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Computation offloading is a main issue in multi-access edge computing (MEC). In particular, in aerial MEC (AMEC) relying on UAVs/ drones, due to limited resources of single devices in providing services to end users, we always have to offload tasks to different devices within the network. However, in wireless communications, there are obstacles in transmission distance between devices sending out offloading requests and others with idle resources. Furthermore, UAVs in AMEC also have to face the challenges of limited energy supply from batteries. As a result, in this article, we design a Monte Carlo tree search enhanced hybrid strategy in achieving time- and energy-aware computation offloading for AMEC. The simulation results show that the proposed solutions can greatly reduce time cost and energy consumption while using UAVs as flying offloaders.