  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
