On the Effectiveness of Pretraining for Graph Combinatorial Optimization

2026-07-21

AI Summary

This work addresses the limited generalization of neural solvers on large-scale graph-based combinatorial optimization problems, such as the Traveling Salesman Problem (TSP), by proposing a geometry-enhanced self-supervised pretraining framework. The method introduces rotational and axial symmetry transformations as inductive biases into graph contrastive learning—a novel integration that compels the model to capture structural invariances and global relative distance distributions. The proposed hybrid geometric augmentation strategy substantially improves performance on high-dimensional instances, reducing tour lengths by 6.57% on TSP1000 compared to non-pretrained baselines. These results demonstrate the efficacy of geometric pretraining in scaling up neural solvers for complex combinatorial tasks.

Abstract

This paper introduces a self-supervised pretraining framework for graph combinatorial optimization specifically designed to address the nature of routing problems like the Traveling Salesman Problem. By utilizing graph contrastive learning with geometric augmentations (specifically, rotations and axial reflections) the model is forced to learn invariant structural representations and global relative distance distributions. Results demonstrate that this pretraining strategy outperforms non-pretrained models across various problem scales. Notably, the hybrid strategy (combining rotation and reflection) achieved a 6.57% improvement in tour length for TSP1000, proving that geometric pretraining is an important inductive bias for effectively scaling neural solvers to high-dimensional instances.

Problem

• graph combinatorial optimization
• Traveling Salesman Problem
• pretraining
• neural solvers
• geometric invariance

Innovation

• graph contrastive learning
• geometric augmentations
• self-supervised pretraining
• combinatorial optimization
• inductive bias