The compact Genetic Algorithm for likelihood estimator of first order moving average model

Recently Genetic Algorithms (GAs) have frequently been used for optimizing the solution of estimation problems. One of the main advantages of using these techniques is that they require no knowledge or gradient information about the response surface. The poor behavior of genetic algorithms in some problems, sometimes attributed to design operators, has led to the development of other types of algorithms. One such class of these algorithms is compact Genetic Algorithm (cGA), it dramatically reduces the number of bits reqyuired to store the poulation and has a faster convergence speed. In this paper compact Genetic Algorithm is used to optimize the maximum likelihood estimator of the first order moving avergae model MA(1). Simulation results based on MSE were compared with those obtained from the moments method and showed that the Canonical GA and compact GA can give good estimator of θ for the MA(1) model. Another comparison has been conducted to show that the cGA method has less number of function evaluations, minimum searched space percentage, faster convergence speed and has a higher optimal precision than that of the Canonical GA.