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.

翻译：近年来，针对旅行商问题等组合优化问题，研究者提出了许多基于神经网络的方法。其中多数方法基于图神经网络（GNN）或相关Transformer模型，这些模型在表示路径问题的欧几里得坐标上运行。然而，GNN本质上并不适合在稠密图（如路径问题中的图）上运行。此外，基于欧几里得坐标的模型无法应用于现实场景中常见的非欧几里得版本路径问题。为克服这些局限，我们提出了一种新型的基于边的GNN相关神经网络模型——图边注意力网络（GREAT）。我们通过边分类任务评估GREAT在预测旅行商问题（TSP）中最优边的性能。利用训练好的GREAT模型可生成稀疏TSP图实例，仅保留模型识别出的潜在最优边。与其他非学习型TSP图稀疏化方法相比，GREAT能在保留绝大多数最优边的同时生成极稀疏的图。此外，我们构建了基于强化学习的GREAT框架，并将其应用于欧几里得与非欧几里得非对称TSP问题，该框架取得了当前最优的性能表现。