Adaptation and Fine-tuning with TabPFN for Travelling Salesman Problem

TL;DR

This paper demonstrates that TabPFN, a foundation model for tabular data, can be adapted and fine-tuned to efficiently solve the Travelling Salesman Problem with minimal training and strong generalization, outperforming traditional methods.

Contribution

First application of TabPFN to combinatorial optimization, specifically TSP, showing effective adaptation, minimal training, and strong generalization capabilities.

Findings

Requires minimal training and adapts with a single sample.

Achieves competitive performance without post-processing.

Generalizes well across different TSP instance sizes.

Abstract

Tabular Prior-Data Fitted Network (TabPFN) is a foundation model designed for small to medium-sized tabular data, which has attracted much attention recently. This paper investigates the application of TabPFN in Combinatorial Optimization (CO) problems. The aim is to lessen challenges in time and data-intensive training requirements often observed in using traditional methods including exact and heuristic algorithms, Machine Learning (ML)-based models, to solve CO problems. Proposing possibly the first ever application of TabPFN for such a purpose, we adapt and fine-tune the TabPFN model to solve the Travelling Salesman Problem (TSP), one of the most well-known CO problems. Specifically, we adopt the node-based approach and the node-predicting adaptation strategy to construct the entire TSP route. Our evaluation with varying instance sizes confirms that TabPFN requires minimal training, adapts to TSP using a single sample, performs better generalization across varying TSP instance sizes, and reduces performance degradation. Furthermore, the training process with adaptation and fine-tuning is completed within minutes. The methodology leads to strong solution quality even without post-processing and achieves performance comparable to other models with post-processing refinement. Our findings suggest that the TabPFN model is a promising approach to solve structured and CO problems efficiently under training resource constraints and rapid deployment requirements.