As a standardized software framework and open E/E system architecture, the AUTomotive Open System ARchitecture (AUTOSAR) has been widely applied to autonomous driving systems to enable real-time control. However, due to the increasing design complexity and the lack of efficient algorithms and design automation tools, it is difficult to quickly figure out an optimal task scheduling scheme for an AUTOSAR-based system. To address this problem, we introduce a novel task scheduling method that can parallelly search for an optimal solution with the help of our proposed pruning strategy. Experimental results on a real-world AUTOSAR-based autonomous driving system demonstrate that our approach can achieve much better task scheduling solutions than the ones obtained manually and significantly reduce the overall task scheduling time.