Simultaneous topology and sizing optimization of trusses by an improved Genetic algorithm

The paper presents an improved Genetic algorithm for the topology optimization of trusses to minimize the weight with stress and displacement constraints under multiple load cases. Based on given planar nodes, the initial population of Genetic algorithm, i.e., the topology of truss structures is generated by Delaunay triangulation and heuristic method. This method can ensure the feasibility and diversity of initial individuals. The upper triangle of adjacent matrix is used to encode the topology of trusses with the corresponding relationship between chromosomes and truss members. The position of a gene is used to represent a member and the value of a gene is used to represent cross-sectional area of corresponding member. So, mixed representation with binary string and real-value vector is chosen. This representation makes the chromosomes have the same and shorter length depended on the nodes´ numbers of the truss structure and realizes simultaneous topology and sizing optimization. q-tournament selection strategy enables the good individuals being held in the next generation. Two-point crossover is adopted to mainly change the topology and Gaussian mutation acts on every gene with non-zero value to evolve cross-sectional areas. A penalty term is added to the objective function for any violation of the constraints. Full stress method is used to prevent premature convergence. Finally, the effectiveness of the algorithm is demonstrated by one numerical example.