The detailed design of a turbo generator rotor system is highly constrained by feasible regions for the damped natural frequencies of the system. A major problem for the designer is to find a solution that fulfills the design criterion for the damped natural frequencies. The bearings and some geometrical variables of the rotor are used as the primary design variables in order to achieve a feasible design. This paper presents an alternative approach to search for feasible designs. The design problem is formulated as an optimization problem and a genetic algorithm (GA) is used to search for feasible designs. Then, the problem is extended to include another objective (i.e., multiobjective optimization) to show the potential of using the optimization formulation and a Pareto-based GA in this rotordynamic application. The results show that the presented approach is promising as an engineering design tool.