An optimization method for nutrition requirement of hai lan brown egg cock based on response surface method and artificial neural network

Abstract

The present application relates to livestock nutrition demand optimization technical field, more particularly to a kind of nutrition demand optimization method of Hailan brown egg cock feed based on response surface method and artificial neural network.Under the condition of standardization feeding management, carry out feeding test, determine the body weight gain and feed conversion ratio of test chicken in each growth stage in repeated unit, construct research data set;Response surface model and artificial neural network model are constructed respectively, both with feed metabolizable energy and crude protein as input variable, with the maximization of body weight gain and the minimization of feed conversion ratio as double optimization target, the first preliminary optimal combination is obtained by response surface method, the second preliminary optimal combination is obtained by multi-objective genetic algorithm optimization with the trained neural network as fitness function;Construct evaluation index to compare the fitting effect of two models under different growth stages and different optimization targets, match corresponding optimal adaptive model, output the optimal nutrition parameters of feed metabolizable energy and crude protein in each stage of whole feeding cycle.

Description

Technical Field

[0001] This invention relates to the field of livestock and poultry nutritional requirement optimization technology, and more specifically to a method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks. Background Technology

[0002] Hy-Line Brown roosters have become a popular choice for broiler chicken farming in some parts of my country due to their strong disease resistance, low feeding costs, and unique flavor. However, the lack of corresponding nutritional standards means that current practices often rely on standard broiler feed formulations, leading to significant fluctuations in production performance and unsatisfactory feed conversion rates. Developing a precise nutritional model for Hy-Line Brown roosters is a crucial step in establishing their nutritional standards.

[0003] Animal nutrition requirement models based on the Response Surface Method (RSM) are widely used in biological system optimization. Leveraging its unique experimental design and modeling methods, it can analyze complex relationships among multiple nutritional factors and study the main effects and interactions of multiple factors simultaneously with fewer experiments. However, RSM models have limitations in capturing the inherent nonlinearity and dynamic interactions in biological systems, necessitating the introduction of more adaptive modeling methods. In recent years, Artificial Neural Network (ANN) models, due to their advantages in handling complex nonlinear relationships, have been increasingly applied to poultry growth and nutrition optimization, used to analyze data on poultry growth rates, feed consumption, and environmental factors. By simulating the connection weights and nonlinear activation functions between neurons, ANNs can accurately fit the complex mapping relationships between input variables (such as metabolizable energy and crude protein) and output variables (such as body weight gain and feed conversion ratio), achieving high-precision predictions for multiple inputs and outputs. However, the core bottleneck in the accurate application of machine learning models in the livestock and poultry field lies in the rigid dependence on large-scale, high-quality training data. In actual production, breed specificity, fragmented scenarios, and high label acquisition costs make it difficult to train and generalize reliable models.

[0004] Therefore, how to provide a method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks, aiming to solve the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks includes the following steps: S1. Conduct feeding trials under standardized feeding management conditions, and measure the body weight gain and feed conversion ratio of experimental chickens at each growth stage in replicates to construct a dataset; S2. Using dietary metabolizable energy and crude protein as input variables, and body weight gain and feed conversion ratio as response variables, a response surface model is constructed. With maximizing body weight gain and minimizing feed conversion ratio as dual optimization objectives, the response surface model is used to solve for the dietary metabolizable energy and crude protein corresponding to each growth stage of the experimental chickens, and the first preliminary optimal combination is obtained. S3. Using dietary metabolizable energy and crude protein as input variables, and body weight gain and feed conversion ratio as output variables, an artificial neural network model is constructed. The artificial neural network model is trained based on the dataset. The trained artificial neural network model is used as the fitness function. Multi-objective optimization is performed by combining a non-dominated sorting genetic algorithm with an elite strategy. The dietary metabolizable energy and crude protein corresponding to each growth stage of the experimental chickens are solved with the dual optimization objectives of maximizing body weight gain and minimizing feed conversion ratio, and the second preliminary optimal combination is obtained. S4. Construct evaluation indicators to quantitatively compare the fitting effects of response surface models and artificial neural network models based on different growth stages and different optimization objectives, and obtain the optimal fitting model corresponding to each growth stage and different optimization objective. S5. Based on the optimal adaptation model corresponding to each optimization objective at each growth stage, output the final optimal nutritional parameters of dietary metabolizable energy and crude protein for each stage of the entire feeding cycle of Hy-Line Brown roosters.

[0007] Furthermore, S1 specifically refers to: One-day-old Hy-Line Brown male chickens were selected and a 4×3 two-factor completely randomized experimental design was adopted. They were randomly divided into 12 treatment groups, with 6 replicates in each group and 30 chickens in each replicate. The entire feeding cycle was divided into three growth stages: 1-21 days old, 22-56 days old, and 57-70 days old. Four dietary metabolizable energy levels and three dietary crude protein levels were set for each growth stage. The corn-soybean meal experimental diet was formulated according to the nutritional requirements of broilers. The feeding experiment was carried out under standardized feeding management conditions. The body weight gain and feed conversion ratio of the experimental chickens at each growth stage were measured in replicates to obtain the original dataset for modeling.

[0008] Furthermore, S2 specifically refers to: The response surface model is constructed in the general form of a second-order polynomial regression model, as shown in the equation: , In the formula, Y is the response variable, including body weight gain and feed conversion ratio, ME is the dietary energy level in MJ / kg, and CP is the dietary protein level. For constant terms, , The linear effect coefficient, , This is the squared effect coefficient, reflecting whether the effect of a factor decreases or increases. The interaction coefficient quantifies the synergistic or antagonistic effects between proteins and energy. This is random error; The model was simplified by removing insignificant variables from the response surface model through analysis of variance. Finally, the maximum weight gain and minimum material-to-weight ratio were obtained through multiple response optimization.

[0009] Furthermore, S3 specifically refers to: The ANN structure consists of an input layer, a hidden layer, and an output layer. The input layer includes two input neurons, which represent the dietary energy level (ME) and dietary protein level (CP), respectively. The hidden layer includes ten hidden neurons. The output layer includes output neurons corresponding to the output variables body weight gain (BWG) or feed conversion ratio (F / G). The ANN model was constructed using repeated levels of data from 12 treatment groups as samples. The dataset was randomly divided into three subsets according to the ratio of 70% training set, 15% validation set, and 15% test set. A feedforward neural network was constructed using the feedforwardnet function. The hidden layer activation function was the hyperbolic tangent sigmoid function (tansig), and the output layer activation function was the linear function (purelin). The training algorithm used was the Levenberg-Marquardt backpropagation algorithm (trainlm). The training parameters were set as follows: maximum training epochs (1000), performance goal (0), and minimum performance gradient (min_grad) (1e). -7 The maximum number of verification failures (max_fail) is set to 6, the initial value of the Marquardt adjustment parameter (mu) is set to 0.001, the increment / decrement coefficients (mu_dec and mu_inc) are set to 0.1 and 10 respectively, and the maximum value (mu_max) is set to 1e. 10 .

[0010] Furthermore, it also includes: Before modeling, all input variables ME, CP, BWG, and F / G were normalized. MATLAB's mapminmax function was used to linearly map each variable to the interval [-1, 1]. The normalization formula is as follows: , in and These are the minimum and maximum values ​​of each variable in the training set. During the normalization process, the normalization parameters of the training set, i.e. the minimum and maximum values, are recorded. The same parameters are applied to the validation and test sets for normalization. After the model prediction is completed, the output results are restored to the original dimensions through inverse normalization. Outlier identification is performed using box plots. The outlier discrimination formula is as follows: X < Q1 - 1.5 × IQR or X > Q3 + 1.5 × IQR, In the formula, X is the value of the data point to be detected; Q1 is the first quartile, i.e., the 25th quartile, representing the value at the lower quartile of the dataset; Q3 is the third quartile, i.e., the 75th quartile, representing the value at the upper quartile of the dataset; IQR is the interquartile range, IQR = Q3 - Q1, representing the dispersion of the middle 50% of the data in the dataset; 1.5 is an empirical coefficient, which is used to remove outliers that meet any of the above conditions and exclude them from the modeling dataset.

[0011] Furthermore, ANN model training also includes: Early stopping is used to prevent overfitting of the system. The validation set error is monitored in real time during training. When the validation set error does not decrease in max_fail iterations, training is automatically terminated to prevent the model from overlearning training set noise.

[0012] Furthermore, the parameter configuration for the non-dominated sorting genetic algorithm is as follows: Population Size is set to 100; Maximum Iterations is set to 200; Crossover Probability is set to 0.8; Mutation Probability is set to 0.3; The number of offspring after crossover is determined based on the crossover probability; Elite Ratio is set to 0.4 to ensure that superior individuals from the parent generation are preserved to the next generation. The selection criteria for the Pareto optimal solution set are as follows: the population is stratified by fast non-dominated sorting, and individuals in the same stratum are sorted by crowding distance. Individuals with low non-dominated stratum and large crowding distance are selected to enter the next generation in order to maintain the diversity and uniform distribution of the solution set.

[0013] Furthermore, the convergence criterion for the non-dominated sorting genetic algorithm is set to terminate the iteration when any of the following conditions are met: (1) The maximum number of iterations is 200; (2) The change in congestion distance of the Pareto front over 50 consecutive generations is less than the preset threshold 1e -4 ; (3) The Pareto optimal solution set is stable in size and the proportion of non-dominated solutions exceeds 90%.

[0014] Furthermore, S4 specifically includes: First, the coefficient of determination, mean squared error, and mean absolute error are selected as quantitative evaluation indicators of model performance, which are used to characterize the goodness of fit, overall error level, and average prediction deviation of the model, respectively. Secondly, the scenarios are further subdivided according to the growth stage and optimization objectives. For the two optimization objectives of body weight gain and feed conversion ratio at each growth stage, the values ​​of various evaluation indicators corresponding to the response surface model and artificial neural network model are calculated respectively. Finally, for each specific scenario, the evaluation metrics of the two types of models are compared. The model with the higher coefficient of determination and the lower error index is used as the criteria to determine the model with better fitting performance in that scenario, and to clarify the optimal fit model corresponding to different growth stages and different optimization objectives.

[0015] Furthermore, S5 specifically includes: Based on the results of the optimal model determination for each growth stage and optimization target, the preliminary optimal nutritional combination results output by the corresponding model with better adaptability are adopted for the body weight gain index and feed conversion ratio index for each growth stage, replacing the scheme of covering the entire feeding cycle with a single model. For each growth stage, with the dual constraints of maximizing body weight gain and minimizing feed conversion ratio, the optimal nutrient parameter ranges corresponding to each of the two indicators for that stage are matched and converged. The combination of dietary metabolizable energy and crude protein that can simultaneously take into account growth rate and feed utilization efficiency is selected as the final optimal nutrient parameter for that growth stage.

[0016] Compared to existing technologies, this invention, through systematic feeding experiments, successfully constructed RSM and ANN predictive models of the effects of ME and CP levels on BWG and F / G in Hy-Line Brown male chickens at different growth stages (1–21 days, 22–56 days, and 57–70 days). The two models showed different predictive performances for BWG and F / G: in the 1–21 day age range, RSM was better at predicting BWG, while ANN was better at predicting F / G; in the 22–56 day and 57–70 day age ranges, ANN was better than RSM at predicting BWG, while RSM was slightly better than ANN at predicting F / G. Optimal nutritional parameters for each stage were obtained through multi-objective response optimization and genetic algorithms. Under the experimental conditions, the optimized values ​​for each stage could balance higher BWG and lower F / G within the current variable range, providing a scientific basis for precise nutritional supply to Hy-Line Brown male chickens. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of an ANN architecture according to the present invention; Figure 2 These are isopleth maps showing the relationship between BWG and F / G levels and ME and CP levels in Hy-Line Brown male chickens at different growth stages according to this invention; A, B, and C are isopleth maps showing the relationship between BWG and ME and CP levels in Hy-Line Brown male chickens aged 1–21 days, 22–56 days, and 57–70 days, respectively; D, E, and F are isopleth maps showing the relationship between F / G and ME and CP levels in Hy-Line Brown male chickens aged 1–21 days, 22–56 days, and 57–70 days, respectively. Figure 3 This invention presents an ANN model analysis and prediction regression graph. The horizontal axis represents the actual experimental values, and the vertical axis represents the ANN predicted values. R represents the correlation coefficient between the two, with a value closer to 1 indicating a more accurate fit. A and D are BWG and F / G regression graphs of the ANN model for ages 1–21; B and E are BWG and F / G regression graphs of the ANN model for ages 22–56; C and F are BWG and F / G regression graphs of the ANN model for ages 57–70. Detailed Implementation

[0019] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] The specific embodiments of the method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks provided by this invention are described below: Two hundred and sixty one-day-old Hy-Line Brown male chickens were randomly divided into 12 groups (6 replicates per group, 30 chickens per replicate). The experiment was conducted in three phases: 1–21 days old, 22–56 days old, and 57–70 days old. Detailed groupings are shown in Table 1. A 4×3 two-factor experimental design was used, with ME (medium) levels at four levels and CP (concentration phosphate) levels at three levels in each phase. For the 1–21 day old chickens, the ME levels were 12.13, 11.92, 11.72, and 11.51 MJ / kg, and the CP levels were 20, 19, and 18%, respectively. For the 22–56 day old chickens, the ME levels were 12.13, 11.92, 11.72, and 11.51 MJ / kg, and the CP levels were 19, 18, and 17%, respectively. For the 57–70 day old chickens, the ME levels were 11.92, 11.72, 11.51, and 11.30 MJ / kg, and the CP levels were 18, 17, and 16%, respectively. The experimental diets were formulated with corn and soybean meal according to the "Nutritional Requirements Standards for Broilers" (NY / T 33-2004). The composition and nutrient levels of the basal diets for 1–21 days, 22–56 days, and 57–70 days of age are shown in Tables 2, 3, and 4.

[0021] Table 1. Experimental Design of Energy and Protein Nutritional Requirements for Hy-Line Brown Roosters

[0022] Table 2. Dietary composition and nutrient levels for 1-21 day old infants (air-dried basal diet)

[0023] Table 3. Dietary composition and nutrient levels for patients aged 22–56 days (air-dried basal diet)

[0024] Table 4. Dietary composition and nutrient levels for patients aged 57–70 days (air-dried basal diet)

[0025] 1. Feeding and Management The experimental chicken house was a closed system with automatic control of lighting, ventilation, and temperature, and an automatic manure conveyor belt for cleaning. H-shaped, two-layer stacked cages were used, with 30 birds per cage constituting one replicate. Replicas for each experimental group were evenly distributed throughout the chicken house. The chickens had free access to feed and water. The ambient temperature was maintained at 35℃ from day 1 to 7, then decreased by 1℃ every two days until it gradually decreased to 25℃. Relative humidity was controlled at 60%–70%, and water was provided freely.

[0026] 2. Measurement Indicators and Methods The number of dead or culled chickens was observed and recorded daily in replicates. The amount of leftover feed and the weight of the chickens were accurately measured at the beginning of the experiment (1 day old) and at the end of each experimental stage (21, 56 and 70 days old). The BWG and F / G ratios for each experimental stage were calculated.

[0027] BWG (g) = Average body weight at the end of the trial phase - Average body weight at the beginning of the trial phase; F / G = Amount of feed consumed / Weight gain of the flock.

[0028] 3. Model Building This study analyzed datasets from 12 groups generated during production trials to construct RSM and ANN models, respectively. Two input features (ME and CP) were selected as predictors for model development. These variables were used to train the ANN and RSM models, which were then applied to predict BWG and F / G, respectively. To compare the RSM and ANN models, mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²) were introduced. 2 ).

[0029] 3.1 RSM Model The RSM was constructed and analyzed using Minitab software. The general form of the second-order polynomial regression model used in this application is shown in the equation: , In the formula, Y is the response variable (e.g., body weight gain, feed conversion ratio); ME is the dietary energy level (MJ / kg); and CP is the dietary protein level (CP%). This is a constant term (intercept); , The linear effect coefficient; , This is the square effect coefficient (reflecting whether the effect of a factor decreases or increases); The interaction coefficient (quantifies the synergistic or antagonistic effect between proteins and energy). This is random error.

[0030] The model was simplified by removing insignificant variables (P < 0.05) through analysis of variance. Finally, the maximum weight gain and minimum material weight ratio were obtained through multiple response optimization.

[0031] 3.2 ANN Model ANN modeling was performed using the Neural Network Toolbox in MATLAB to simulate the nutritional model of Hy-Line Brown roosters. The ANN structure consists of an input layer, hidden layers, and an output layer. Two input neurons represent dietary ME and CP levels, respectively, along with ten hidden neurons and one output neuron corresponding to either BWG or F / G levels. Figure 1 Similar to the RSM model construction, an ANN model was built using 12 datasets generated in the production trial as samples. The data was divided into three subsets: 70% for training, 15% for validation, and 15% for testing.

[0032] This application uses the `feedforwardnet` function from the MATLAB Neural Network Toolbox to construct a feedforward neural network. The hyperbolic tangent sigmoid activation function (tansig) is used for the hidden layer, and the linear activation function (purelin) is used for the output layer. The Levenberg-Marquardt backpropagation algorithm (trainlm) is used for training. The training parameters are set as follows: maximum number of training epochs is set to 1000; performance goal is set to 0; minimum performance gradient (min_grad) is set to 1e. -7 The maximum number of validation failures (max_fail) is set to 6; the initial value of the Marquardt adjustment parameter (mu) is set to 0.001, the increment / decrement coefficients of mu (mu_dec, mu_inc) are set to 0.1 and 10 respectively, and the maximum value of mu (mu_max) is set to 1e. 10 Since the Levenberg-Marquardt algorithm is a batch processing algorithm, it does not involve independent settings for the learning rate and batch size.

[0033] Before modeling, all input variables (ME, CP) and output variables (BWG, F / G) were normalized. The MATLAB function `mapminmax` was used to linearly map each variable to the interval [-1, 1]. The normalization formula is: Pn = 2 × (P - P_min) / (P_max - P_min) - 1, where P_min and P_max are the minimum and maximum values ​​of each variable in the training set, respectively. During normalization, the normalization parameters (minimum and maximum values) of the training set were recorded, and the same parameters were applied to the validation and test sets. After model prediction, the output results were restored to their original dimensions through inverse normalization. For outlier handling, box plots (interquartile range criterion) were used for identification: outliers were judged based on values ​​less than Q1 - 1.5 × IQR or greater than Q3 + 1.5 × IQR, and detected outliers were removed from the modeling dataset.

[0034] In addition to requiring the test set MSE to be smaller than the training set MSE, this application further employs early stopping to prevent overfitting. The validation set error is monitored in real time during training, and training is automatically terminated when the validation set error fails to decrease within a continuous max_fail iteration, preventing the model from overlearning training set noise.

[0035] The parameters of the NSGA-II algorithm are configured as follows: Population Size is set to 100; Maximum Iterations is set to 200; Crossover Probability is set to 0.8; Mutation Probability is set to 0.3; the number of offspring after crossover is determined based on the crossover probability; and the Elite Ratio is set to 0.4 to ensure that superior individuals from the parent generation are retained to the next generation. The selection criteria for the Pareto optimal solution set are as follows: the population is stratified using fast non-dominated sorting, and individuals in the same stratum are sorted by crowding distance. Individuals with lower non-dominated strata and larger crowding distances are given priority to enter the next generation to maintain the diversity and uniform distribution of the solution set. The convergence criterion is set to terminate the iteration when any of the following conditions are met: (1) the maximum number of iterations of 200 is reached; (2) the change in crowding distance of the Pareto front is less than the preset threshold (1e-4) for 50 consecutive generations; and (3) the size of the Pareto optimal solution set is stable and the proportion of non-dominated solutions exceeds 90%. During the optimization process, the trained ANN model is used as the fitness function to simultaneously evaluate two objective functions, BWG (maximizing the objective) and F / G (minimizing the objective), for the candidate solutions (ME and CP combinations), and finally outputs the optimal parameter combination on the Pareto front.

[0036] 4. Statistics and Analysis Experimental data were analyzed using the GLM program in SAS 9.1.3 system software. First, the ANOVA procedure in the statistical software was used to perform analysis of variance for each indicator, and then Duncan's method was used for multiple comparisons. Results are expressed as mean and standard error of the mean. P < 0.05 was considered statistically significant, and P < 0.01 was considered highly statistically significant.

[0037] This application systematically analyzed the regulatory effects of dietary ME and CP levels on body weight gain (BWG) in Hy-Line Brown male chickens. From 1 to 21 days of age, dietary ME levels had no significant effect on BWG in Hy-Line Brown male chickens (P=0.1125), while dietary CP levels showed a highly significant effect (P<0.0001), with the BWG in the 18% CP group significantly lower than those in the 19% and 20% CP groups. From 22 to 56 days of age, ME levels showed a highly significant effect on BWG in Hy-Line Brown male chickens (P<0.0001), with the 11.92 MJ / kg group showing the highest BWG. CP levels also showed a highly significant effect (P<0.0001), with the BWG in the 17% CP group significantly lower than those in the 18% and 19% CP groups. Between 57 and 70 days of age, the effect of ME level on BWG was not significant (P=0.0698), but CP level still had a highly significant effect on BWG (P<0.0001), with BWG in the 16% CP group being significantly lower than that in the 17% and 18% CP groups.

[0038] F / G is a core indicator for evaluating feed conversion efficiency. In this application, the regulatory patterns of ME and CP levels on F / G at each stage are closely related to body weight gain. From 1 to 21 days of age, ME level had no significant effect on F / G (P=0.1225), while CP level had a significant effect on F / G (P=0.0003). The F / G of the 18% CP group was significantly higher than that of the 19% and 20% CP groups.

[0039] A highly significant interaction effect was observed between dietary energy and protein levels in Hy-Line Brown male chickens aged 22–56 days on their BWG (body weight gain) ratio (BWG) (P = 0.0003). Group 6 (BWG = 724.14 g) showed significantly higher BWG than all other groups. A highly significant interaction effect was also observed between dietary energy and protein levels in Hy-Line Brown male chickens aged 22–56 days on their F / G ratio (F / G) ratio (P = 0.0018). Groups 1, 2, 5, and 6 showed the best feed conversion efficiency. A highly significant interaction effect was also observed between dietary energy and protein levels in Hy-Line Brown male chickens aged 57–70 days on their F / G ratio (P = 0.0124). Group 5 showed the best feed conversion efficiency.

[0040] Table 5. Effects of dietary energy and protein levels on the production performance of Hy-Line Brown male chickens.

[0041] No letters or the same letters in the same row of data indicate no significant difference (P>0.05), while different lowercase letters indicate significant difference (P<0.05).

[0042] Table 6 presents the results of quadratic polynomial response surface model analysis of BWG and F / G with ME and CP levels for Hy-Line Brown male chickens at different growth stages. This model was used to describe the nonlinear effects of the two factors on production performance and to evaluate their optimal combination range. The results show that, except for the BWG model for 22–56 days of age, the models for each stage were statistically significant (P<0.05).

[0043] Table 6. Quadratic polynomial response surface model analysis of performance indicators of Hy-Line Brown roosters and dietary energy and protein levels.

[0044] Figure 2 Contour plots showing the relationship between weight gain (BWG) and fat-to-growth (F / G) levels and mean gravidarum (ME) and total cinnamon (CP) levels at different growth stages of Hy-Line Brown roosters were presented. This provides a more intuitive understanding of the combined effects of ME and CP on BWG and F / G at different growth stages. The shape of the contour plots at each stage closely matches the signs of the quadratic and interaction terms in the regression equation, validating the effectiveness of the response surface model. From 1 to 21 days old: Both weight gain and F / G are primarily regulated by CP, with an optimal CP of approximately 19%. ME has a weaker influence and exhibits an independent optimal point. From 22 to 56 days old: F / G is most significantly affected by the combined effects of ME and CP (significant interaction term), forming a clear optimal ratio region (ME 11.9–12.1, CP 18–19). From 57 to 70 days old: Both weight gain and F / G show significant negative or positive interactions (F / G) with ME × CP.

[0045] This application uses ME and CP levels as input variables and BWG and F / G as output variables. ANN prediction models were constructed for three growth stages of Hy-Line Brown male chickens: 1–21 days old, 22–56 days old, and 57–70 days old. The core fitting parameters of the models are shown in Table 7. All models were uniformly configured with 10 hidden neurons. A three-sample partitioning method (training set, validation set, and test set) was used for network training and performance evaluation. The correlation coefficient (R) was used as the core evaluation index for model fitting accuracy and generalization ability. The results show that the correlation coefficients between the validation set and the test set for each growth stage and each performance index reached 1.000, indicating that the model has extremely strong generalization ability on unknown data and no risk of overfitting. The correlation coefficients in the training set were all ≥0.9, with R=1.000 for the BWG training set in the 22–56 day old age group. The R-values ​​for the full dataset of material weight ratio (F / G) were 0.984, 0.943, and 0.976 at each stage, respectively, and the overall fitting accuracy was significantly better than that of BWG; the R-values ​​for the full dataset of BWG were 0.939, 0.964, and 0.969, respectively.

[0046] Table 7. ANN model relating Hy-Line Brown rooster performance indicators to dietary energy and protein levels.

[0047] To further verify the predictive accuracy of the ANN model, this application plotted regression diagrams of the experimentally measured values ​​and model predicted values ​​of BWG and F / G in Hy-Line Brown roosters at each growth stage. Figure 3 In all regression plots, the data points are closely distributed on both sides of the fitted straight line (red line) without significant deviation. The model predictions and experimental measurements are in high agreement, with no systematic bias, further verifying the reliability and generalization ability of the model and providing solid model support for the optimization of precision nutrition formulas for laying roosters.

[0048] As shown in Table 8, to compare the differences between the RSM and ANN models, this application calculated the MSE, MAE, and R of each model. 2 The results showed that the two models differed in their predictive performance for BWG and F / G in Hy-Line Brown roosters at different growth stages: From 1 to 21 days of age, the RSM model was better at predicting BWG (R²=0.95), with lower error indices (MSE and MAE) than the ANN model; while the ANN model was better at predicting F / G (R²=0.966). From 22 to 56 days of age and from 57 to 70 days of age, the ANN model was better at predicting BWG than the RSM model (R²=0.929 and 0.938, respectively), while the RSM model was slightly better at predicting F / G than the ANN model (R²=0.971 and 0.975, respectively).

[0049] Table 8 Comparison of parameters between ANN model and RSM model

[0050] The maximum body weight gain and minimum feed conversion ratio of Hy-Line Brown male chickens during this growth stage were determined using multiple response optimization and the NSGA-II function, respectively, within the experimental range. The results are as follows: From 1 to 21 days of age, the optimal RSM nutrient concentration was 12.13 MJ / kg ME and 20.00% CP, corresponding to a BWG of 171.45 g and a F / G ratio of 2.04. The ANN recommended 11.89 MJ / kg ME and 19.50% CP, achieving higher body weight gain (175.47 g) and a slightly better feed conversion ratio (2.03) at a lower nutrient level. From 22 to 56 days of age, the optimal RSM nutrient concentration was 12.13 MJ / kg ME and 18.31% CP, corresponding to a BWG of 709.18 g and a F / G ratio of 2.76. The ANN used a lower ME of 11.92 MJ / kg ME and 18.00% CP, increasing body weight gain to 724.14 g, but the feed conversion ratio increased slightly to 2.78. From 57 to 70 days of age, the recommended nutrient concentrations of the two models became similar (RSM: ME 11.92 MJ / kg, CP 19.50%). 16.82%; ANN: ME 11.91 MJ / kg, CP 16.83%, ANN body weight gain (328.72 g) and feed ratio (3.34) are both better than RSM (BWG 325.14g, F / G 3.62).

[0051] The RSM and ANN models each have their own advantages and disadvantages at different stages and for different indicators, which precisely proves that a combined strategy (selecting the best option at each stage) is superior to a single fixed model. If a single RSM model is used exclusively, the average BWG predicted MSE over the entire period is approximately (0.258 + 66.25 + 13.527) / 3 = 26.68; using the combined RSM + ANN strategy (selecting the best option at each stage), the average BWG predicted MSE over the entire period is approximately (0.258 + 12.107 + 4.748) / 3 = 5.70, with an average reduction of 78.6%. For F / G, the combined strategy reduces the average MSE over the entire period by approximately (0.000136 + 0.000332 + 0.000505) / 3 = 0.000324 compared to the single RSM, decreasing to (0.000007 + 0.000332 + 0.000421) / 3 = 0.000253, with an average reduction of approximately 21.9%. This indicates that the combined strategy not only leverages the strong fitting ability of ANN in complex nonlinear stages but also retains the stability of RSM in simple linear response stages.

[0052] Table 9. Predicted metabolizable energy and crude protein nutritional requirements of Hy-Line Brown male chicken diets based on RSM and ANN.

[0053] Taking the market price of feed ingredients at the time of this experiment as an example, the economic benefits were estimated as follows: Basic feed price: 3.2 yuan / kg; Market price of live laying roosters (growing period): 8 yuan / kg; Formula cost: For every 0.2 MJ / kg reduction in feed ME, approximately 15 yuan / ton of formula cost was saved; For every 0.5 percentage point reduction in CP, approximately 20 yuan / ton of formula cost was saved. After adopting the ANN-optimized formula, although feed costs increased slightly from 1 to 21 days of age (due to increased feed intake), and net income remained basically flat from 22 to 56 days of age, in the later period from 57 to 70 days of age, ANN significantly reduced feed consumption by drastically reducing the feed conversion ratio (3.62→3.34, a decrease of 7.7%), resulting in an increase of 0.282 yuan in net income per bird. Overall, the net increase in income per Hy-Line Brown laying rooster was approximately 0.303 yuan.

[0054] Based on a standard batch size of 100,000 birds per batch, each batch can generate approximately 30,300 yuan in additional economic benefits; if 5 batches are raised annually, the annual additional benefit will be approximately 151,500 yuan. Given the current high prices of feed raw materials, the cost reduction potential of this combined strategy will be further amplified (for every 0.1 yuan / kg increase in feed prices, the relative profit advantage of this proposed strategy will increase by approximately 0.35 yuan / bird). This application successfully constructed RSM and ANN predictive models of the effects of ME and CP levels on BWG and F / G in Hy-Line Brown male chickens at different growth stages (1–21 days, 22–56 days, and 57–70 days). The two models showed different predictive performances for BWG and F / G: in the 1–21 day age range, RSM was better at predicting BWG, while ANN was better at predicting F / G; in the 22–56 day and 57–70 day age ranges, ANN was better than RSM at predicting BWG, while RSM was slightly better than ANN at predicting F / G. Optimal nutritional parameters for each stage were obtained through multi-objective response optimization and genetic algorithms. Under the experimental conditions, the optimized values ​​for each stage could balance higher BWG and lower F / G within the current variable range, providing a scientific basis for precise nutritional supply to Hy-Line Brown male chickens.

[0055] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0056] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks, characterized in that, Includes the following steps: S1. Conduct feeding trials under standardized feeding management conditions, and measure the body weight gain and feed conversion ratio of experimental chickens at each growth stage in replicates to construct a dataset; S2. Using dietary metabolizable energy and crude protein as input variables, and body weight gain and feed conversion ratio as response variables, a response surface model is constructed. With maximizing body weight gain and minimizing feed conversion ratio as dual optimization objectives, the response surface model is used to solve for the dietary metabolizable energy and crude protein corresponding to each growth stage of the experimental chickens, and the first preliminary optimal combination is obtained. S3. Using dietary metabolizable energy and crude protein as input variables, and body weight gain and feed conversion ratio as output variables, an artificial neural network model is constructed. The artificial neural network model is trained based on the dataset. The trained artificial neural network model is used as the fitness function. Multi-objective optimization is performed by combining a non-dominated sorting genetic algorithm with an elite strategy. The dietary metabolizable energy and crude protein corresponding to each growth stage of the experimental chickens are solved with the dual optimization objectives of maximizing body weight gain and minimizing feed conversion ratio, and the second preliminary optimal combination is obtained. S4. Construct evaluation indicators to quantitatively compare the fitting effects of response surface models and artificial neural network models based on different growth stages and different optimization objectives, and obtain the optimal fitting model corresponding to each growth stage and different optimization objective. S5. Based on the optimal adaptation model corresponding to each optimization objective at each growth stage, output the final optimal nutritional parameters of dietary metabolizable energy and crude protein for each stage of the entire feeding cycle of Hy-Line Brown roosters.

2. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 1, characterized in that, Specifically, S1 is: One-day-old Hy-Line Brown male chickens were selected and a 4×3 two-factor completely randomized experimental design was adopted. They were randomly divided into 12 treatment groups, with 6 replicates in each group and 30 chickens in each replicate. The entire feeding cycle was divided into three growth stages: 1-21 days old, 22-56 days old, and 57-70 days old. Four dietary metabolizable energy levels and three dietary crude protein levels were set for each growth stage. The corn-soybean meal experimental diet was formulated according to the nutritional requirements of broilers. The feeding experiment was carried out under standardized feeding management conditions. The body weight gain and feed conversion ratio of the experimental chickens at each growth stage were measured in replicates to obtain the original dataset for modeling.

3. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 1, characterized in that, Specifically, S2 is: The response surface model is constructed in the general form of a second-order polynomial regression model, as shown in the equation: ， In the formula, Y is the response variable, including body weight gain and feed conversion ratio, ME is the dietary energy level in MJ / kg, and CP is the dietary protein level. For constant terms, , The linear effect coefficient, , This is the squared effect coefficient, reflecting whether the effect of a factor decreases or increases. The interaction coefficient quantifies the synergistic or antagonistic effects between proteins and energy. This is random error; The model was simplified by removing insignificant variables from the response surface model through analysis of variance. Finally, the maximum weight gain and minimum material-to-weight ratio were obtained through multiple response optimization.

4. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 1, characterized in that, Specifically, S3 is: The ANN structure consists of an input layer, a hidden layer, and an output layer. The input layer includes two input neurons, which represent the dietary energy level (ME) and dietary protein level (CP), respectively. The hidden layer includes ten hidden neurons. The output layer includes output neurons corresponding to the output variables body weight gain (BWG) or feed conversion ratio (F / G). The ANN model was constructed using repeated levels of data from 12 treatment groups as samples. The dataset was randomly divided into three subsets according to the ratio of 70% training set, 15% validation set, and 15% test set. A feedforward neural network was constructed using the feedforwardnet function. The hidden layer activation function was the hyperbolic tangent sigmoid function (tansig), and the output layer activation function was the linear function (purelin). The training algorithm used was the Levenberg-Marquardt backpropagation algorithm (trainlm). The training parameters were set as follows: maximum training epochs (1000), performance goal (0), and minimum performance gradient (min_grad) (1e). -7 The maximum number of verification failures (max_fail) is set to 6, the initial value of the Marquardt adjustment parameter (mu) is set to 0.001, the increment / decrement coefficients (mu_dec and mu_inc) are set to 0.1 and 10 respectively, and the maximum value (mu_max) is set to 1e. 10 .

5. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 4, characterized in that, Also includes: Before modeling, all input variables ME, CP, BWG, and F / G were normalized. MATLAB's mapminmax function was used to linearly map each variable to the interval [-1, 1]. The normalization formula is as follows: ， in and These are the minimum and maximum values ​​of each variable in the training set. During the normalization process, the normalization parameters of the training set, i.e. the minimum and maximum values, are recorded. The same parameters are applied to the validation and test sets for normalization. After the model prediction is completed, the output results are restored to the original dimensions through inverse normalization. Outlier identification is performed using box plots. The outlier discrimination formula is as follows: X < Q1 - 1.5 × IQR or X > Q3 + 1.5 × IQR, In the formula, X is the value of the data point to be detected; Q1 is the first quartile, i.e., the 25th quartile, representing the value at the lower quartile of the dataset; Q3 is the third quartile, i.e., the 75th quartile, representing the value at the upper quartile of the dataset; IQR is the interquartile range, IQR = Q3 - Q1, representing the dispersion of the middle 50% of the data in the dataset; 1.5 is an empirical coefficient, which is used to remove outliers that meet any of the above conditions and exclude them from the modeling dataset.

6. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 4, characterized in that, ANN model training also includes: Early stopping is used to prevent overfitting of the system. The validation set error is monitored in real time during training. When the validation set error does not decrease in max_fail iterations, training is automatically terminated to prevent the model from overlearning training set noise.

7. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 4, characterized in that, The parameter configuration for the non-dominated sorting genetic algorithm is as follows: Population Size is set to 100; Maximum Iterations is set to 200; Crossover Probability is set to 0.8; Mutation Probability is set to 0.3; The number of offspring after crossover is determined based on the crossover probability; Elite Ratio is set to 0.4 to ensure that superior individuals from the parent generation are preserved to the next generation. The selection criteria for the Pareto optimal solution set are as follows: the population is stratified by fast non-dominated sorting, and individuals in the same stratum are sorted by crowding distance. Individuals with low non-dominated stratum and large crowding distance are selected to enter the next generation in order to maintain the diversity and uniform distribution of the solution set.

8. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 4, characterized in that, The convergence criterion for the non-dominated sorting genetic algorithm is set to terminate the iteration when any of the following conditions are met: (1) The maximum number of iterations is 200; (2) The change in congestion distance of the Pareto front over 50 consecutive generations is less than the preset threshold 1e -4 ; (3) The Pareto optimal solution set is stable in size and the proportion of non-dominated solutions exceeds 90%.

9. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 1, characterized in that, Specifically, S4 is: First, the coefficient of determination, mean squared error, and mean absolute error are selected as quantitative evaluation indicators of model performance, which are used to characterize the goodness of fit, overall error level, and average prediction deviation of the model, respectively. Secondly, the scenarios are further subdivided according to the growth stage and optimization objectives. For the two optimization objectives of body weight gain and feed conversion ratio at each growth stage, the values ​​of various evaluation indicators corresponding to the response surface model and artificial neural network model are calculated respectively. Finally, for each specific scenario, the evaluation metrics of the two types of models are compared. The model with the higher coefficient of determination and the lower error index is used as the criteria to determine the model with better fitting performance in that scenario, and to clarify the optimal fit model corresponding to different growth stages and different optimization objectives.

10. The method for optimizing the nutritional requirements of Hy-Line Brown rooster diets based on response surface methodology and artificial neural networks according to claim 1, characterized in that, Specifically, S5 is: Based on the results of the optimal model determination for each growth stage and optimization target, the preliminary optimal nutritional combination results output by the corresponding model with better adaptability are adopted for the body weight gain index and feed conversion ratio index for each growth stage, replacing the scheme of covering the entire feeding cycle with a single model. For each growth stage, with the dual constraints of maximizing body weight gain and minimizing feed conversion ratio, the optimal nutrient parameter ranges corresponding to each of the two indicators for that stage are matched and converged. The combination of dietary metabolizable energy and crude protein that can simultaneously take into account growth rate and feed utilization efficiency is selected as the final optimal nutrient parameter for that growth stage.

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