This paper addresses the Capacitated Vehicle Routing Problem (CVRP) by comparing classical and quantum Reinforcement Learning (RL) approaches. An Advantage Actor-Critic (A2C) agent is implemented in classical, full quantum, and hybrid variants, integrating transformer architectures to capture the relationships between vehicles, clients, and the depot through self- and cross-attention mechanisms. The experiments focus on multi-vehicle scenarios with capacity constraints, considering 20 clients and 4 vehicles, and are conducted over ten independent runs. Performance is assessed using routing distance, route compactness, and route overlap. The results show that all three approaches are capable of learning effective routing policies. However, quantum-enhanced models outperform the classical baseline and produce more robust route organization, with the hybrid architecture achieving the best overall performance across distance, compactness, and route overlap. In addition to quantitative improvements, qualitative visualizations reveal that quantum-based models generate more structured and coherent routing solutions. These findings highlight the potential of hybrid quantum-classical reinforcement learning models for addressing complex combinatorial optimization problems such as the CVRP.

翻译：本文通过比较经典与量子强化学习方法，研究带容量约束的车辆路径问题。我们实现了经典、全量子和混合三种变体的优势演员-评论家智能体，并集成Transformer架构，通过自注意力与交叉注意力机制捕捉车辆、客户与配送中心之间的关联关系。实验聚焦于具有容量约束的多车辆场景，考虑20个客户和4辆车辆，并进行了十次独立运行。性能通过路径距离、路径紧凑性和路径重叠度进行评估。结果表明，三种方法均能学习到有效的路径规划策略。然而，量子增强模型在性能上超越了经典基线，并产生了更稳健的路径组织形式，其中混合架构在距离、紧凑性和路径重叠度方面均取得了最佳综合表现。除量化改进外，定性可视化分析表明，基于量子的模型能生成更具结构性和连贯性的路径解决方案。这些发现凸显了混合量子-经典强化学习模型在解决CVRP等复杂组合优化问题中的潜力。