## 1 Introduction
### Distributed and Hybrid Solutions  
Distributed methods allow AGVs to plan their paths independently using only locally available information, without requiring global data or dependence on a central planning system. These distributed navigation models are typically trained using imitation learning or reinforcement learning techniques. Multi-agent reinforcement learning (MARL) is widely used in MAPF and can be broadly divided into the following four categories:  
First, in the analysis of emergent behaviors, also called independent learning (IL), each agent treats all other agents as part of the environment and independently applies single-agent RL algorithms to interact and act in a way that maximize its own reward (e.g., IQL [20], IPPO [21]). Next, with learning communication, agents exchange explicit messages to share intentions. During training, they learn when and what to communicate based on their local observations, deciding whether to send a message, what information to include, and which peers to address (e.g., NDQ [22]). Learning cooperation involves using centralized training with decentralized execution. Agents learn implicit cooperation strategies by sharing value or policy information during training but acting individually at runtime (e.g., VDN [22], QMIX [23], QTRAN [24], MADDPG [25], COMA [26]). Finally, in agent modeling, agents build models of the policies, goals, or types of other agents to predict their actions and achieve more effective coordination (e.g., ToMnet [27]). However, reinforcement learning-based distributed navigation strategies face challenges such as sparse rewards, leading to slow convergence. Several approaches have been explored to address these issues, including the following:  
Imitation and Reinforcement Learning: A previous study [28] proposed a learning framework called PRIMAL to train a distributed solution model, which combined reinforcement learning and imitation learning to improve model convergence and reduce training costs. Based on PRIMAL, PRIMAL2 [29] was developed and introduced specialized optimizations for corridor structures on the obstruction map to alleviate the problem of AGV blocking in narrow aisles. The centralized system would provide the distributed system with early warnings of corridor structures, as well as information about other AGVs in the corridor structures. Task Decomposition to Shorten Decision Chain: Previous research [30; 31] proposed an evolutionary reinforcement learning-based method called MAPPER. Under the guidance of a central planner, the algorithm would decompose long-duration tasks into multiple simpler tasks to help the distributed planner. This method mitigates the sparse rewards problem and improves agent performance in large-scale environments. Enhanced Communication Methods: The literature [32] proposed a distributed method based on prioritized communication learning called PICO. PICO would integrate implicit planning priorities into a decentralized MARL framework, enabling a dynamic communication topology for effective collision avoidance. Another study [33] proposed a distributed method based on Message-Aware Graph Attention Networks (MAGATs), which use a query-key mechanism to determine the relative importance of information from neighboring agents. A request-response communication protocol, DCC [34] was proposed to allow each agent to select the nearby agents whose messages are more likely to influence its own policy. Problem Decomposition: A previous study [35] proposed a hybrid solution that divided MAPF into two sub-tasks to reach the goal and avoid collisions, solved each with RL methods, and then merged the learned \"goal reach\" and \"collision avoidance\" policies into a unified strategy. Providing Additional Immediate Rewards: Some methods introduce artificial potential fields as extra rewards to mitigate the sparse reward problem [36]. Others use A* guidance, offering extra rewards for following or returning to the guided path [37].