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.Comment: 35 pages, 7 figure