Topology optimization of trusses using genetic algorithm, force method and graph theory

摘要

In this article size/topology optimization of trusses is performed using a genetic algorithm (GA), the force method and some concepts of graph theory. One of the main difficulties with optimization with a GA is that the parameters involved are not completely known and the number of operations needed is often quite high. Application of some concepts of the force method, together with theory of graphs, make the generation of a suitable initial population well-matched with critical paths for the transformation of internal forces feasible. In the process of optimization generated topologically unstable trusses are identified without any matrix manipulation and highly penalized. Identifying a suitable range for the cross-section of each member for the ground structure in the list of profiles, the length of the substrings representing the cross-sectional design variables are reduced. Using a contraction algorithm, the length of the strings is further reduced and a GA is performed in a smaller domain of design space. The above process is accompanied by efficient methods for selection, and by using a suitable penalty function in order to reduce the number of numerical operations and to increase the speed of the optimization toward a global optimum. The efficiency of the present method is illustrated using some examples, and compared to those of previous studies.