Learning-Based TSP-Solvers Tend to Be Overly Greedy

TL;DR

This paper investigates the tendency of deep learning-based TSP solvers to behave greedily, especially out-of-distribution, revealing their limitations and proposing data augmentation techniques to improve their generalization.

Contribution

The study introduces a statistical measure to analyze dataset properties, uncovers the greedy behavior of learning-based TSP solvers, and develops augmentation methods to enhance their robustness.

Findings

Learning-based TSP solvers tend to be overly greedy.

Augmentation with distribution shifts degrades solver performance.

Fine-tuning with augmented data improves generalization.

Abstract

Deep learning has shown significant potential in solving combinatorial optimization problems such as the Euclidean traveling salesman problem (TSP). However, most training and test instances for existing TSP algorithms are generated randomly from specific distributions like uniform distribution. This has led to a lack of analysis and understanding of the performance of deep learning algorithms in out-of-distribution (OOD) generalization scenarios, which has a close relationship with the worst-case performance in the combinatorial optimization field. For data-driven algorithms, the statistical properties of randomly generated datasets are critical. This study constructs a statistical measure called nearest-neighbor density to verify the asymptotic properties of randomly generated datasets and reveal the greedy behavior of learning-based solvers, i.e., always choosing the nearest neighbor nodes to construct the solution path. Based on this statistical measure, we develop interpretable data augmentation methods that rely on distribution shifts or instance perturbations and validate that the performance of the learning-based solvers degenerates much on such augmented data. Moreover, fine-tuning learning-based solvers with augmented data further enhances their generalization abilities. In short, we decipher the limitations of learning-based TSP solvers tending to be overly greedy, which may have profound implications for AI-empowered combinatorial optimization solvers.