arXiv:2601.15038cs.LGcs.AI2026-01被引 1

用分阶段训练让AI更稳定地解决电动车配送路线难题。

A Curriculum-Based Deep Reinforcement Learning Framework for the Electric Vehicle Routing Problem

  • 分三阶段逐步提升难度,先学距离与车队优化,再学电池管理,最后处理完整问题。
  • 在10个客户的小规模数据上训练,能准确应对5到100个客户的未知场景。
  • 适合需要快速生成可靠配送方案的物流与能源领域从业者使用。

电动车辆路径问题带时间窗(EVRPTW)是可持续物流中的复杂优化问题,需在满足严格客户时间约束的前提下,最小化总行驶距离、车队规模和电池消耗。尽管深度强化学习(DRL)展现出替代传统启发式与精确求解器的潜力,现有DRL模型常因约束密集而难以保持训练稳定性,出现无法收敛或泛化失败。本文提出一种基于课程学习的深度强化学习框架(CB-DRL),通过结构化的三阶段课程逐步增加问题复杂度:第一阶段(Phase A)学习距离与车队优化,第二阶段(Phase B)学习电池管理,第三阶段(Phase C)处理完整EVRPTW。为确保各阶段学习稳定,采用改进的近端策略优化算法,结合阶段特定超参数、值函数与优势裁剪及自适应学习率调度。策略网络基于异构图注意力编码器,融合全局-局部注意力与特征逐维线性调制,显式建模仓库、客户与充电站的差异属性。模型仅在小规模实例(N=10)上训练,即可稳健泛化至未见实例(N=5至100),在中等规模问题上显著优于标准基线。实验表明,该课程引导方法在分布外实例上实现高可行性率与竞争力解质量,有效弥合神经网络速度与实际运行可靠性之间的差距。

原文摘要 · Abstract (English)

The electric vehicle routing problem with time windows (EVRPTW) is a complex optimization problem in sustainable logistics, where routing decisions must minimize total travel distance, fleet size, and battery usage while satisfying strict customer time constraints. Although deep reinforcement learning (DRL) has shown great potential as an alternative to classical heuristics and exact solvers, existing DRL models often struggle to maintain training stability-failing to converge or generalize when constraints are dense. In this study, we propose a curriculum-based deep reinforcement learning (CB-DRL) framework designed to resolve this instability. The framework utilizes a structured three-phase curriculum that gradually increases problem complexity: the agent first learns distance and fleet optimization (Phase A), then battery management (Phase B), and finally the full EVRPTW (Phase C). To ensure stable learning across phases, the framework employs a modified proximal policy optimization algorithm with phase-specific hyperparameters, value and advantage clipping, and adaptive learning-rate scheduling. The policy network is built upon a heterogeneous graph attention encoder enhanced by global-local attention and feature-wise linear modulation. This specialized architecture explicitly captures the distinct properties of depots, customers, and charging stations. Trained exclusively on small instances with N=10 customers, the model demonstrates robust generalization to unseen instances ranging from N=5 to N=100, significantly outperforming standard baselines on medium-scale problems. Experimental results confirm that this curriculum-guided approach achieves high feasibility rates and competitive solution quality on out-of-distribution instances where standard DRL baselines fail, effectively bridging the gap between neural speed and operational reliability.

强化学习路径优化电动车课程学习

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