提出新框架提升神经方法处理复杂车辆路径约束能力。
Learning to Handle Complex Constraints for Vehicle Routing Problems
- 用拉格朗日乘子增强约束感知,提前预防不可行解
- 在TSPTW和TSPDL上降低不可行率,提升解质量
- 通用框架可适配多种神经模型,训练更高效
车辆路径问题(VRP)可建模众多现实场景,常涉及复杂约束。现有神经方法虽能基于可行性掩码构造解,但在处理复杂约束时表现不佳,尤其当掩码获取本身属于NP难问题。本文提出一种新型主动不可行预防(Proactive Infeasibility Prevention, PIP)框架,推动神经方法应对更复杂的VRP。PIP以拉格朗日乘子为基础增强约束感知,并引入预防性不可行掩码,主动引导解的构建过程。此外,我们提出PIP-D,采用辅助解码器和两种自适应策略,学习并预测定制化掩码,在显著降低训练计算成本的同时提升性能。通过在具有挑战性的带时间窗旅行商问题(TSPTW)和带拖曳限制旅行商问题(TSPDL)上进行大量实验,验证了PIP设计的有效性。结果表明,PIP具有通用性,能显著降低不可行解率并大幅提升解的质量。
原文摘要 · Abstract (English)
Vehicle Routing Problems (VRPs) can model many real-world scenarios and often involve complex constraints. While recent neural methods excel in constructing solutions based on feasibility masking, they struggle with handling complex constraints, especially when obtaining the masking itself is NP-hard. In this paper, we propose a novel Proactive Infeasibility Prevention (PIP) framework to advance the capabilities of neural methods towards more complex VRPs. Our PIP integrates the Lagrangian multiplier as a basis to enhance constraint awareness and introduces preventative infeasibility masking to proactively steer the solution construction process. Moreover, we present PIP-D, which employs an auxiliary decoder and two adaptive strategies to learn and predict these tailored masks, potentially enhancing performance while significantly reducing computational costs during training. To verify our PIP designs, we conduct extensive experiments on the highly challenging Traveling Salesman Problem with Time Window (TSPTW), and TSP with Draft Limit (TSPDL) variants under different constraint hardness levels. Notably, our PIP is generic to boost many neural methods, and exhibits both a significant reduction in infeasible rate and a substantial improvement in solution quality.
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