizing the patterns in data and predicting a PI based on investigating inputs. 3. The genetic approach could be used to provide optimal networks in terms of hidden layers, the number of neurons and their configuration of connectivities, or both so that a polynomial expression for dependent variables of the process can consequently be achieved. 4. The polynomials obtained could be used to optimize broiler performance based on nutritional factors by optimizing methods such as the GA.
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
Statistic1
AHMADI ET AL.: NEURAL NETWORKS AND BROILER PERFORMANCE
501
REFERENCES AND NOTES 1. NRC. 1994. Nutrient Requirements of Poultry. 9th rev. ed. Natl. Acad. Sci., Washington, DC.
11. Ivakhnenko, A. G. 1971. Polynomial theory of complex systems. IEEE Trans., Syst. Man Cybern. MC-1. 4:364–378.
2. Hruby, M., M. L. Hamre, and C. N. Coon. 1996. Non-linear and linear functions in body protein growth. J. Appl. Poult. Res. 5:109–115.
12. Farlow, S. J. 1984. Self-Organizing Methods in Modeling. GMDH Type Algorithms. Vol. 54. Marcel Dekker Inc., New York, NY.
3. Gous, R. M. 1998. Making progress in the nutrition of broilers. Poult. Sci. 77:111–117.
13. Lohmann, Niko Poultry Breeding Co., Distributor of Aviagen Group Ltd., Tehran, Iran.
5. Phillips, R. D. 1981. Linear and nonlinear models for measuring protein nutritional quality. J. Nutr. 111:1058–1066.
14. Nariman-Zadeh, N., A. Darvizeh, and R. Ahmad-Zadeh. 2003. Hybrid genetic design of GMDH-type neural networks using singular value decomposition for modelling and prediction of the explosive cutting process. J. Eng. Manuf. 217:779–790.
6. Roush, W. B., Y. K. Kirby, T. L. Cravener, and R. F. Wideman. 1996. Artificial neural network prediction of ascites in broilers. Poult. Sci. 75:1479–1487.
15. 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.
7. Roush, W. B., and R. F. Wideman. 2000. Evaluation of broiler growth velocity and acceleration in relation to pulmonary hypertension syndrome. Poult. Sci. 79:180–191.
16. GEvoM. For more information refer to http://research. guilan.ac.ir/gevom Accessed Jul. 10, 2007.
8. Kirby, Y. K., R. W. McNew, J. D. Kirby, and R. F. Wideman. 1997. Evaluation of logistic versus linear regression models for predicting pulmonary hypertension syndrome (ascites) using cold exposure or pulmonary artery clamp models in broilers. Poult. Sci. 76:392–399. 9. Salle, C. T., A. S. Guahyba, V. B. Wald, A. B. Silva, F. O. Salle, and V. P. Nascimento. 2003. Use of artificial neural networks to estimate production variables of broilers breeders in the production phase. Br. Poult. Sci. 44:211–217. 10. Roush, W. B., W. A. Dozier III, and S. L. Branton. 2006. Comparision of Gompertz and neural networks models of broiler growth. Poult. Sci. 85:794–797.
17. Oberstone, J. 1990. Management Science—Concepts, Insights, and Applications. West Publ. Co., New York, NY. 18. Summers, J. D., D. Spratt, and J. L. Atkinson. 1992. Broiler weight gain and carcass composition when fed diets varying in amino acid balance, dietary energy, and protein level. Poult. Sci. 71:263–273. 19. Lesson, S., L. Caston, and J. D. Summers. 1996. Broiler response to diet energy. Poult. Sci. 75:529–535. 20. Morris, T. R., R. M. Gous, and S. Abbeb. 1992. Effect of dietary protein concentration on the response of growing chicks to methionine. Br. Poult. Sci. 33:795–803.
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
4. Sibbald, I. R. 1987. Estimation of bioavailable amino acids in feedingstuffs for poultry and pigs: A review with emphasis on balance experiments. Can. J. Anim. Sci. 67:221–301.
Group Method of Data Handling-Type Neural Network Prediction of Broiler Performance Based on Dietary Metabolizable Energy, Methionine, and Lysine
*Department of Animal Science, Faculty of Agriculture, University of Guilan, PO Box 41635-1314, Rasht, Iran; and †Department of Mechanical Engineering, Faculty of Engineering, University of Guilan, PO Box 41635-3756, Rasht, Iran
Primary Audience: Poultry Scientists, Poultry Nutrition Experts SUMMARY Artificial neural networks have been shown to be powerful tools for system modeling. One submodel of artificial neural networks is the group method of data handling-type neural networks (GMDH-type NN). The use of such self-organizing networks leads to successful application in a broad range of areas. However, in some fields, such as poultry science, the use of GMDH-type NN is still scarce. Broiler nutrition is recognized as a biological system consisting of a complex set of interconnected variables. Knowledge of an adequate description of variables, such as broiler ME and amino acid requirements, can help in establishing specific feeding programs, defining optimal performance, and reducing production costs. In this way, a genetic algorithm is deployed in a new approach to design the whole architecture of the GMDH-type NN (i.e., the number of neurons in each hidden layer and the configuration of their connectivities). This study addressed the question of whether GMDH-type NN could be used to estimate broiler performance (outputs) based on specified variables—inputs (level of dietary ME, Met, and Lys)—on a broiler farm. Results suggest that GMDH-type NN provide an effective means of efficiently recognizing the patterns in data and accurately predicting a performance index based on investigating inputs, and also can be used to optimize broiler performance based on nutritional factors. Key words: broiler performance index, nutritional factor, modeling, neural network 2007 J. Appl. Poult. Res. 16:494–501 doi:10.3382/japr.2006-00074
DESCRIPTION OF PROBLEM In broiler chicken production, cereal grains and oilseeds, such as corn and soybean meal, make up the majority of the dietary ingredients and account for a large portion of ME, protein, and amino acids (AA) [1]. When considering the effects of nutrition on broiler performance, 1
Corresponding author: [email protected]
several nutrients may influence the breast meat yield, feed:gain ratio, and number of days required to produce the market BW; among them, ME and AA, such as Lys and Met, are more important [2, 3]. In terms of AA, whatever system is used to describe the essential AA requirements for broiler chickens, predicting the performance to be used in deciding the most advan-
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
H. Ahmadi,* M. Mottaghitalab,*1 and N. Nariman-Zadeh†
AHMADI ET AL.: NEURAL NETWORKS AND BROILER PERFORMANCE
495
Table 1. Samples (10 sets) of data used to develop the group method of data handling-type neural network model for the performance index (PI) Input Met
Lys
Output (PI)
0 to 21 d
2,995 2,700 2,864 3,000 2,895 2,775 3,200 2,995 2,995 3,000
0.52 0.6 0.59 0.5 0.58 0.77 0.63 0.44 0.52 0.52
1.18 1.28 1.2 1.23 1.22 1.44 1.16 1.17 1.18 1.17
19.8 14.1 12.3 15.71 15.15 11.53 11.06 17.87 19.8 18.52
21 to 42 d
3,100 2,890 2,824 3,090 2,836 3,000 3,100 3,200 2,800 2,767
0.38 0.51 0.54 0.49 0.46 0.36 0.53 0.38 0.50 0.53
1.07 1.11 1.15 1.02 1.13 0.98 1.09 1 1.12 1
20.36 18.3 17.46 20.4 16.3 18.86 20.2 18.12 15.81 15.7
42 d to final day
3,100 2,887 3,200 2,921 2,880 3,100 3,150 2,905 2,995 2,887
0.38 0.57 0.31 0.377 0.4 0.38 0.29 0.51 0.4 0.57
1.07 1.05 0.85 0.78 0.83 1.07 0.85 0.83 0.84 1.05
20.36 19.45 17.25 16.1 15 20.6 18 15.44 19.54 15.5
tageous dietary AA patterns in practical and useful terms is still difficult, even when the digestibility or availability of AA is specified [1, 4]. This difficulty is partly due to the nonlinearity of growth responses related to changes in dietary AA concentrations [2, 5]. A more useful method is to model the system, which in turn requires an explicit mathematical inputoutput relationship. Such explicit mathematical modeling is, however, very difficult and is not readily tractable in poorly understood systems. Alternatively, soft-computing methods, which concern computation in an imprecise environment, have gained significant attention. One of the soft-computing methods is artificial neural networks (ANN), which have shown great ability in solving complex nonlinear system identification and control problems. Artificial neural
networks are applied in many fields to model and predict the behaviors of unknown systems, very complex systems, or both based on given input-output data. Several studies have been conducted to examine the potential for use of ANN in poultry science, such as in the prediction of ascites in broilers [6, 7], the comparison of logistic and linear regression models for predicting pulmonary hypertension syndrome [8], the estimation of production variables of broilers breeders in the production phase [9], and the comparison of Gompertz and neural network models of broiler growth [10]. One submodel of ANN is group method of data handling-type neural networks (GMDHtype NN), which is a self-organizing approach by which gradually more complicated models are generated based on the evaluation of their
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
ME, kcal/kg
Growth
JAPR: Research Report (15.5 ± 5.5) (18.9 ± 2.1) (18.2 ± 2) (1.245 ± 0.128) (1.096 ± 0.076) (0.903 ± 0.085) (0.614 ± 0.097) (0.519 ± 0.067) (0.384 ± 0.088)
MATERIALS AND METHODS Database
0 to 21 d 21 to 42 d 42 d to final day
2,700–3,200 2,760–3,200 2,852–3,200
(2,911 ± 81) (2,950 ± 91) (3,205 ± 113)
0.4–0.7 0.35–0.68 0.3–0.55
Met ME, kcal/kg Growth
Input, maximum-minimum (mean ± SD)
0.91–1.44 0.97–1.25 0.74–1.1
Lys
10.8–19.9 15.47–22.5 15.1–22
Output [PI, maximumminimum (mean ± SD)]
performance on a set of multi-input, singleoutput data pairs. The GMDH was firstly developed by Ivakhnenko [11] as a multivariate analysis method for modeling and identification of complex systems. Group method of data handling-type neural networks were used to circumvent the difficulty of having prior knowledge of the mathematical model of the process being considered. In other words, GMDH can be used to model complex systems without having specific knowledge of the systems. The main idea of GMDH is to build an analytical function in a feed-forward network based on a quadratic node transfer function [12] whose coefficients are obtained by using a regression technique. In recent years, however, the use of such self-organizing networks has led to successful application of the GMDH-type algorithm in a broad range of areas in engineering, science, and economics. This study was conducted to address whether GMDH-type NN could be used to estimate broiler performance (outputs) based on specified variables—inputs (level of dietary ME, Met, and Lys)—on a broiler farm.
Data were collected from 10 commercial broiler farms from a single genetic line (Lohmann) [13] during the period between March 2003 and April 2005. Over this period, 10 flocks produced 52 data sets (input-output data). The collected data consisted of ME (kcal/kg), Met (% of DM), and Lys (% of DM) as the input variables and data related to the FCR, length of production (days), mortality, and live weight, which are required to calculate a performance index (PI) as the system output. The PI is calculated by using the formula PI = L × LW × 10/FCR × t, where L is livability (%), LW is live weight (kg), FCR is the feed conversion ratio, and t is age in days. Data were collected from 3 separate growth periods, at 0 to 21 d, 21 to 42 d, and 42 d to the final day old, referred to as growth periods 1, 2 and 3, respectively. Diets were formulated
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
Table 2. Ranges of data patterns (input-output) from the database used to develop the group method of data handling-type neural network model for the performance index (PI)
496
AHMADI ET AL.: NEURAL NETWORKS AND BROILER PERFORMANCE
497
based on corn and soybean meal (as the energy and protein-AA source, respectively) and supplemented with fishmeal to establish an appropriate balance between the ration and bird re-
quirements. Forty-two data lines (training set) and 10 data lines (validation set) were randomly extracted from the database to train and calibrate the GMDH-type NN. Tables 1 and 2 show
Figure 2. Neural network model-predicted performance index (PI) in comparison with actual data in growth period 2 (21 to 42 d) for the training (42 input-output data) and validation sets (10 unforeseen input-output data).
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
Figure 1. Neural network model-predicted performance index (PI) in comparison with actual data in growth period 1 (0 to 21 d) for the training (42 input-output data) and validation sets (10 unforeseen input-output data).
JAPR: Research Report
498 samples as well as ranges of data patterns (input-output) collected from 3 growth periods to develop the GMDH-type NN model for a PI. Model Development
n
MAD =
⎢
⎢
∑ ⎢⎢yi − yˆi ⎢⎢ i=1
n
;
2) the mean absolute percentage error (MAPE), computed as − yˆi) ⎢ ⎢ yi ⎢ × 100; and n
⎢ (yi
MAPE =
∑ ⎢⎢
3) the MS error (MSE), computed as n
MSE =
⎢
⎢2
∑ ⎢⎢yˆi − yi ⎢⎢ i=1
n
,
where yi equals the actual value, yˆi equals the predicted value, and n equals the number of observations (42 for training and 10 for validation).
RESULTS AND DISCUSSION The optimal structures of the evolved 2hidden-layer GMDH-type NN that were suggested by GA for PI modeling were found with 2, 4, and 4 hidden neurons for growth periods 1, 2, and 3, respectively. In the first period, the structure obtained appeared with the GA, which was less complex than in the second and third periods, in which the GA suggested 2 hidden neurons to fit the network. All models constructed from this data set were characterized by a superb response for all input variables from the learning set. The partial descriptions of the GMDH-type NN were found with 2 hidden layers and 2 hidden neurons for growth period 1 (which are shown as polynomial equations [1] to [3]), whereas it appeared with 2 hidden layers and 4 hidden neurons for growth periods 2 (polynomial equations [4] to [8]) and 3 (polynomial equations [9] to [13]). In fact, these equations revealed the quantitative relation between input (ME, Met, and Lys) and output (PI) variables under investigation. The corresponding polynomial equation representations of such a model for growth period 1 were obtained as follows
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
A detailed description of GMDH-type NN terminology, development, and application is beyond the scope of this paper. Suggested references include Nariman-Zadeh et al. [14, 15]. The GMDH-type NN models were developed with GMDH-type NN designed by an evolutionary method of modeling (GEvoM) [16], which is a program based on GMDH-type NN that generates polynomial neural networks to model either simulation or experimental data of any kind. Such a neural network identification process, in turn, needs some optimization methods to find the best network architecture. In this way, genetic algorithms (GA) are deployed in a new approach to design the whole architecture of the GMDH-type NN, that is, the number of neurons in each hidden layer and their configuration of connectivities, in combination with singular value decomposition to find the optimal set of appropriate coefficients of quadratic expressions to model a broiler PI. The parameters of interest in this multi-input, single-output system that affect the broiler PI are dietary ME (kcal/kg), Met (%), and Lys (%). Forty-two input-output actual data lines obtained from 3 rearing periods were used to train the GMDHtype NN models. The validation sets, which consisted of 10 unpredictable input-output data lines during the training process, were used merely for validation to show the prediction ability of such evolved neural networks during the training process. Databases were imported into GEvoM for GMDH-type NN training. Two hidden layers were considered for each model. To genetically design such neural networks, a population of 10 individuals with a crossover probability of 0.7, mutation probability of 0.07, and 600 generations was used; it appeared that no further improvement could be achieved for such a population size. All procedures were applied for 3 growth periods as 3 separate models, and all results were recorded. A quantitative examination of the fit of the predictive models was made by using error measurement indices, which are commonly used to evaluate forecasting models [17]. The accuracy of the models
was determined by using the 1) mean absolute deviation (MAD), computed as
AHMADI ET AL.: NEURAL NETWORKS AND BROILER PERFORMANCE
499
Y1 = −0.0000000549 − 0.0000801ME + 0.000000185Met + 0.0000017ME2 + 0.00000024Met2 + 0.00058MEMet, Y2 = −156.37 + 17.4Y1 + 52.54Lys − 0.59Y12 − 32.5Lys2 + 16.57Y1Lys, and PI = 322.7 − 38.84Y1 − 35.96Y2 + 0.28Y12 − 0.819Y22 + 1.89Y1Y2.
and [1]
And polynomial equations for growth period 3 were developed as
[3]
Y1 = 0.0000019 + 0.00295ME + 0.0000022Lys − 0.00000023ME2 + 0.0000024Lys2 + 0.0041MELys,
[9]
Y2 = 0.0000038 + 0.0058ME + 0.00000087Met − 0.000000066ME2 − 0.00000021Met2 + 0.0009MEMet,
[10]
Y1 = −0.000004 − 0.0059ME + 0.00000074Met + 0.00000339ME2 [4] + 0.000002Met2 + 0.0049MEMet,
Y3 = −92.2 + 11.4Y1 − 32.8Met − 0.32Y12 − 46.4Met2 + 4.1Y1Met, Y4 = −161.8 + 13.27Y1 + 4.52Y2 − 0.57Y12 − 0.329Y22 + 0.47Y1Y2,
[8]
[2]
Polynomial equations for growth period 2 were
Y2 = −0.00000011 − 0.00016ME + 0.0000004Lys + 0.00000179ME2 + 0.0000001Lys2 + 0.0013MELys,
PI = 10.79 − 16.78Y3 + 16.63Y4 + 7.91Y32 − 6.92Y42 − 14.81Y3Y4.
[5]
[6]
[7]
Y3 = −19.7 + 48.28Y1 − 517Lys − 2.57Y12 − 241Lys2 + 52Y1Lys,
[11]
Y4 = −406.9 − 624Met + 58.47Y2 + 117Met2 − 1.87Y22 [12] + 291.1MetY2, and PI = 190 − 5.11Y3 − 15.82Y4 [13] 2 2 − 0.24Y3 + 0.064Y4 + 0.8Y3Y4.
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
Figure 3. Neural network model-predicted performance index (PI) in comparison with actual data in growth period 3 (42 to final d) for the training (42 input-output data) and validation sets (10 unforeseen input-output data).
JAPR: Research Report
500
Table 3. Model statistics and information for the group method of data handling-type neural network model for predicting the broiler performance index Growth 0 to 21 d
21 to 42 d
42 d to final day
Neural training
Neural validation
Neural training
Neural validation
Neural training
Neural validation
R2 MSE RMSE MAD MAPE
0.9914 2.0485 1.4313 1.0014 6.8376
0.9948 1.3527 1.1631 1.008 6.1470
0.9943 1.9800 1.4071 1.0781 5.7539
0.9925 2.8773 1.6963 1.2742 6.7014
0.99559 1.4710 1.2128 0.9896 5.5665
0.9861 4.8941 2.2123 1.5531 9.1159
Number of hidden layers Hidden neurons
2 2
2 4
2 4
1 MSE = MS error (standard deviation); RMSE = root MS error; MAD = mean absolute deviation; MAPE = mean absolute percentage error; hidden neurons = number of hidden neurons suggested by the genetic algorithm to fit the group method of data handling-type neural network models.
As described earlier, the validation of results was tested by using 10 sets of data (validation sets) that were extracted from the database. The neural networks were trained with only 42 sets, and 10 sets were omitted. After the training process, the predicted values of neural networks were compared with those of actual values (the remaining 10 sets). The findings are demonstrated in Figures 1, 2, and 3. Results (training and validation values) showed very good agreement with actual and predicted PI with GMDH-type NN for 3 growth periods. Comparisons showed the behavior of such neural network models in predicting PI. These results suggest that the levels of 3 chosen variables demonstrated strong effects
on the broiler PI, which is similar to the results reported in other studies, for example, for AA balance, dietary energy, and protein level [18], effect of energy [19], and response to Met [20]. Table 3 summarizes the statistical results for the training and validation sets of GMDHtype NN models. These results indicate forecasting error measurements based on differences between the model and actual values. By considering these training data, the lowest MSE, MAD, and MAPE, and the highest R2 were calculated for growth period 3. For validation data, however, the lowest MSE, MAD, and MAPE, and the highest R2 were observed for growth period 1.
CONCLUSIONS AND APPLICATIONS 1. Knowledge of an adequate description of broiler ME and AA requirements can help in establishing specific feeding programs, defining optimal performance, and reducing production costs. 2. Calculated statistics indicate that GMDH-type NN provide an effective means of efficiently recognizing the patterns in data and predicting a PI based on investigating inputs. 3. The genetic approach could be used to provide optimal networks in terms of hidden layers, the number of neurons and their configuration of connectivities, or both so that a polynomial expression for dependent variables of the process can consequently be achieved. 4. The polynomials obtained could be used to optimize broiler performance based on nutritional factors by optimizing methods such as the GA.
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
Statistic1
AHMADI ET AL.: NEURAL NETWORKS AND BROILER PERFORMANCE
501
REFERENCES AND NOTES 1. NRC. 1994. Nutrient Requirements of Poultry. 9th rev. ed. Natl. Acad. Sci., Washington, DC.
11. Ivakhnenko, A. G. 1971. Polynomial theory of complex systems. IEEE Trans., Syst. Man Cybern. MC-1. 4:364–378.
2. Hruby, M., M. L. Hamre, and C. N. Coon. 1996. Non-linear and linear functions in body protein growth. J. Appl. Poult. Res. 5:109–115.
12. Farlow, S. J. 1984. Self-Organizing Methods in Modeling. GMDH Type Algorithms. Vol. 54. Marcel Dekker Inc., New York, NY.
3. Gous, R. M. 1998. Making progress in the nutrition of broilers. Poult. Sci. 77:111–117.
13. Lohmann, Niko Poultry Breeding Co., Distributor of Aviagen Group Ltd., Tehran, Iran.
5. Phillips, R. D. 1981. Linear and nonlinear models for measuring protein nutritional quality. J. Nutr. 111:1058–1066.
14. Nariman-Zadeh, N., A. Darvizeh, and R. Ahmad-Zadeh. 2003. Hybrid genetic design of GMDH-type neural networks using singular value decomposition for modelling and prediction of the explosive cutting process. J. Eng. Manuf. 217:779–790.
6. Roush, W. B., Y. K. Kirby, T. L. Cravener, and R. F. Wideman. 1996. Artificial neural network prediction of ascites in broilers. Poult. Sci. 75:1479–1487.
15. 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.
7. Roush, W. B., and R. F. Wideman. 2000. Evaluation of broiler growth velocity and acceleration in relation to pulmonary hypertension syndrome. Poult. Sci. 79:180–191.
16. GEvoM. For more information refer to http://research. guilan.ac.ir/gevom Accessed Jul. 10, 2007.
8. Kirby, Y. K., R. W. McNew, J. D. Kirby, and R. F. Wideman. 1997. Evaluation of logistic versus linear regression models for predicting pulmonary hypertension syndrome (ascites) using cold exposure or pulmonary artery clamp models in broilers. Poult. Sci. 76:392–399. 9. Salle, C. T., A. S. Guahyba, V. B. Wald, A. B. Silva, F. O. Salle, and V. P. Nascimento. 2003. Use of artificial neural networks to estimate production variables of broilers breeders in the production phase. Br. Poult. Sci. 44:211–217. 10. Roush, W. B., W. A. Dozier III, and S. L. Branton. 2006. Comparision of Gompertz and neural networks models of broiler growth. Poult. Sci. 85:794–797.
17. Oberstone, J. 1990. Management Science—Concepts, Insights, and Applications. West Publ. Co., New York, NY. 18. Summers, J. D., D. Spratt, and J. L. Atkinson. 1992. Broiler weight gain and carcass composition when fed diets varying in amino acid balance, dietary energy, and protein level. Poult. Sci. 71:263–273. 19. Lesson, S., L. Caston, and J. D. Summers. 1996. Broiler response to diet energy. Poult. Sci. 75:529–535. 20. Morris, T. R., R. M. Gous, and S. Abbeb. 1992. Effect of dietary protein concentration on the response of growing chicks to methionine. Br. Poult. Sci. 33:795–803.
Downloaded from http://japr.oxfordjournals.org/ at Bibliotheque Commune De ChimieUNIL - EPFL on March 21, 2015
4. Sibbald, I. R. 1987. Estimation of bioavailable amino acids in feedingstuffs for poultry and pigs: A review with emphasis on balance experiments. Can. J. Anim. Sci. 67:221–301.