A combined compact genetic algorithm and local search method for optimizing the ARMA(1,1) model of a likelihood estimator

In this paper, a compact genetic algorithm (CGA) is enhanced by integrating its selection strategy with a steepest descent algorithm (SDA) as a local search method to give I-CGA-SDA. This system is an attempt to avoid the large CPU time and computational complexity of the standard genetic algorithm. Here, CGA dramatically reduces the number of bits required to store the population and has a faster convergence. Consequently, this integrated system is used to optimize the maximum likelihood function ln L(phi(1), theta(1)) of the mixed model. Simulation results based on MSE were compared with those obtained from the SDA and showed that the hybrid genetic algorithm (HGA) and I-CGA-SDA can give a good estimator of (phi(1), theta(1)) for the ARMA(1,1) model. Another comparison has been conducted to show that the I-CGA-SDA has fewer function evaluations, minimum search space percentage, faster convergence speed and has a higher optimal precision than that of the HGA.