Multimodal Large Language Models (MLLMs) harness comprehensive knowledge spanning text, images, and audio to adeptly tackle complex problems, including zero-shot in-context learning scenarios. This study explores the ability of MLLMs in visually solving the Traveling Salesman Problem (TSP) and Multiple Traveling Salesman Problem (mTSP) using images that portray point distributions on a two-dimensional plane. We introduce a novel approach employing multiple specialized agents within the MLLM framework, each dedicated to optimizing solutions for these combinatorial challenges. Our experimental investigation includes rigorous evaluations across zero-shot settings and introduces innovative multi-agent zero-shot in-context scenarios. The results demonstrated that both multi-agent models. Multi-Agent 1, which includes the Initializer, Critic, and Scorer agents, and Multi-Agent 2, which comprises only the Initializer and Critic agents; significantly improved solution quality for TSP and mTSP problems. Multi-Agent 1 excelled in environments requiring detailed route refinement and evaluation, providing a robust framework for sophisticated optimizations. In contrast, Multi-Agent 2, focusing on iterative refinements by the Initializer and Critic, proved effective for rapid decision-making scenarios. These experiments yield promising outcomes, showcasing the robust visual reasoning capabilities of MLLMs in addressing diverse combinatorial problems. The findings underscore the potential of MLLMs as powerful tools in computational optimization, offering insights that could inspire further advancements in this promising field. Project link: https://github.com/ahmed-abdulhuy/Solving-TSP-and-mTSP-Combinatorial-Challenges-using-Visual-Reasoning-and-Multi-Agent-Approach-MLLMs-.git

翻译：多模态大语言模型（MLLMs）整合了涵盖文本、图像和音频的广泛知识，能够熟练处理复杂问题，包括零样本上下文学习场景。本研究探讨了MLLMs通过视觉方式解决旅行商问题（TSP）与多旅行商问题（mTSP）的能力，所使用的图像描绘了二维平面上的点分布。我们提出了一种在MLLM框架内采用多个专用智能体的新颖方法，每个智能体专门负责优化这些组合优化挑战的解决方案。我们的实验研究包括在零样本设置下的严格评估，并引入了创新的多智能体零样本上下文场景。结果表明，两种多智能体模型——包含初始化器、评判器和评分器智能体的多智能体1，以及仅包含初始化器和评判器智能体的多智能体2——均显著提升了TSP和mTSP问题的求解质量。多智能体1在需要详细路径优化与评估的环境中表现卓越，为复杂优化提供了稳健框架。相比之下，多智能体2专注于通过初始化器和评判器进行迭代优化，在需要快速决策的场景中证明是有效的。这些实验取得了有希望的结果，展示了MLLMs在应对多样化组合问题方面强大的视觉推理能力。研究结果强调了MLLMs作为计算优化强大工具的潜力，所提供的见解有望推动这一前景广阔领域的进一步发展。项目链接：https://github.com/ahmed-abdulhuy/Solving-TSP-and-mTSP-Combinatorial-Challenges-using-Visual-Reasoning-and-Multi-Agent-Approach-MLLMs-.git