The optimization problem of the design of orthogrid-stiffened cylinder under combined axial force and external pressure is a complex problem. It involves finding the optimal layout of stiffening rings and stringers (number of rings and stringers which are discrete variables) and sizing of members and skin (continuous variables) while minimizing the mass of the stiffened cylinder and satisfying the buckling constraints. Also, the presence of multiple modes of buckling adds to the complexity of the optimization problem. Further, the design space is nonconvex with multiple local minima, and steps must be taken to avoid sub-optimal solutions. In this paper, a methodology for carrying out systematic optimization for the stiffened cylinder is presented. The optimization problem statement is defined as the minimization of mass with buckling load factor as the constraint, and two methods are presented to evaluate the buckling load. The first method is a simplified analytical method for evaluating individual buckling modes, and the second method is a high-fidelity method where buckling load is calculated using FEM. The optimization problem is solved using both methods. A comparison is made between the optimal solutions by the two fidelity models in terms of accuracy and cost. It is observed that the low-fidelity method is suited for preliminary calculations and screening the design space. The high-fidelity method gives an optimal solution which is having significant mass savings (28.13%) compared to results in the literature.