Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances (2012.10658v2)

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.

Overview of "Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances"

This paper presents a novel approach to solving the Traveling Salesman Problem (TSP) by enhancing the generalization ability of machine learning-based algorithms. Traditional algorithms for TSP, both exact and heuristic, rely heavily on expert knowledge and handcrafted rules, making them difficult to generalize to other combinatorial problems. Machine learning algorithms, particularly those based on supervised learning (SL), struggle with the scalability and generalization when faced with larger instances of the problem due to their training on fixed-sized inputs.

Methodologies

The authors propose an innovative method to overcome these drawbacks by training a small-scale SL model which can be applied to TSP instances of arbitrarily large sizes. The approach involves several key techniques, including:

1. Graph Sampling and Converting: A sub-graph sampling strategy extracts smaller sub-problems from a larger TSP instance. These are converted to ensure uniform distribution for effective SL inference.
2. Heat Map Construction: The pre-trained model, a graph convolutional residual network with an attention mechanism (Att-GCRN), is used to construct heat maps by predicting the probability of each edge being part of an optimal tour on the sampled sub-graphs.
3. Heat Map Merging: Merging sub-graphs' heat maps results in a comprehensive heat map for the entire instance, enabling its application to larger TSP instances without retraining.
4. Reinforcement Learning via MCTS: Based on the comprehensive heat map, a Monte Carlo Tree Search (MCTS) method is leveraged for solution optimization, which searches for high-quality TSP solutions by refining them continuously.

This novel integration of SL and reinforcement learning (RL) forms a hybrid method that utilizes the strengths of both approaches to tackle larger TSP instances effectively.

Results and Implications

The experimental evaluation demonstrates that the proposed hybrid methodology outperforms existing ML-based TSP solvers across various problem sizes, including instances with up to 10,000 cities. Notably, it provides solutions close to optimal with significantly enhanced scalability and adaptability.

The implication of this research extends beyond TSP, suggesting a robust framework for dealing with other combinatorial optimization problems by employing a similar methodology that bridges SL and RL. This capability of the method to generalize well to larger instances suggests a promising step toward more efficient and adaptive ML approaches in combinatorial optimization.

Future Directions

The paper suggests avenues for future developments, including extending the approach to larger and more complex TSP variations (e.g., non-Euclidean TSPs) and other related optimization problems. Additionally, further exploration into automating sub-problem selection and integrating more sophisticated learning models could further improve generalization and efficiency.

Overall, while avoiding overly sensational terms, the research demonstrates a significant step forward in improving the generalization ability of machine learning models for large-scale combinatorial optimization problems such as the Traveling Salesman Problem.