This study deals with the parametric design and the optimization of pedestrian steel structures that are particularly significant in the field of civil engineering. Structural optimization is performed through the use of genetic algorithms. In particular, Grasshopper parametric analysis solver is used, by implementing the Galapagos algorithm. The optimization is carried out in terms of both weight and shape. Three models of simply-supported beams, with a span equal to 20 m, are considered: a truss girder, an arch with orthogonal ropes and a network arch. In the first structure, the design variables are represented by the cross-section and the geometric arrangement of the elements constituting the beam. In the case of the arch and the network beams, the design variables are the width of the arch curvature, the cross-section of the different components and the arrangement of internal ropes. In all optimization procedures the weight of the structure is assumed as the objective function and the attention is focused on hollow circular sections. The performed analyses show that the network arch represents the optimal model. In fact, it is characterized by normal and bending stresses lower than the other typologies and by the lowest weight and then cost. There is an inverse relationship between the angle of curvature of the top chord and the number of ropes. The cross section of the top chord is bigger than the one of the bottom chord, as well as diagonals are characterized by smaller cross sections, coherently with previous literature studies.