Unified and Generalizable Reinforcement Learning for Facility Location Problems on Graphs

Facility location problems on graphs are ubiquitous in the real world and hold significant importance, yet their resolution is often impeded by NP-hardness. MIP solvers can find the optimal solutions but fail to handle large instances, while algorithm efficiency has a higher priority in cases of emergency. Recently, machine learning methods have been proposed to tackle such classical problems with fast inference, but they are limited to the myopic constructive pattern and only consider simple cases in Euclidean space. This paper introduces a unified and generalizable approach to tackle facility location problems on weighted graphs with deep reinforcement learning, demonstrating a keen awareness of complex graph structures. Striking a harmonious balance between solution quality and running time, our method stands out with superior efficiency and steady performance. Our model trained on small graphs is highly scalable and consistently generates high-quality solutions, achieving a speedup of more than 2000 times to Gurobi on instances with 1000 nodes. The experiments on Shanghai road networks further demonstrate its practical value in solving real-world problems. The source codes are available at https://github.com/AryaGuo/PPO-swap.