Abstract: The research in this paper focuses on establishing an accurate displacement model for giant magnetostrictive actuators (GMA)that may be istalled in a very large telescope to drive its segmented mirrors. A hierarchical genetic algorithm (HGA)is proposed and employed to identify the parameters for effectively deploying the GMA model. In practice, the HGA is proved to be able to avoid the problem of conventional genetic algorithms that the algorithms converge to suboptimal solutions. The HGA allows more initial population diversity in calculation and practically improves significantly the accuracy in predicting the actuator displacement. The deviations between experimental data and predicted values are less than 1.3% across the entire displacement range. Comparisons between the predicted values and experimental results imply that the established model precisely describes the hysteretic behavior and displacement characterization of GMA. The paper also analyzes effects on the key parameters in the model (such as hysteresis, loss, saturation magnetization, and saturation magnetostriction)from the applied magnetic field strength and the prestress level.