Growth responses of quail chicks to dietary energy and protein: artificial neural network and multi-objective optimization of response surface methodology

Metabolizable energy (ME) and crude protein (CP) are key dietary factors for quail, with CP providing essential amino acids for growth and efficiency. Estimating their requirements is crucial for production. While response surface methodology (RSM) has been widely used, artificial neural networks (ANN) offer potential advantages by capturing nonlinear responses. However, few studies have directly compared ANN and RSM in quail nutrition. A dataset of 40 treatments was generated from a central composite design (CCD) platform (ME: 2600–3000 kcal/kg; CP: 19–24.8%) durig growth phase of quail chicks. ANN models included a radial basis function network (RBFN, 2 inputs, 7 hidden neurons) for body weight gain (BW gain) and a multilayer perceptron (MLP, 2 inputs, 6 hidden neurons) for feed conversion ratio (FCR), trained with backpropagation. ANN and RSM models were assessed using R², mean absolute deviation (MAD), mean squared error (MSE), average absolute deviation (AAD), and bias, with residuals compared for accuracy. Variable sensitivity ratios (VSR) were used to assess ME and CP importance, and multi-objective optimization was applied to estimate optimal dietary levels. Overlearning did not occur in the ANN models. ANN showed slightly higher R² values than RSM for BW gain and FCR (0.92 vs. 0.89), but residual analysis indicated similar performance, with RSM occasionally more accurate. VSR analysis confirmed quail growth was more sensitive to CP than ME. Both models predicted comparable ME optima, while ANN estimated slightly lower CP values. The overall optimum was 2980 kcal/kg ME and 23% CP, consistent with literature though lower than some recommendations. Differences between ANN and RSM may relate to the backpropagation algorithm’s tendency to trap in local optima and the limited dataset size (40 lines). This study demonstrated that CCD-based dose–response data can be effectively modeled using both ANN and RSM to estimate dietary ME and CP requirements in quail chicks. Although ANN showed slightly higher prediction ability, it was not consistently superior to RSM. The optimal levels for maximizing performance were 2980 kcal/kg ME and 23% CP. Importantly, the choice of analytical method significantly influences the estimated nutrient requirements, and reliance on BP-trained ANN models may introduce bias due to local optima. Future work should apply global optimization algorithms, such as genetic algorithms (GA), to improve the robustness of ANN-based nutritional modeling.