A new interval optimization algorithm is presented in this paper. In engineering, most optimization algorithms focus on exact parameters and optimum objectives. However, exact parameters are not easy to be manufactured to because of manufacturing errors and expensive manufacturing cost. To account for these problems, it is necessary to estimate interval design parameters and allowable objective error. This is the first paper to propose a new interval optimization algorithm within the context of Genetic Algorithms. This new algorithm, the Interval Genetic Algorithm (IGA), can neglect interval analysis and determines the optimum interval parameters. Furthermore, it can also effectively maximize the design scope. The optimizing ability of the IGA is tested through the interval optimization of a two-dimensional function. Then the IGA is applied to rotor-bearing systems. The results show that the IGA is effective in deriving optimal interval design parameters within the allowable error when minimizing shaft weight and/or transmitted force of rotor-bearing systems.