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.

翻译：图上的设施选址问题在现实世界中普遍存在且具有重要意义，但其求解常受限于NP难问题。近期，机器学习方法被提出用于解决此类经典问题，但局限于短视的构造性模式且仅考虑欧几里得空间中的问题。为克服这些局限，我们提出一个通用的基于交换的框架，用于解决图上的p-中值问题和设施重定位问题，并设计了一种对复杂图结构具有敏锐感知能力的新型强化学习模型。该方法在解质量与运行时间之间取得了和谐平衡，在复杂图数据集上超越了手工设计的启发式算法。此外，我们引入了一个图生成过程来模拟带有需求的实际城市道路网络，从而为经典问题构建大规模数据集。针对设施位置的初始化，我们为p-中值问题提出了一种受物理学启发的策略，能比随机策略获得更稳定的解。所提出的将经典交换方法与深度强化学习相结合的流水线，在处理图上设施选址相关的实际挑战方面迈出了重要一步。