This paper proposes a genetic algorithm (GA) based design method for arbitrarily-shaped resonant elements that offer enhanced reflectarray antenna performance. All elements have the specified phase property over the range of 360°, and also have dual-polarization and low cross-polarization properties for better reflectarray performance. In addition, the proposal is suitable for linear-to-circular polarization conversion elements. Thus, polarizer reflectarray elements are also presented in this paper. The proposed elements are validated using both numerical simulations and experiments.