Comparison of Some Artificial Intelligence Algorithms with the Two Non-Linear Least Squares Method and the Maximum Likelihood Method of Estimating the Ratkowsky Model Using Simulation

Abstract

In this paper, one of the models of nonlinear regression is the Ratkowsky model. The parameters of this model are characterized by the difficulty of obtaining estimates as nonlinear parameters. Two classical methods were used for estimating these parameters: the method of nonlinear least squares and the method of maximum likelihood. In addition to these two methods two artificial intelligence algorithms, namely particle swarm optimization algorithm and the genetic algorithm were taken. These algorithms were based on two types of fitness functions, the first is the function of the sum of the squares error , the second the function of likelihood and using the simulation.The results showed the superiority of particle swarm optimization algorithm based on the function of the sum of squares of error on others methods.