This paper is to find optimum design of plane framed structures with discrete variables. Global search algorithms for this problem are Genetic Algorithms(GAs), Simulated Annealing(SA) and Shuffled Complex Evolution(SCE), and hybrid methods (GAs-SA, GAs-SCE). GAs and SA are heuristic search algorithms and effective tools which is finding global solution for discrete optimization. In particular, GAs is known as the search method to find global optimum or near global optimum. In this paper, reinforced concrete plane frames with rectangular section and steel plane frames with W-sections are used for the design of discrete optimization. These structures are designed for stress constraints. The robust and effectiveness of Genetic Algorithms are demonstrated through several examples.