A multi-objective graph reinforcement learning framework for urban public facility location problem

Effective public facility location planning plays a crucial role in sustainable urban development, requiring the reconciliation of conflicting objectives to determine an optimal spatial configuration. Deep reinforcement learning (DRL) has shown great promise in single-objective facility location problems, offering adaptive and end-to-end learning capabilities for complex spatial decision-making. However, previous works in this domain either fail to approximate the entire Pareto front (PF), or are restricted by the limited representational capacity of a single policy to accurately generalize across the highly non-linear spatial topology. To address these shortcomings, this study introduced the framework of Multi-Objective Graph Reinforcement Learning (MOGRL), a decomposition-based multi-policy approach. This framework decomposes multi-objective optimization tasks into a series of single-objective subproblems and employs a parameter transfer strategy to establish a collaborative learning process across subproblems, thereby enhancing the quality of the final PF. By incorporating graph-based spatial representations, the framework flexibly adapts to diverse spatial topologies. Extensive experiments on simulated and real-world datasets in this study demonstrated that MOGRL not only approximates high-quality PF more effectively than classical multi-objective evolutionary algorithms, but also maintains robust performance across varying problem scales and scenarios. This work contributes a spatially generalizable DRL-based approach to multi-objective facility location optimization, offering promising potential for real-world urban decision-making.