In this paper, we propose an approach for design optimization aiming at reduction of mechanical vibration under complicated conditions. Machine structures in operation generally require reduced vibrational response, which must be evaluated at many response and excitation points. Moreover, multiple vibrational natural modes of the machines must also be taken into account. The design optimization problem is first formulated on the basis of a multiobjective optimization method. Then, the weighted mini-max method with the Tchebychev norm is presented to solve the optimization problem. This approach is then demonstrated for a motorcycle frame design in which the frame is subjected to engine excitation with many directional components and the vibrational response is evaluated at three points : the handlebar end, the front footrest and the rear footrest.