A comparison of fitting growth models with a genetic algorithm and nonlinear regression

USDA/ARS, South Central Poultry Research Laboratory, Mississippi State, Mississippi 39762, USA. broush@msamsstate.ars.usda.gov

A genetic algorithm (GA), an optimization procedure based on the theory of evolution, was compared with nonlinear regression for the ability of the 2 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 nonlinear regression. Two sets of growth data from the literature, consisting of male broiler BW grown for 168 and 170 d, were used in the study. The growth data were fit to 2 forms of the logistic model, the Gompertz, the Gompertz-Laird, and the saturated kinetic models using the SAS nonlinear algorithm (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 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.