  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.
