VAGPO：面向图路由问题的视觉增强非对称群组偏好优化
VAGPO: Vision-augmented Asymmetric Group Preference Optimization for Graph Routing Problems
AI总结：
本文提出视觉增强非对称群组偏好优化方法（VAGPO），结合ResNet和Transformer捕获图路由问题的时空特征，通过非对称群组偏好优化加速收敛，在TSP和CVRP上实现高质量求解并具备大规模泛化能力。
摘要：
图路由问题在网络相关的网络中扮演着至关重要的角色，其中在图中寻找最优路径对于高效的数据传输和内容分发必不可少。诸如旅行商问题（TSP）和带容量约束的车辆路径问题（CVRP）等经典路由形式化代表了基础的图优化挑战。近期数据驱动的优化方法取得了显著进展，但它们在训练效率和对大规模实例的泛化能力上常面临局限。在本文中，我们提出了一种新颖的视觉增强非对称群组偏好优化（VAGPO）方法。通过利用基于ResNet的视觉编码和基于Transformer的序列建模，VAGPO同时捕获了空间结构和时间依赖性。此外，我们引入了一种非对称群组偏好优化策略，与常用的策略梯度方法相比，该策略显著加速了收敛。在生成的TSP和CVRP实例以及真实世界数据集上的实验结果表明，所提出的VAGPO方法实现了极具竞争力的求解质量。此外，VAGPO在不重新训练的情况下对更大实例（多达1000个节点）展现出强大的泛化能力，突显了其在学习效率和可扩展性方面的有效性。
英文摘要：
Graph routing problems play a vital role in web-related networks, where finding optimal paths across graphs is essential for efficient data transmission and content delivery. Classic routing formulations such as the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) represent fundamental graph optimization challenges. Recent data-driven optimization methods have made significant progress, yet they often face limitations in training efficiency and generalization to large-scale instances. In this paper, we propose a novel Vision-augmented Asymmetric Group Preference Optimization (VAGPO) approach. By leveraging ResNet-based visual encoding and Transformer-based sequential modeling, VAGPO captures both spatial structure and temporal dependencies. Furthermore, we introduce an asymmetric group preference optimization strategy that significantly accelerates convergence compared to commonly used policy gradient methods. Experimental results on generated TSP and CVRP instances, as well as real-world datasets, demonstrate that the proposed VAGPO approach achieves highly competitive solution quality. Additionally, VAGPO exhibits strong generalization to larger instances (up to 1000 nodes) without re-training, highlighting its effectiveness in both learning efficiency and scalability.
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