mlsanityData to 7 Oct 2026

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

arXiv 2406.06865 ↗First posted 11 Jun 2024cs.AIcited by 8

On the map: Multimodal LLMs / vision-language models → VLM benchmarks and visual reasoning

Abstract (arXiv)

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.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models. Builds on 13 of its 15 references that are in the map. First posted on arXiv 11 Jun 2024.

Builds on

13 of 15 references.

References · 13

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  3. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
  4. 2022Large Language Models are Zero-Shot Reasonerscited by 4,323
  5. 2021Finetuned Language Models Are Zero-Shot Learnerscited by 3,747
  6. 2022Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?cited by 1,413
  7. 2023Large Language Models as Optimizerscited by 830
  8. 2022Automatic Chain of Thought Prompting in Large Language Modelscited by 684
  9. 2023Multimodal Large Language Models: A Surveycited by 193
  10. 2023Large Language Models as Evolutionary Optimizerscited by 122
  11. 2023Boosted Prompt Ensembles for Large Language Modelscited by 36
  12. 2024How Multimodal Integration Boost the Performance of LLM for Optimization: Case Study on Capacitated Vehicle Routing Problemscited by 12
1 more
  1. 2024Can Large Language Models Solve Robot Routing?cited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 5; 2026: 1.

8 papers.

  1. 2024Visual Reasoning and Multi-Agent Approach in Multimodal Large Language Models (MLLMs): Solving TSP and mTSP Combinatorial Challengescited by 21
  2. 2025GraphThought: Graph Combinatorial Optimization with Thought Generationcited by 9
  3. 2025Multimodal LLM-assisted Evolutionary Search for Programmatic Control Policiescited by 8
  4. 2024Leveraging Large Language Models (LLMs) for Traffic Management at Urban Intersections: The Case of Mixed Traffic Scenarioscited by 6
  5. 2025Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimizationcited by 6
  6. 2025Large Language Models in Operations Research: Methods, Applications, and Challengescited by 4
  7. 2025General Intelligence-based Fragmentation (GIF): A framework for peak-labeled spectra simulationcited by 0
  8. 2026Budget-Efficient Automatic Algorithm Design via Code Graphcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Exploring Combinatorial Problem Solving with Large Language Models: A Case Study on the Travelling Salesman Problem Using GPT-3.5 Turbo
  2. 2025ViTSP: A Vision Language Models Guided Framework for Solving Large-Scale Traveling Salesman Problems
  3. 2024NPHardEval4V: Dynamic Evaluation of Large Vision-Language Models with Effects of Vision
  4. 2026VLM Fine-Tuning for End-to-End Combinatorial Optimization
  5. 2024Are Language Models Puzzle Prodigies? Algorithmic Puzzles Unveil Serious Challenges in Multimodal Reasoning
  6. 2024Cantor: Inspiring Multimodal Chain-of-Thought of MLLM
  7. 2024Plug-and-Play Grounding of Reasoning in Multimodal Large Language Models
  8. 2025Thinking with Programming Vision: Towards a Unified View for Thinking with Images