Most Deep Learning approaches for TSP rely on pre-training with large-scale datasets. I wanted to see if a solver could learn "on the fly" for a specific instance without any priors from other problems.

I built a solver using PPO that learns from scratch per instance. It achieved a 1.66% gap on TSPLIB d1291 in about 5.6 hours on a single A100.

The Core Idea: My hypothesis was that while optimal solutions are mostly composed of 'minimum edges' (nearest neighbors), the actual difficulty comes from a small number of 'exception edges' outside of that local scope.

Instead of pre-training, I designed an inductive bias based on the topological/geometric structure of these exception edges. The agent receives guides on which edges are likely promising based on micro/macro structures, and PPO fills in the gaps through trial and error.

It is interesting to see RL reach this level without a dataset. I have open-sourced the code and a Colab notebook for anyone who wants to verify the results or tinker with the 'exception edge' hypothesis.

Code & Colab: https://github.com/jivaprime/TSP_exception-edge

Happy to answer any questions about the geometric priors or the PPO implementation!