# Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models

arXiv: https://arxiv.org/abs/2510.21906 · HTML: https://mlsanity.com/paper/2510.21906/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 22 of its 50 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 22 of 22)

- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [Can Language Models Solve Graph Problems in Natural Language?](https://mlsanity.com/paper/2305.10037/) (2023)
- [Talk like a Graph: Encoding Graphs for Large Language Models](https://mlsanity.com/paper/2310.04560/) (2023)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [Language Model Crossover: Variation through Few-Shot Prompting](https://mlsanity.com/paper/2302.12170/) (2023)
- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (2024)
- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [GITA: Graph to Visual and Textual Integration for Vision-Language Graph Reasoning](https://mlsanity.com/paper/2402.02130/) (2024)
- [VisionGraph: Leveraging Large Multimodal Models for Graph Theory Problems in Visual Context](https://mlsanity.com/paper/2405.04950/) (2024)
- [Large Language Model for Multi-objective Evolutionary Optimization](https://mlsanity.com/paper/2310.12541/) (2023)
- [Influence maximization in complex networks through optimal percolation](https://mlsanity.com/paper/1506.08326/) (2015)
- [LLM Guided Evolution -- The Automation of Models Advancing Models](https://mlsanity.com/paper/2403.11446/) (2024)
- [Enhancing Genetic Improvement Mutations Using Large Language Models](https://mlsanity.com/paper/2310.19813/) (2023)
- [Network dismantling](https://mlsanity.com/paper/1603.08883/) (2016)
- [How Multimodal Integration Boost the Performance of LLM for Optimization: Case Study on Capacitated Vehicle Routing Problems](https://mlsanity.com/paper/2403.01757/) (2024)
- [Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms](https://mlsanity.com/paper/2410.20848/) (2024)
- [Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimization](https://mlsanity.com/paper/2501.11968/) (2025)
- [Higher-order Knowledge Transfer for Dynamic Community Detection with Great Changes](https://mlsanity.com/paper/2211.15043/) (2022)
- [A Multi-Transformation Evolutionary Framework for Influence Maximization in Social Networks](https://mlsanity.com/paper/2204.03297/) (2022)
- [Can Large Language Models Be Trusted as Evolutionary Optimizers for Network-Structured Combinatorial Problems?](https://mlsanity.com/paper/2501.15081/) (2025)
- [Multidomain Evolutionary Optimization on Combinatorial Problems in Complex Networks](https://mlsanity.com/paper/2406.14865/) (2024)

## Abstract (arXiv)

Evolutionary algorithms (EAs) have proven effective in exploring the vast solution spaces typical of graph-structured combinatorial problems. However, traditional encoding schemes, such as binary or numerical representations, often fail to straightforwardly capture the intricate structural properties of networks. Through employing the image-based encoding to preserve topological context, this study utilizes multimodal large language models (MLLMs) as evolutionary operators to facilitate structure-aware optimization over graph data. To address the visual clutter inherent in large-scale network visualizations, we leverage graph sparsification techniques to simplify structures while maintaining essential structural features. To further improve robustness and mitigate bias from different sparsification views, we propose a cooperative evolutionary optimization framework that facilitates cross-domain knowledge transfer and unifies multiple sparsified variants of diverse structures. Additionally, recognizing the sensitivity of MLLMs to network layout, we introduce an ensemble strategy that aggregates outputs from various layout configurations through consensus voting. Finally, experiments on real-world networks through various tasks demonstrate that our approach improves both the quality and reliability of solutions in MLLM-driven evolutionary optimization.