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Recent years have witnessed a surge in research on machine learning forcombinatorial optimization since learning-based approaches can outperformtraditional heuristics and approximate exact solvers at a lower computationcost. However, most existing work on supervised neural combinatorialoptimization focuses on TSP instances with a fixed number of cities andrequires 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 methodfor solving travelling salesman problems (TSPs) with various numbers of cities.To this end, we propose an edge-aware graph autoencoder (EdgeGAE) model thatcan learn to solve TSPs after being trained on solution data of various sizeswith an imbalanced distribution. We formulate the TSP as a link prediction taskon sparse connected graphs. A residual gated encoder is trained to learn latentedge embeddings, followed by an edge-centered decoder to output linkpredictions in an end-to-end manner. To improve the model's generalizationcapability of solving large-scale problems, we introduce an active samplingstrategy into the training process. In addition, we generate a benchmarkdataset containing 50,000 TSP instances with a size from 50 to 500 cities,following an extremely scale-imbalanced distribution, making it ideal forinvestigating the model's performance for practical applications. We conductexperiments using different amounts of training data with various scales, andthe experimental results demonstrate that the proposed data-driven approachachieves a highly competitive performance among state-of-the-art learning-basedmethods for solving TSPs.

An Edge-Aware Graph Autoencoder Trained on Scale-Imbalanced Data for Travelling Salesman Problems