In combinatorial optimization problems, the traveling salesman problem (TSP) and the vehicle routing problem (VRP) have been widely used in many business scenarios such as transportation management and disaster response. However, conventional methods for these problems still have potential for improvement in terms of accuracy and scalability. Meanwhile, in practical business applications, issues such as routing and re-planning while considering real road conditions remain unsolved. In this paper, we propose a Graph Edge Attention Routing (GEAR) model that solves the above-mentioned problems in both academic research and real-world applications. Specifically, GEAR embeds the features of nodes (destinations to be visited) and edges (moving costs between each two nodes) through Graph Convolutional Networks (GCN). We then combine GCN features and Pointer Networks  to construct the policy network model of the GEAR and train it by minimizing the total edge cost through REINFORCE with baseline. Experimental results show that GEAR outperforms the conventional methods in both standard and large-scale combinatorial optimization problems. Additionally, GEAR also enables routes to be re-planned when impassable sections of roads appear, which commonly occurs in real-world business scenarios. Furthermore, by testing GEAR on an enterprise-level business dataset by using the commercial Map API to extract real distances between nodes, GEAR can achieve tour efficiency without real data being used to train it and proves its effectiveness and robustness in real-world combinatorial optimization applications.