Eyeballing Combinatorial Problems: A Case Study of Using Multimodal Large Language Models to Solve Traveling Salesman Problems
<|reference_start|>Eyeballing Combinatorial Problems: A Case Study of Using Multimodal Large Language Models to Solve Traveling Salesman Problems: 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.<|reference_end|>
@article{elhenawy2024eyeballing,
    title={Eyeballing Combinatorial Problems: A Case Study of Using Multimodal
  Large Language Models to Solve Traveling Salesman Problems},
    author={Mohammed Elhenawy, Ahmed Abdelhay, Taqwa I. Alhadidi, Huthaifa I
  Ashqar, Shadi Jaradat, Ahmed Jaber, Sebastien Glaser, and Andry Rakotonirainy},
    journal={arXiv preprint arXiv:2406.06865},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.06865},
    primaryClass={cs.AI}
}