AIAM: Adaptive interactive attention model for solving p-Median problem via deep reinforcement learning

The p-Median Problem (PMP) is a classical discrete facility location problem with significant implications for optimizing the placement of urban public service facilities. Improved heuristics, a well-established method for solving the PMP, aim to iteratively enhance solution quality through efficient neighborhood exploration. In this study, we model the neighborhood exploration process as a Markov decision process and propose a novel deep reinforcement learning approach to solving the PMP, achieving higher problem-solving efficiency and quality. The proposed method introduces an encoder-decoder structure, consisting of an Interactive Attention Encoder (IAE), a Node Removal Decoder (NRD), and a Node Insertion Decoder (NID), aimed at learning an optimal strategy for node selection. The experimental results demonstrate that our approach outperforms genetic algorithms in terms of both accuracy and computational efficiency. While the solution time is slightly longer than that of the Attention Model (AM), our method achieves a reduced gap to the optimal solution. Furthermore, ablation studies confirm that the proposed adaptive interactive encoder and the two decoders significantly enhance the model performance. Finally, we applied the Adaptive Interactive Attention Model (AIAM) to a real-world scenario, demonstrating its practical utility in guiding medical facility location decisions.