Dynamic graph Conv-LSTM model with dynamic positional encoding for the large-scale traveling salesman problem

Recent research has showen that deep reinforcement learning (DRL) can be used to design better heuristics for the traveling salesman problem (TSP) on the small scale, but does not do well when generalized to large instances. In order to improve the generalization ability of the model when the nodes change from small to large, we propose a dynamic graph Conv-LSTM model (DGCM) to the solve large-scale TSP. The noted feature of our model is the use of a dynamic encoder-decoder architecture and a convolution long short-term memory network, which enable the model to capture the topological structure of the graph dynamically, as well as the potential relationships between nodes. In addition, we propose a dynamic positional encoding layer in the DGCM, which can improve the quality of solutions by providing more location information. The experimental results show that the performance of the DGCM on the large-scale TSP surpasses the state-of-the-art DRL-based methods and yields good performance when generalized to real-world datasets. Moreover, our model compares favorably to heuristic algorithms and professional solvers in terms of computational time.