[Paper Review] Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances

Zhang-Hua Fu, Kai-Bin Qiu+1 more|arXiv (Cornell University)|Dec 19, 2020

Metaheuristic Optimization Algorithms Research35 references22 citations

TL;DR

This paper proposes a hybrid machine learning approach that generalizes a small, supervised model to arbitrarily large TSP instances using graph sampling, graph conversion, and heat map merging. By leveraging a pre-trained attention-based graph convolutional residual network to generate heat maps, and combining it with Monte Carlo Tree Search (MCTS), the method achieves near-optimal solutions on 10,000-city instances with an average gap of only 4.39% to LKH3, significantly outperforming existing learning-based methods.

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.

Motivation & Objective

• To overcome the poor generalization of supervised learning models in TSP, which typically fail on large-scale instances due to distribution shifts.
• To enable a single small pre-trained model to be reused across TSP instances of any size without retraining.
• To develop a scalable, generalizable framework that combines supervised learning with reinforcement learning for combinatorial optimization.
• To significantly reduce reliance on expert-designed heuristics while maintaining high solution quality on large instances.

Proposed method

• Train a small-scale attention-based graph convolutional residual network (Att-GCRN) on small TSP instances (e.g., 20–100 cities) using supervised learning with pre-computed optimal solutions.
• For large TSP instances, repeatedly apply graph sampling to extract subgraphs of size matching the pre-trained model’s input.
• Convert each sampled subgraph into a standard TSP instance and use the pre-trained Att-GCRN to generate a sub-heat map indicating edge quality.
• Merge all sub-heat maps into a complete heat map over the original large graph, preserving spatial and structural relevance.
• Use the merged heat map as a policy prior in a Monte Carlo Tree Search (MCTS) algorithm to guide the search for high-quality TSP tours.
• Implement a conversion-based MCTS, where each state is a complete tour and actions involve edge swaps, differing from traditional constructive MCTS.

Experimental results

Research questions

• RQ1 Can a small, supervised model trained on small TSP instances be generalized to solve arbitrarily large TSP instances?
• RQ2 How effective is graph sampling and heat map merging in preserving model generalization across different instance sizes?
• RQ3 Does combining a pre-trained supervised model with MCTS yield better performance than pure reinforcement learning or supervised baselines?
• RQ4 Can this method achieve near-optimal solutions on large-scale TSP instances (e.g., 10,000 cities) without retraining?

Key findings

• The proposed Att-GCRN+MCTS method achieved an average gap of only 4.3902% from the LKH3 optimal solution on 16 TSP instances with 10,000 cities.
• Without the heat map, MCTS alone produced solutions with an average gap of 1,293.22% on 10,000-city instances, demonstrating the critical role of the heat map.
• The method outperformed three existing learning-based baselines, which had average gaps of 501.27%, 97.39%, and 80.28% respectively on the same 10,000-city instances.
• The runtime of the proposed method was 4.16 minutes on average for 10,000-city instances, significantly faster than the 1.69-hour runtime of the best baseline.
• On smaller instances (e.g., 20–1000 cities), the method consistently produced near-optimal solutions with gaps below 5%.
• The ablation study confirmed that the heat map is essential, as disabling it caused a drastic performance drop across all instance sizes.