Optimization of response surface and neural network models in conjugation with desirability function for estimation of nutritional needs of methionine, lysine, and threonine in broiler chickens

Abstract

The optimization algorithm of a model may have significant effects on the final optimal values of nutrient requirements in poultry enterprises. In poultry nutrition, the optimal values of dietary essential nutrients are very important for feed formulation to optimize profit through minimizing feed cost and maximizing bird performance. This study was conducted to introduce a novel multi-objective algorithm, desirability function, for optimization the bird response models based on response surface methodology (RSM) and artificial neural network (ANN). The growth databases on the central composite design (CCD) were used to construct the RSM and ANN models and optimal values for 3 essential amino acids including lysine, methionine, and threonine in broiler chicks have been reevaluated using the desirable function in both analytical approaches from 3 to 16 d of age. Multi-objective optimization results showed that the most desirable function was obtained for ANN-based model (D = 0.99) where the optimal levels of digestible lysine (dLys), digestible methionine (dMet), and digestible threonine (dThr) for maximum desirability were 13.2, 5.0, and 8.3 g/kg of diet, respectively. However, the optimal levels of dLys, dMet, and dThr in the RSM-based model were estimated at 11.2, 5.4, and 7.6 g/kg of diet, respectively. This research documented that the application of ANN in the broiler chicken model along with a multi-objective optimization algorithm such as desirability function could be a useful tool for optimization of dietary amino acids in fractional factorial experiments, in which the use of the global desirability function may be able to overcome the underestimations of dietary amino acids resulting from the RSM model.

Estimation of lysine requirements for growing Japanese quails

“…In this study, we used several regression models, five types of broken line models and the quadratic polynomial, to estimate the lysine requirement of growing quails. Different models and design of experiments (DOE) have been used for estimation of nutritional requirements in birds and domestic animals (Baker, Batal, Parr, Augspurger, & Parsons, 2002;De Leon, Kidd, & Corzo, 2010;Ghazaghi, Mehri, Yousef-Elahi, & Rokouei, 2012;Mehri, 2012Mehri, , 2014Mehri, Davarpanah, & Mirzaei, 2012;Mehri & Ghazaghi, 2014;Mehri, Nassiri Moghaddam, Kermanshahi, & Danesh-Mesgaran, 2013;Mercer, 1992) but as Pesti et al (2009) suggested, each model may have some advantages and disadvantages. For instance, although second-order polynomials are easy to fit to data, the inclusion of input data below or above those points that are required for maximum or minimum responses, resulting in remarkable changes in requirement estimates ).…”

A simple estimation of ideal profile of essential amino acids and metabolizable energy for growing Japanese quail

“…() who used steepest descent algorithms work by iteratively moving to better positions in the search space as a local search algorithm. The main reason for this discrepancy may be the methodology used in the studies in which the local search algorithms may trap in local minima or maxima resulting in under‐ or over‐estimation of nutritional requirements respectively (Mehri, ). Assuming 0.93 of digestibility coefficient for experimental diets on average, Lys estimate would be 1.42% on total basis, which is much more than that reported by NRC ().…”

“…Although ANN models would require much more observations (experimental runs) than conventional statistical methods, they could work very well even with relatively fewer data set if the data are statistically well distributed in the input domain (Lou and Nakai, ; Desai et al., ). In addition, application of ANN modelling along with global optimization algorithm such as desirability function could be efficiently used for nutritional studies in poultry (Mehri, ). The most problem in the use of literature data on nutritional needs of the bird is to choose the appropriate ‘ response ’ because the estimated values as ‘ requirements ’ may be changed for each response.…”

“…After training the networks, the constructed ANN models for G and FCR were subjected to an optimization process to find optimum levels of inputs for maximizing G and minimizing FCR. In this research, a multiobjective optimization approach, Derringer's desirability function ( D ), was used to get optimal values of input variables (Mehri, ). This approach was originally proposed by Harrington () and later modified by Derringer and Suich ().…”

“…Factorial experiments take into account interrelationships among nutrients resulting in optimum ratios between different variables. In this regard, fractional factorial experiments along with artificial neural networks (ANN) may help to draw out complex relationships of independent variables efficiently (Ahmadi and Golian, ; Ghazaghi et al., ; Mehri, , ; Mehri et al., ; Mehri and Ghazaghi, ). ANN is a nonlinear data‐mining tool, which has been modelled based on mammalian cerebral cortex.…”