The success of a consumer product is the result of not only engineering specifications but also emotional effects. Therefore, product design must be multidisciplinary as well as transdisciplinary across both natural and social science. In this work, we investigate the optimal design of vehicle silhouettes considering various aesthetic and engineering measures. The entire design problem is modeled as a bi-level structure with the top level being the aesthetic subproblem and the lower level consists of subproblems in the engineering discipline. This multi-level system provides a feasible approach in solving complex design problems; it also resembles the interactions of different departments in the auto industry. The aesthetic subproblem uses 11 proportionality measures and curvature to quantify a vehicle silhouette. The engineering discipline includes safety, handling, and aerodynamics of a vehicle with physical constraints on vehicle geometry. The design variables are the locations of 15 nodal points in describing the silhouette of a vehicle. The linking variables between subsystems are body and chassis dimensions that must be consistent for a design to be feasible. The optimal desi
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