On Size and Hardness Generalization in Unsupervised Learning for the
  Travelling Salesman Problem
Yimeng Min Carla P. Gomes
We study the generalization capability of Unsupervised Learning in solving
the Travelling Salesman Problem (TSP). We use a Graph Neural Network (GNN)
trained with a surrogate loss function to generate an embedding for each node.
We use these embeddings to construct a heat map that indicates the likelihood
of each edge being part of the optimal route. We then apply local search to
generate our final predictions. Our investigation explores how different
training instance sizes, embedding dimensions, and distributions influence the
outcomes of Unsupervised Learning methods. Our results show that training with
larger instance sizes and increasing embedding dimensions can build a more
effective representation, enhancing the model's ability to solve TSP.
Furthermore, in evaluating generalization across different distributions, we
first determine the hardness of various distributions and explore how different
hardnesses affect the final results. Our findings suggest that models trained
on harder instances exhibit better generalization capabilities, highlighting
the importance of selecting appropriate training instances in solving TSP using
Unsupervised Learning.