Present paper describes the use of a stochastic search procedure that is the bases of genetic algorithms (GAs), in developing near-optimal topologies of load-bearing truss structures. Many works have been already published until today on the structural optimization of truss topology using the genetic algorithms. In most cases these works express the truss topology as a combination of members, and existence of each member is directly connected to the genetic code. These methods, however, have a fatal weak point. Namely when the topology is made along these methods, they might include needless members or those which lies on the other members. In addition to these problems, generated structures are not always stable. These problems become more remarkable when freedom of the problem becomes large. We have already proposed a new method that resolves those problems by expressing the truss topology as a combination of triangles that are joined with each other. However, the length of chromosome tends to become long. This paper proposes brand-new implements for effective optimization. Detail of the proposed methodology is presented as well as the results of numerical examples that clearly show effectiveness and efficiency of the present method.