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This paper describes a method to arrive at a feasible solution which can not be found in the linearly approximated constrained domain and a process which would reduce the number of finite element analyses to obtain a designer's preferable solution. The feasible solution is obtained by adapting the goal programming method, in which the weighting factors depending on maximum allowable performance variables and performance sensitivities are used. The designer's preferable solution is obtained by presenting the linear approximated trade-off curves after taking into account the designer's rough preference. Two applications of optimization for compliances of a passenger car rear suspension system are described, in which spring stiffness and installation angles of insulators are treated as the design variables.