Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input instances may follow distributions with salient patterns that can be leveraged to overcome the worst-case computational hardness. For optimization problems over graphs, the common practice of neural combinatorial solvers consumes the inputs in the form of adjacency matrices. In this paper, we explore a vision-based method that is conceptually novel: can neural models solve graph optimization problems by \textit{taking a look at the graph pattern}? Our results suggest that the performance of such vision-based methods is not only non-trivial but also comparable to the state-of-the-art matrix-based methods, which opens a new avenue for developing data-driven optimization solvers.

翻译：数据驱动方法已被证明在解决图上的组合优化问题（如旅行商问题和车辆路径问题）中行之有效。此类方法的基本原理在于，输入实例可能遵循具有显著模式的分布，这些模式可用于克服最坏情况下的计算复杂性。对于图上的优化问题，神经组合求解器的常见做法是以邻接矩阵的形式处理输入。本文探索了一种概念上新颖的基于视觉的方法：神经网络能否通过“观察图模式”来解决图优化问题？我们的结果表明，此类基于视觉的方法不仅表现可观，而且可与最先进的基于矩阵的方法相媲美，这为开发数据驱动的优化求解器开辟了新途径。