标题： 观察组合问题：使用多模态大语言模型解决旅行商问题的案例研究 显示英文标题

标题： Eyeballing Combinatorial Problems: A Case Study of Using Multimodal Large Language Models to Solve Traveling Salesman Problems

摘要： 多模态大语言模型（MLLMs）已展现出处理多种模态的能力，包括文本、图像和音频。 这些模型利用大量的现有知识，使其能够在几乎没有或没有特定训练示例的情况下解决复杂问题，这在少样本和零样本上下文学习场景中得到了证明。 本文研究了利用MLLM的视觉能力通过分析二维平面上点分布的图像来“粗略查看”旅行商问题（TSP）的解决方案。 我们的实验旨在验证这样一个假设，即MLLM可以有效地“粗略查看”可行的TSP路径。 零样本、少样本、自集成和自精炼零样本评估的结果显示出了有希望的结果。 我们预计这些发现将激发对MLLM视觉推理能力的进一步探索，以解决其他组合问题。 显示英文摘要

摘要： 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.