A graph convolutional encoder and multi-head attention decoder network for TSP via reinforcement learning

For the traveling salesman problem (TSP), it is usually hard to find a high-quality solution in polynomial time. In the last two years, graph neural networks emerge as a promising technique for TSP. However, most related learning-based methods do not make full use of the hierarchical features; thereby, resulting in relatively-low performance. Furthermore, the decoder in those methods only generates single permutation and needs additional search strategies to improve the permutation, which leads to more computing time. In this work, we propose a novel graph convolutional encoder and multi-head attention decoder network (GCE-MAD Net) to fix the two drawbacks. The graph convolutional encoder realizes to aggregate neighborhood information through updated edge features and extract hierarchical graph features from all graph convolutional layers. The multi-head attention decoder takes the first and last selected node embeddings and fused graph embeddings as input to generate probability distributions of selecting next unvisited node in order to consider global features. The GCE-MAD Net further allows to choose several nodes at each time step and generate a permutations pool after decoding to increase diversity of solution space. To assess the performance of GCE-MAD Net, we conduct experiments with randomly generated instances. The simulation results show the proposed GCE-MAD Net outperforms the traditional heuristics methods and existing learning-based algorithms on all evaluation metrics. Especially, when encountering large scale problem instances, the small scale pretrained GCE-MAD Net can get much better solutions than CPLEX solver with less time.