A hybrid genetic algorithm for estimating the optimal time scale of linear systems approximations using Laguerre models

We deal with the problem of finding the optimal time scale of the truncated Laguerre series using numerical search techniques. We develop a hybrid genetic algorithm (GA) to search the nonlinear, multimodal squared-error function that results from least-squares approximations of the impulse response of causal linear time-invariant stable systems. The hybrid GA incorporates a Newton-Raphson (NR) local optimizer for fast convergence to the global minimum point. The proposed method competes favorably with the pure GA in solution accuracy (the number of function evaluations being the same) and with an established gradient-directed optimization algorithm in number of function evaluations (the solution accuracy being the same).