Geometric Pretraining Boosts Graph Combinatorial Optimization Performance

Researchers have introduced an innovative self-supervised pretraining framework specifically designed to enhance the performance of neural solvers for graph combinatorial optimization problems, such as the Traveling Salesman Problem (TSP). This framework leverages graph contrastive learning, incorporating geometric augmentations like rotations and axial reflections. The core idea is to compel the model to learn robust, invariant structural representations and global relative distance distributions within graphs, which are crucial for effectively tackling complex routing challenges. The study's findings demonstrate that this pretraining strategy consistently outperforms models that do not undergo such pretraining across various problem scales. Notably, a hybrid approach combining both rotation and reflection augmentations yielded a 6.57% improvement in tour length for TSP1000 instances. This outcome underscores the importance of geometric pretraining as a powerful inductive bias, enabling neural solvers to scale more effectively to high-dimensional combinatorial optimization problems.