  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.
