The airflow into the engine bay of a passenger car is used for cooling down essential components of the vehicle, such as powertrain, air-conditioning compressor, intake charge air, batteries, and brake systems, before it returns back to the external flow. When the intake ram pressure becomes high enough to supply surplus cooling air flow, this flow can be actively regulated by using arrays of grille shutters, namely active grille shutters (AGS), in order to reduce the drag penalty due to excessive cooling. In this study, the operation of AGS for a generic SUV-type model vehicle is optimized for improved fuel economy on a highway drive cycle (part of SFTP-US06) by using surrogate models. Both vehicle aerodynamic power consumption and under-hood cooling performance are assessed by using PowerFLOW, a high-fidelity flow solver that is fully coupled with powertrain heat exchanger models. The fuel economy calculation is based on a quasi-static drive cycle simulation where the engine power is calculated to match drive cycle loads from aerodynamic forces, translational and rotational inertia, rolling resistance, transmission and tire slip losses, and auxiliary parts. The engine heat rejection is calculated from these same loads. The operation of AGS opening is determined by minimizing instantaneous vehicle aerodynamic power constrained by the radiator heat rejection requirement. The improved fuel economy of actively controlled AGS is then compared to the cases with fully open and scheduled operations. The approach in this study provides an effective framework for the design of fuel-efficient vehicles in earlier design stages.