GatedGCN with GraphSage to Solve Traveling Salesman Problem

Graph neural networks have shown good performance in many domains, as well as in combinatorial optimization. This paper proposes a new graph neural network framework to deal with the classical combinatorial optimization problem, the traveling salesman problem (TSP). The proposed framework is composed of GraphSage and Gated-GCN jointly, named GGCN GSG, where the output of GraphSage is the input of GatedGCN. With each TSP graph being used as data input, each node and its neighbors in the graph are embedded into the d-dimensional feature vector through GraphSage, and GatedGCN adds the distance information of the edge into the update function, and controls whether the TSP node enters the update function through the gated mechanism. Experimental results show that our proposed framework can get closer to the optimal solution than comparable graph neural network frameworks and other learning-based methods, achieving an optimal solution of 3.83 at 20 nodes and an optimal ratio of 30 nodes 2x increase.