Abstract: To improve the accuracy and convergence efficiency of the generalized genetic algorithm, heterogeneity strategy is proposed firstly to avoid inbreeding and premature. Furthermore, an expression to estimate the extent of inbreeding and two methods for selecting heterogeneity were given. A new generalized genetic algorithm was presented in this paper. Many new techniques such as population isolation, arithmetical crossover and adaptive random mutation were used. This method was used for support-position optimization of structure dynamic response. Numerical examples demonstrated that heterogeneous strategy can improve the convergence efficiency and avoid premature effectively. The new generalized genetic algorithm can optimize the support positions when both elastic and bending rigidity are considered. It has extensive applicability in complicated support-position optimization problem of dynamic response.