用量子增强的Transformer模型解决车辆路径优化问题，效果优于传统方法。
Quantum Reinforcement Learning with Transformers for the Capacitated Vehicle Routing Problem
- 结合Transformer与量子计算的混合强化学习框架
- 混合模型在距离、紧凑性、重叠度上均表现最佳
- 适合研究量子机器学习在组合优化中的应用
本文通过对比经典与量子强化学习方法，解决带容量约束的车辆路径问题（CVRP）。采用A2C智能体实现经典、全量子和混合三种变体，引入Transformer架构，利用自注意力与交叉注意力捕捉车辆、客户与枢纽之间的关系。实验设定20个客户点和4辆车辆，进行十次独立运行，评估指标包括路径距离、路线紧凑性和重叠度。结果表明，三种方法均能学习有效路径策略；其中，量子增强模型优于经典基线，生成更稳健的路线结构，混合架构在距离、紧凑性和重叠度上综合表现最优。定性可视化显示，量子模型生成的路径更具结构性与一致性。这些发现凸显了混合量子-经典强化学习在解决复杂组合优化问题中的潜力。
原文摘要 · Abstract (English)
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.
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