In the last six decades closed-box orthotropic steel girders have been widely used in cable supported bridges. Several parametric studies were previously carried out in order to reduce inherent fatigue stress problems and in general to improve the bridge girder designs. However, in most cases, only one or two parameters were studied simultaneously, hence the full potential of orthotropic girders is not achieved. In the present work, a multi-scale FE model of a suspension bridge is established with sophisticated boundary conditions applied to a local parametric sub-model of a bridge girder. With this local model an automated gradient-based parametric optimization is carried out with the goal of minimizing weight or price of the girder. It is thus possible to optimize several design variables simultaneously, and concurrently fulfilling constraint functions on fatigue stresses, deformation and buckling. The results show potential weight savings of 6-14% and price savings of 9-17%, mainly found by thinner plates and narrower troughs. Besides the explicit savings, the results indicate the potential of applying gradient-based optimization in civil engineering designs.