This article is concerned with the optimization of the mechanical structure of a one-degree-of-freedom vibration isolator. An efficient optimization algorithm based on an interval-computation method is used. The authors' general objective is to include and develop an optimization step in the pre-design process of a smart structure. In this article, the idea of this pre-design is to obtain, very quickly and very simply, the global structural geometry of the passive isolation device. For this purpose, a simplified mathematical model is built, which describes the main natural mode shapes of the suspension device. The method is applicable to large-scale dynamic systems for a first optimization process step because it's clearly an effective time-saving optimization approach. The results obtained are quite sufficient for a first predesign step. For a real case scenario, the optimized structure is applied to a numerical active vibration control process.