In the last years, many neural network-based approaches have been proposed to tackle combinatorial optimization problems such as routing problems. Many of these approaches are based on graph neural networks (GNNs) or related transformers, operating on the Euclidean coordinates representing the routing problems. However, GNNs are inherently not well suited to operate on dense graphs, such as in routing problems. Furthermore, models operating on Euclidean coordinates cannot be applied to non-Euclidean versions of routing problems that are often found in real-world settings. To overcome these limitations, we propose a novel GNN-related edge-based neural model called Graph Edge Attention Network (GREAT). We evaluate the performance of GREAT in the edge-classification task to predict optimal edges in the Traveling Salesman Problem (TSP). We can use such a trained GREAT model to produce sparse TSP graph instances, keeping only the edges GREAT finds promising. Compared to other, non-learning-based methods to sparsify TSP graphs, GREAT can produce very sparse graphs while keeping most of the optimal edges. Furthermore, we build a reinforcement learning-based GREAT framework which we apply to Euclidean and non-Euclidean asymmetric TSP. This framework achieves state-of-the-art results.

本研究针对图神经网络在处理密集图和非欧几里得路由问题中的局限性，提出了一种新颖的边缘基础神经模型——图边注意力网络（GREAT）。通过在旅行商问题的边分类任务中评估GREAT的性能，研究发现GREAT能够有效地生成稀疏图实例，同时保持大部分最优边，从而在处理欧几里得和非欧几里得旅行商问题时达到最先进的结果。

用于边缘图问题（如旅行商问题）的GREAT架构