Eyeballing Combinatorial Problems: A Case Study of Using Multimodal Large Language Models to Solve Traveling Salesman Problems
This work explores a novel application of MLLMs for solving combinatorial problems like TSP, which could inspire further research in visual reasoning for such tasks.
This paper investigated whether multimodal large language models (MLLMs) can 'eyeball' solutions for the Traveling Salesman Problem (TSP) by analyzing images of point distributions, and the results from zero-shot, few-shot, self-ensemble, and self-refine evaluations show promising outcomes.
Multimodal Large Language Models (MLLMs) have demonstrated proficiency in processing di-verse modalities, including text, images, and audio. These models leverage extensive pre-existing knowledge, enabling them to address complex problems with minimal to no specific training examples, as evidenced in few-shot and zero-shot in-context learning scenarios. This paper investigates the use of MLLMs' visual capabilities to 'eyeball' solutions for the Traveling Salesman Problem (TSP) by analyzing images of point distributions on a two-dimensional plane. Our experiments aimed to validate the hypothesis that MLLMs can effectively 'eyeball' viable TSP routes. The results from zero-shot, few-shot, self-ensemble, and self-refine zero-shot evaluations show promising outcomes. We anticipate that these findings will inspire further exploration into MLLMs' visual reasoning abilities to tackle other combinatorial problems.