Recently, laminated composite plates have been applied to many aircraft structures because their mechanical properties are superior to those of conventional materials. Since the laminates have anisotropic elastic properties, an optimum design is needed to make advantageous use of composite laminates. The authors have proposed a successful object-oriented expert system to design laminated composites with actual constraints. A solution to optimize the fiber orientation of stiffeners around open holes, however, has not yet been developed because it is very difficult and requires stress redistribution analysis. In this study, therefore, genetic algorithms (GA) were applied to solve the optimization problem by the object-oriented finite-element stress analysis method. Results obtained were as follows. (1) The GA method is applicable to an open hole model. (2) The random search method is easily applicable to any model.