The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different vehicle profiles, with each having a preference or constraint on a per-client basis. While existing learning methods have shown promise for solving the HCVRP in real-time, no learning method exists to solve the more practical and challenging PVRP. In this paper, we propose a Collaborative Attention Model with Profiles (CAMP), a novel approach that learns efficient solvers for PVRP using multi-agent reinforcement learning. CAMP employs a specialized attention-based encoder architecture to embed profiled client embeddings in parallel for each vehicle profile. We design a communication layer between agents for collaborative decision-making across profiled embeddings at each decoding step and a batched pointer mechanism to attend to the profiled embeddings to evaluate the likelihood of the next actions. We evaluate CAMP on two variants of PVRPs: PVRP with preferences, which explicitly influence the reward function, and PVRP with zone constraints with different numbers of agents and clients, demonstrating that our learned solvers achieve competitive results compared to both classical state-of-the-art neural multi-agent models in terms of solution quality and computational efficiency. We make our code openly available at https://github.com/ai4co/camp.

本研究解决了档案车辆路径规划问题（PVRP），这是异质限制车辆路径规划问题（HCVRP）的一个扩展，旨在优化车辆服务客户需求的路线。提出的协作注意力模型（CAMP）利用多智能体强化学习，采用专门的注意力编码器架构，实现对不同车辆档案的高效求解，实验表明CAMP在解决质量和计算效率上与传统前沿神经多智能体模型竞争。 

基于档案的协作注意力模型（CAMP）用于车辆路径规划问题