On Size and Hardness Generalization in Unsupervised Learning for the Travelling Salesman Problem

TL;DR

This paper investigates how unsupervised learning methods, particularly graph neural networks, generalize across different instance sizes and distributions in solving the Traveling Salesman Problem, emphasizing the impact of training data hardness.

Contribution

The study systematically analyzes the effects of training instance size, embedding dimensions, and distribution hardness on the generalization ability of unsupervised GNN-based TSP solvers.

Findings

Larger training instances improve solution quality.

Higher embedding dimensions enhance model representation.

Training on harder instances leads to better generalization.

Abstract

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.