Exploring Combinatorial Problem Solving with Large Language Models: A Case Study on the Travelling Salesman Problem Using GPT-3.5 Turbo

TL;DR

This paper explores the application of GPT-3.5 Turbo to solve the Travelling Salesman Problem, demonstrating promising results through fine-tuning and ensemble methods, and analyzing different prompting strategies.

Contribution

It introduces a novel approach to applying large language models to combinatorial optimization, specifically TSP, with fine-tuning and ensemble techniques for improved performance.

Findings

Fine-tuned GPT-3.5 Turbo performs well on trained problem sizes.

The model generalizes effectively to larger problem instances.

Self-ensemble improves solution quality without extra training.

Abstract

Large Language Models (LLMs) are deep learning models designed to generate text based on textual input. Although researchers have been developing these models for more complex tasks such as code generation and general reasoning, few efforts have explored how LLMs can be applied to combinatorial problems. In this research, we investigate the potential of LLMs to solve the Travelling Salesman Problem (TSP). Utilizing GPT-3.5 Turbo, we conducted experiments employing various approaches, including zero-shot in-context learning, few-shot in-context learning, and chain-of-thoughts (CoT). Consequently, we fine-tuned GPT-3.5 Turbo to solve a specific problem size and tested it using a set of various instance sizes. The fine-tuned models demonstrated promising performance on problems identical in size to the training instances and generalized well to larger problems. Furthermore, to improve the performance of the fine-tuned model without incurring additional training costs, we adopted a self-ensemble approach to improve the quality of the solutions.