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In order to achieve the purpose of saving energy and reducing emission, the improvement of aerodynamic performance plays an increasingly crucial role for car manufacturers. Previous studies have confirmed the validity of gradient-based adjoint algorithm for its high efficiency in shape optimization. In this paper, two important aspects of adjoint approach were explored. One is vehicle aerodynamic optimization with multiple objectives, and the other is using time-averaged flow results as the primal solution, both are issues of high interest in recent applications. First, adjoint shape optimization with steady-state and time-averaged flow simulations were respectively calculated and comparatively discussed based on a production SUV. The shape modifications of the two cases indicated that the impact of primal solution on design change could not be neglected, due to the different intrinsic codes of steady and transient turbulence models.