An immune system has powerful abilities such as memory, recognition and learning how to respond to invading antigens, and has been applied to many engineering algorithms in recent year. In this pap er, the combined optimization algorithm (Immune- Genetic Algorithm: IGA) is proposed for multi-optimization problems by introducing the capability of the immune system that controls the proliferation of clones to the genetic algorithm. The optimizing ability of the proposed combined algorithm is identified by comparing the result of optimization with simple genetic algorithm for two dimensional multi-peak function which have many local optimums. Also the new combined algorithm is applied to minimize the total weight of the shaft and the transmitted forces at the bearings. The inner diameter oil the shaft and the bearing stiffness are chosen as the design variables. The dynamic characteristics are determined by applying the generalized FEM. The results show that the combined algorithm and reduce both the weight of the shaft and the transmitted forces at the bearing with dynamic conatriants.