Facility location problems on graphs are ubiquitous in real world and hold significant importance, yet their resolution is often impeded by NP-hardness. Recently, machine learning methods have been proposed to tackle such classical problems, but they are limited to the myopic constructive pattern and only consider the problems in Euclidean space. To overcome these limitations, we propose a general swap-based framework that addresses the p-median problem and the facility relocation problem on graphs and a novel reinforcement learning model demonstrating a keen awareness of complex graph structures. Striking a harmonious balance between solution quality and running time, our method surpasses handcrafted heuristics on intricate graph datasets. Additionally, we introduce a graph generation process to simulate real-world urban road networks with demand, facilitating the construction of large datasets for the classic problem. For the initialization of the locations of facilities, we introduce a physics-inspired strategy for the p-median problem, reaching more stable solutions than the random strategy. The proposed pipeline coupling the classic swap-based method with deep reinforcement learning marks a significant step forward in addressing the practical challenges associated with facility location on graphs.

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