Comparing the genetic algorithm with the two methods of nonlinear least squares and the greatest possibility to estimate the nonlinear boxBOD model using simulation

Abstract

In this research, one of the nonlinear regression models is studied, which is BoxBOD,
which is characterized by nonlinear parameters, as the difficulty of this model lies in
estimating its parameters for being nonlinear, as its parameters were estimated by some
traditional methods, namely the method of non-linear least squares and the greatest
possible method and one of the methods of artificial intelligence, it is a genetic algorithm,
as this algorithm was based on two types of functions, one of which is the function of the
sum of squares of error and the second is the function of possibility. For comparison
between the methods used in the research, the comparison scale was based on the average
error squares, and for the purpose of data generation, five linear models were used as
simulation models. The results of the first four models showed that the non-linear least
squares method outperformed the rest of the methods used in the research. As for the
results of the fifth simulated model, the genetic algorithm based on the function of
possibility overtook the rest of the methods.