Recent years have witnessed a surge in research on machine learning for combinatorial optimization since learning-based approaches can outperform traditional heuristics and approximate exact solvers at a lower computation cost. However, most existing work on supervised neural combinatorial optimization focuses on TSP instances with a fixed number of cities and requires large amounts of training samples to achieve a good performance, making them less practical to be applied to realistic optimization scenarios. This work aims to develop a data-driven graph representation learning method for solving travelling salesman problems (TSPs) with various numbers of cities. To this end, we propose an edge-aware graph autoencoder (EdgeGAE) model that can learn to solve TSPs after being trained on solution data of various sizes with an imbalanced distribution. We formulate the TSP as a link prediction task on sparse connected graphs. A residual gated encoder is trained to learn latent edge embeddings, followed by an edge-centered decoder to output link predictions in an end-to-end manner. To improve the model's generalization capability of solving large-scale problems, we introduce an active sampling strategy into the training process. In addition, we generate a benchmark dataset containing 50,000 TSP instances with a size from 50 to 500 cities, following an extremely scale-imbalanced distribution, making it ideal for investigating the model's performance for practical applications. We conduct experiments using different amounts of training data with various scales, and the experimental results demonstrate that the proposed data-driven approach achieves a highly competitive performance among state-of-the-art learning-based methods for solving TSPs.

该论文提出了一种数据驱动的图表示学习方法，用于解决具有不同数量城市的旅行推销员问题，并通过实验证明该方法在解决旅行推销员问题方面具有与最先进的基于学习的方法相媲美的性能。

基于边缘感知的图自编码器用于规模不平衡数据的旅行商问题