Submitted to: Poultry Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/26/2004
Publication Date: 2/15/2005
Citation: Roush, W.B., Branton, S.L. 2005. A comparison of fitting growth models with a genetic algorithm and nonlinear regression. Poultry Science. v. 84. pp. 494-502. Interpretive Summary: The accurate and precise fitting of observed growth data with growth models is necessary to gain a mathematical understanding of the biological relationship between animals and their physical environment. Researchers have shown that some of the commonly used growth models do not represent observed growth responses. This research involved the examination of genetic algorithms (GA), a procedure from the artificial intelligence discipline, as a mathematical modeling approach to fitting nonlinear growth equations. The GA was chosen for its ability to model very complex data. The GA results were compared to those obtained with traditional nonlinear regression. The results showed that genetic algorithms fit the observed data equally as well as regression analysis. However, the oscillatory nature of the difference between the observed and predicted growth responses was still present. It was concluded that the fitting of the growth equations was not so much a problem with the fitting methodology as it is with the form of the equation. Thus the form of growth equations will have to augmented to more precisely account for the oscillatory nature of the difference between predicted and observed growth responses.
Technical Abstract: A Genetic Algorithm (GA), an optimization procedure based on the theory of evolution, was compared with nonlinear regression for the ability of the two algorithms to fit the coefficients of poultry growth models. It was hypothesized that the nonlinear approach of using GA to define the parameters of growth equations would better fit the growth equations than the use of non-linear regression. Two sets of growth data from the literature, consisting of male broiler BWs grown over periods of 168 and 170 d, respectively, were used in the study. The growth data were fit to two forms of the logistic model, the Gompertz, the Gompertz-Laird, and the Saturated Kinetic Models using both the SAS NLIN procedure and a GA. There were no statistical differences for the comparison of the residuals (the difference between observed and predicted BWs) of growth models fit either by a GA or nonlinear regression. The plotted residuals for the nonlinear regression and GA determined growth values confirmed observations of others that the residuals have oscillations resembling sine waves that are not represented by the growth models. It was found that GA could successfully determine the coefficients of growth equations. A disadvantage of slowness in converging to the solution was found for the GA. The advantage of GA over traditional nonlinear regression is that only ranges need be specified for the parameters of the growth equations; whereas, estimates of the coefficients need to be determined and in some programs the derivatives of the growth equations need to be identified. Depending on the goal of the research, solving multivariable complex functions with an algorithm that considers several solutions at the same time in an evolutionary mode can be considered an advantage especially where there is a chance for the solution to converge on a local optimum when a global optimum is desired. It was concluded that the fitting of the growth equations was not so much a problem with the fitting methodology as it is with the form of the equation.