For the design type of inverse bifurcation problems, there exists previous work in the engineering literature: The distance to bifurcation manifolds has been introduced to quantify the "parametric robustness" of system designs in [15]; in the context of design of chemical processes, optimization problems with constraints involving distance to bifurcation manifolds have been treated in [16]. For a recent review see [17]. For biological applications as we have them in mind, this issue of parametric robustness is also important. In addition, other geometric properties of the bifurcation diagram are of interest. These include the size of the parameter region resulting in bistability of solutions and the parametric distance between regions of different qualitative behavior. We will develop methodolgies by which inverse bifurcation problems involving the optimization of such quantities can be solved.