DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems
<|reference_start|>DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems: The min-max vehicle routing problem (min-max VRP) traverses all given customers by assigning several routes and aims to minimize the length of the longest route. Recently, reinforcement learning (RL)-based sequential planning methods have exhibited advantages in solving efficiency and optimality. However, these methods fail to exploit the problem-specific properties in learning representations, resulting in less effective features for decoding optimal routes. This paper considers the sequential planning process of min-max VRPs as two coupled optimization tasks: customer partition for different routes and customer navigation in each route (i.e., partition and navigation). To effectively process min-max VRP instances, we present a novel attention-based Partition-and-Navigation encoder (P&N Encoder) that learns distinct embeddings for partition and navigation. Furthermore, we utilize an inherent symmetry in decoding routes and develop an effective agent-permutation-symmetric (APS) loss function. Experimental results demonstrate that the proposed Decoupling-Partition-Navigation (DPN) method significantly surpasses existing learning-based methods in both single-depot and multi-depot min-max VRPs. Our code is available at<|reference_end|>
@article{zheng2024dpn:,
    title={DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max
  Vehicle Routing Problems},
    author={Zhi Zheng, Shunyu Yao, Zhenkun Wang, Xialiang Tong, Mingxuan Yuan, Ke
  Tang},
    journal={arXiv preprint arXiv:2405.17272},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.17272},
    primaryClass={cs.LG cs.AI}
}