arXiv 2505.246272025-10-30cs.LG

重新思考面向不同约束紧密度的车辆路径问题的神经组合优化

Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees

School of Automation and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen, China（自动化与智能制造学院，南方科技大学，深圳，中国）；Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology, Shenzhen, China（广东省全驱动系统控制理论与技术重点实验室，南方科技大学，深圳，中国）；Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, Eindhoven, The Netherlands（工业工程与创新科学系，埃因霍温理工大学，埃因霍温，荷兰）；School of Computing, National University of Singapore, Singapore（计算学院，新加坡国立大学）

Fu Luo, Yaoxin Wu, Zhi Zheng, Zhenkun Wang

备注：: Accepted at NeurIPS 2025

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AI总结：

针对现有神经组合优化方法对车辆路径问题约束过拟合、仅适配小范围约束紧密度的问题，提出考虑约束紧密度变化的训练方案与多专家模块，在多类约束紧密度的CVRP、CVRPTW上实现更优性能。

摘要：

近期的神经组合优化（neural combinatorial optimization, NCO）方法已展现出可观的问题求解能力，且无需领域特定专业知识。现有多数NCO方法采用约束值固定的训练与测试数据，缺乏约束紧密度对NCO方法性能影响的相关研究。本文以带容量约束的车辆路径问题（capacity-constrained vehicle routing problem, CVRP）为例，实证分析了容量约束不同紧密度下的NCO性能。分析表明，现有NCO方法会对容量约束过拟合，仅能在小范围约束值上取得令人满意的性能，在其他取值上表现不佳。为解决现有NCO方法的这一缺陷，我们设计了一种显式考虑不同约束紧密度的高效训练方案，并提出多专家模块以学习具备普遍适应性的求解策略。实验结果显示，所提方法能有效克服过拟合问题，在多种约束紧密度的CVRP以及带时间窗的CVRP（CVRPTW）上均展现出更优性能。

英文摘要：

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack research on the effect of constraint tightness on the performance of NCO methods. This paper takes the capacity-constrained vehicle routing problem (CVRP) as an example to empirically analyze the NCO performance under different tightness degrees of the capacity constraint. Our analysis reveals that existing NCO methods overfit the capacity constraint, and they can only perform satisfactorily on a small range of the constraint values but poorly on other values. To tackle this drawback of existing NCO methods, we develop an efficient training scheme that explicitly considers varying degrees of constraint tightness and proposes a multi-expert module to learn a generally adaptable solving strategy. Experimental results show that the proposed method can effectively overcome the overfitting issue, demonstrating superior performances on the CVRP and CVRP with time windows (CVRPTW) with various constraint tightness degrees.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。