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Adaptive cruise control (ACC), as one of the advanced driver assistance systems (ADAS), has become increasingly popular in improving both driving safety and comfort. Since the objectives of ACC can be multi-dimensional, and often conflict with each other, it is a challenging task in its control design. The research presented in this paper takes ACC control design as a constrained optimization problem with multiple objectives. A hierarchical framework for ACC control is introduced, aimed to achieve optimal performance on driving safety and comfort, speed and/or distance tracking, and fuel economy whenever possible. Under the hierarchical framework, the operational mode is determined in the upper layer, in which a model predictive control (MPC) based spacing controller is employed to deal with the multiple control objectives. On the other hand, the lower layer is for actuator control, such as braking and driving control for vehicle longitudinal dynamics.