Numerous Neural Combinatorial Optimization (NCO) solvers have been proposed to address Vehicle Routing Problems (VRPs). However, most of these solvers focus exclusively on single-vehicle VRP variants, overlooking the more realistic min-max Heterogeneous Capacitated Vehicle Routing Problem (MMHCVRP), which involves multiple vehicles. Existing MMHCVRP solvers typically select a vehicle and its next node to visit at each decoding step, but often make myopic decoding decisions and overlook key properties of MMHCVRP, including local topological relationships, vehicle permutation invariance, and node symmetry, resulting in suboptimal performance. To better address these limitations, we propose ECHO, an efficient NCO solver. First, ECHO exploits the proposed dual-modality node encoder to capture local topological relationships among nodes. Subsequently, to mitigate myopic decisions, ECHO employs the proposed Parameter-Free Cross-Attention mechanism to prioritize the vehicle selected in the preceding decoding step. Finally, leveraging vehicle permutation invariance and node symmetry, we introduce a tailored data augment strategy for MMHCVRP to stabilize the Reinforcement Learning training process. To assess the performance of ECHO, we conduct extensive experiments. The experimental results demonstrate that ECHO outperforms state-of-the-art NCO solvers across varying numbers of vehicles and nodes, and exhibits well-performing generalization across both scales and distribution patterns. Finally, ablation studies validate the effectiveness of all proposed methods.

翻译：众多神经组合优化求解器已被提出以解决车辆路径问题。然而，这些求解器大多仅关注单车辆VRP变体，忽视了更贴近实际、涉及多车辆的最小-最大异构容量车辆路径问题。现有的MMHCVRP求解器通常在每个解码步骤中选择一辆车辆及其下一个访问节点，但其解码决策往往具有短视性，且忽略了MMHCVRP的关键特性，包括局部拓扑关系、车辆排列不变性以及节点对称性，从而导致次优性能。为更好地应对这些局限，我们提出了ECHO，一种高效的NCO求解器。首先，ECHO利用所提出的双模态节点编码器来捕捉节点间的局部拓扑关系。随后，为缓解短视决策，ECHO采用所提出的无参数交叉注意力机制，优先考虑前一个解码步骤中选定的车辆。最后，借助车辆排列不变性和节点对称性，我们为MMHCVRP引入了一种定制化的数据增强策略，以稳定强化学习的训练过程。为评估ECHO的性能，我们进行了广泛的实验。实验结果表明，ECHO在不同车辆数量和节点数量的场景下均优于最先进的NCO求解器，并在问题规模和分布模式上均展现出良好的泛化能力。最后，消融研究验证了所有提出方法的有效性。