In this paper, we study the shortest path problem (SPP) with multiple source-destination pairs (MSD), namely MSD-SPP, to minimize average travel time of all shortest paths. The inherent traffic capacity limits within a road network contributes to the competition among vehicles. Multi-agent reinforcement learning (MARL) model cannot offer effective and efficient path planning cooperation due to the asynchronous decision making setting in MSD-SPP, where vehicles (a.k.a agents) cannot simultaneously complete routing actions in the previous time step. To tackle the efficiency issue, we propose to divide an entire road network into multiple sub-graphs and subsequently execute a two-stage process of inter-region and intra-region route planning. To address the asynchronous issue, in the proposed asyn-MARL framework, we first design a global state, which exploits a low-dimensional vector to implicitly represent the joint observations and actions of multi-agents. Then we develop a novel trajectory collection mechanism to decrease the redundancy in training trajectories. Additionally, we design a novel actor network to facilitate the cooperation among vehicles towards the same or close destinations and a reachability graph aimed at preventing infinite loops in routing paths. On both synthetic and real road networks, our evaluation result demonstrates that our approach outperforms state-of-the-art planning approaches.
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