Structural design can significantly improve if numerical optimization is used, especially for large space structures like geodesic dome. However, the optimization problems for structural optimization consist of ill-behaved discontinuous and non-differentiable functions, are difficult to solve by traditional optimization techniques using sensitivity analysis. Therefore the intuitive and heuristic techniques like genetic algorithm and generalized pattern search algorithm which allow the flexible formulation can be the most powerful tools for structural design. For structural design problems it is unclear how the genetic algorithm and generalized pattern search algorithm perform. I am interested in how these algorithms perform if used in conjunction with the functions for the design of geodesic dome. In this paper I will show what can be expected from the two algorithms and compare their performance in minimizing the weight of the geodesic dome structure. From the optimum structural design point of view the objective of dome design is to determine the appropriate steel sections for each member group of a dome from the available steel sections set such that with these set of sections the response of the dome structure is within the limitations imposed by the design code and it has the minimum weight. The optimization algorithms determine the sectional designations for the members of a geodesic dome under the external loads. The steel pipe sections list of the reference [5] which were used commonly in Korea are adopted for the cross sections of dome members. The algorithms select appropriate sections from this list such that the weight of dome becomes the minimum. The numerical results show that the generalized pattern search algorithm is more efficient than the genetic algorithm in the optimization of the geodesic dome.