Graph representation for structural topology optimization using genetic algorithms

This paper proposes a graph representation for evolutionary structural topology design. Based on graph theory, a valid topology in the design domain is represented by a connected simple graph and each edge of the graph is defined by a cubic Bézier curve with varying thickness. The graph is defined to have connecting paths between loading regions and support regions of the structure, to ensure a physically meaningful connected structure. Each path is formed by one or more Bézier curves in order to allow more local control of the shape. A real-valued chromosome encoding and decoding scheme and a partition crossover method are also developed based on graph theory. The graph representation GA is applied to structural topology optimization problems and its performance is compared with those of other methods. Compared with the power-law approach, the present graph representation GA can generate clearly defined and distinct geometries and perform a global search, but it requires more computational cost. The numerical results also demonstrate the improved performance of the present graph representation over that of the Voronoi-bar representation in terms of connectivity of the geometry and convergence speed. It is suggested that this graph representation method is both physically meaningful and computationally effective in the framework of topological optimum design using GAs.