In this paper, a multi-objective nonlinear programming method is proposed. That is, the problems which have fuzzy multiple objective functions and constraints with GUB (Generalized Upper Bounding) structure are solved by the proposed Hybridized Genetic Algorithms (HGA). This approach enables a flexible optimal system design by applying fuzzy goals and fuzzy constraints. In this Genetic Algorithm (GA), we propose a new chromosome representation that represents the GUB structure simply and effectively at the same time. Also, by introducing the HGAs that combine the proposed heuristic algorithm and makes use of the peculiarity of GUB structure to GA, the proposed approach is more efficient than the previous method in finding a solution. Further, to demonstrate the effectiveness of the proposed method, a large-scale optimal system reliability design problem is introduced.