Analyses of the genetic algorithms in the continuous space

General properties of a class of genetic algorithms in the continuous space (GACS) are analyzed. Near-convergence behavior is examined under the assumption of a quadratic approximation of the cost function around the optimal point. It is proved that, near convergence, the mean of the population of solutions follows a modified Newton´s step. The convergence rates for both the mean and the covariance matrix of the random solution vector are determined by the products of the mutation noise power and the eigenvalues of the Hessian of the cost function at the global minimum