The aim of structural optimization design is seeking the best set of design parameters to optimize the performance of the structure, and has been widely used in many engineering practices, especially in the aerospace and aeronautical engineering. In the real engineering, the structural design is often subject to uncertainties, which exists extensively in the nature. Structural design results without considering uncertainties may be sensitive to even small fluctuations of parameters, such as material characteristics, external loads, geometrical sizes, etc. In this manner, uncertainty based design optimization theories, such as reliability based optimization and robust optimization, have seen a rapid development in the past decades. In this work, the variable screening technique based on global sensitivity analysis is discussed. This work investigates the reliability design optimization of an aeronautical hydraulic pipeline system, in which the constraint locations are treated as design parameters. To reduce the size of the optimization problem, two non-probabilistic global sensitivity indices are introduced and modified to screen out those constraint locations which have no or little effects on the optimization target. Considering the rest of constraint locations as the design variables, the complexity of the optimization problem is dramatically reduced. Optimization of the pipeline systems demonstrates that the proposed method is superior to the traditional direct optimization method in both the optimization efficiency and results. This work indicates that introduction of sensitivity analysis can greatly enhance the efficiency and performance of optimization, and is of significant potential especially in those complex engineering problems involving a large number of design variables.