Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances

TL;DR

This paper introduces a method to generalize small pre-trained models for the traveling salesman problem to solve arbitrarily large instances by using heat maps and reinforcement learning, significantly enhancing generalization.

Contribution

It proposes a novel approach combining supervised learning, graph techniques, and reinforcement learning to solve large TSP instances with a small model, improving generalization.

Findings

Outperforms existing ML-based TSP algorithms on large instances

Effectively generalizes to TSP with up to 10,000 vertices

Demonstrates significant improvement in solution quality

Abstract

For the traveling salesman problem (TSP), the existing supervised learning based algorithms suffer seriously from the lack of generalization ability. To overcome this drawback, this paper tries to train (in supervised manner) a small-scale model, which could be repetitively used to build heat maps for TSP instances of arbitrarily large size, based on a series of techniques such as graph sampling, graph converting and heat maps merging. Furthermore, the heat maps are fed into a reinforcement learning approach (Monte Carlo tree search), to guide the search of high-quality solutions. Experimental results based on a large number of instances (with up to 10,000 vertices) show that, this new approach clearly outperforms the existing machine learning based TSP algorithms, and significantly improves the generalization ability of the trained model.