Including a gust analysis in an optimization framework is computationally expensive as the critical load cases are not known a priori and hence a large number of points within the flight envelope have to be analyzed. Model order reduction techniques can provide significant improvement in computational efficiency of an aeroelastic analysis. In this paper, after thorough analysis of 4 commonly used model order reduction methods, balanced proper orthogonal decomposition is selected to reduce the aerodynamic system which is based on potential flow theory. The reduced aerodynamic system is coupled to a structural solver to obtain a reduced-order aeroelastic model. It is demonstrated that the dominant modes of the aerodynamic model can be assumed to be constant for varying equivalent airspeed and Mach number, enabling the use of a single reduced model for the entire flight envelope. A dynamic aeroelastic optimization method is then formulated using the reduced-order aeroelastic model. Results show that both dynamic and static loads play a role in optimization of the wing structure. Furthermore, the worst case gust loads change during the optimization process and it is important to identify the critical loads at every iteration in the optimization.