FIG. 5 illustrates a set of forces generated via the setup engine of FIG. 2 and associated with the design problem geometry of FIG. 3, according to various embodiments of the present invention. As shown, GUI 214 includes, without limitation, a set of forces 500 associated with design problem geometry 330. The end-user may define forces 500 via tools provided in toolbar 310. Each force 500 may represent a force applied to a specific location on design problem geometry 330, a force applied to a specific location on reference geometry 400, or a force applied to a location proximate to design problem geometry 330. Generally, forces 500 are to be balanced by a feasible design solution. Thus, forces 500 represent one form of design objective. The end-user may also add constraints to design geometry 330 via interactions with GUI 214, including geometric constraints, physical constraints, manufacturing constraints, and so forth.

As the end-user generates design problem geometry, adds design objectives and/or design constraints, and generally fleshes out design space 300, setup engine 202 updates problem specification 202, as mentioned above. With each change made to problem specification 202, analysis engine 204 analyzes design space 300, design problem geometry 330, and other data within that problem specification to determine whether sufficient information exists to generate at least a coarse design solution that roughly approximates a feasible design solution.