I think that one of the my favourite software regarding bridge analysis, modeling and advanced simulation is Midas Civil. I had good experience in the past using this kind of numerical fem software.
Once you have the results of analysis. RRP explorer developed by Prof. Benny Raphael can be used for optimization. It is a multi criteria objective optimisation algorithm in which you can give priorities and sensitivities .It would give an optimum results. If you could export different results from Staad or SAP and code to get the required results in excel, this algorithm would create a pareto front and help in identifying an optimal solution based on your priorities and sensitivities.
Sofistik is very good solution for bridge design. A lot of things can be defined in a parametric manner (e.g. cross section dimensions, bridge axis, position of columns, tendon paths, etc.), either by graphical pre-processor or textually by code, so you can change the parameters very quickly and search for the optimal solution. You can even control the software iterativelly by writing your specific code in its input programming language (kind of intuitive). Good luck