Title: Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models
Venue: NeurIPS 2025
Accepted: yes
Keywords: Evolutionary Optimization

Multimodal Large Language Models

Complex Networks

Combinatorial Optimization
Abstract: 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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel Structure-Aware Cooperative Ensemble Evolutionary Optimization framework that integrates Multimodal Large Language Models (MLLMs) into evolutionary optimization for solving combinatorial problems on complex networks. The key idea is to use image-based encodings of network structures, allowing MLLMs to serve as evolutionary operators (crossover and mutation), while incorporating graph sparsification , ensemble strategies, and cooperative frameworks to enhance robustness, reduce bias, and improve performance.\n\nSTRENGTHS AND WEAKNESSES:\nMain strengths\n(1)\tNovel Integration of MLLMs with Evolutionary Algorithms: The paper presents a creative and promising direction by using MLLMs not just as tools for reasoning or generation, but as core components in an evolutionary optimization pipeline.\n(2)\tEnsemble and Cooperative Framework Design: The proposed cooperative framework with multiple sparsified views and layout ensembles shows a strong understanding of how to mitigate MLLM limitations such as sensitivity to input presentation and structural bias.\n(3)\tComprehensive Experimental Evaluation : The evaluation on eight real-world networks, along with ablation studies and statistical significance tests, provides solid empirical support for the claims made.\n\nMain weakness\n(1)\tLimited Theoretical Contribution: While the framework is empirically sound, there is little theoretical analysis or formal guarantees about convergence, optimality, or generalization beyond the specific task of influence maximization.\n(2)\tLack of Broader Applicability Discussion: The experiments focus solely on influence maximization; it’s unclear how easily the framework can be adapted to other combinatorial optimization tasks on graphs.\n(3)\tComputational Cost and Scalability Concerns: Although the paper discusses computational efficiency, the cost of repeated MLLM API calls and the scalability to much larger graphs are underexplored.\n\nQUESTIONS:\n(1)How generalizable is your framework to other combinatorial graph optimization tasks such as node cover, traveling salesman problem, or community detection?\n(2)Table 5 shows significant differences in running time and performance across GPT-4o, Gemini, and Qwen. How does the choice of MLLM fundamentally affect the search behavior and final solution quality?\n(3)The simplified networks used have only 50 nodes and 100 edges. How does the method scale to graphs with thousands or millions of nodes? What architectural changes would be required?\n(4)How does the proposed MLLM-driven framework compare with traditional EA methods that use learned or hand-crafted mutation/crossover operators on graph data?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nTraditional encoding schemes challenge in capturing the intricate structural properties of networks. This paper propose using MLLMs as evolutionary operators to facilitate structure-aware optimization over graph data. The author demonstrates how MLLMs can function as evolutionary optimization operator and  explore the potential of this integration and how this integration can be further extended.\n\nExperiments show that MLLM integration significantly outperforms single-layout approaches, and the collaborative mechanism further improves performance, achieving the best EDV scores on 8 real networks. The overall approach replaces traditional heuristics with visual large models, combining subgraph parallelization with knowledge transfer to balance accuracy and scalability.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. Pioneers feeding multi-layout graph visualisations into a multimodal LLM, using the model itself as the generator of evolutionary operators.\n    \n2. The end-to-end architecture, from sparsified multi-view subgraphs to cross-domain knowledge transfer, is conceptually sound and tightly aligned with the authors’ stated motivation.\n    \n3. Benchmarked on eight large real-world networks against diverse baselines, with rigorous statistical tests that convincingly show the added value of both the ensemble and cooperative components.\n\nWeaknesses:\n\n1. The cooperative framework adds several hyper-parameters, yet offers no sensitivity study or justification of the chosen defaults.\n    \n2. Although the method is claimed to work on full-scale graphs, all experiments use only subgraphs; at least one evaluation on the complete network is needed.\n\n3. ANOVA is performed solely for the initialisation phase, with no quantitative layout-sensitivity analysis for crossover and mutation.\n\n4. The overall optimisation time is not compared against a traditional EO baseline without MLLM.\n\nQUESTIONS:\n1. Your cooperative framework introduces several additional hyperparameters. Could you provide a sensitivity analysis or justify the choices of the default values?\n2. While the method is claimed to be applicable to full-scale graphs, the experiments are conducted only on subgraphs. Could you include or comment on results using the complete network to support the scalability claim?\n3. ANOVA is applied only during the initialisation stage. Have you considered performing a quantitative analysis of layout sensitivity for the crossover and mutation phases as well?\n4. How does the overall optimisation time of your method compare to a traditional evolutionary optimization (EO) baseline without MLLM? Could you provide a runtime comparison?\n\nLIMITATIONS:\nSee weaknesses and questions above.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-05"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes an ensemble framework for structure-aware optimization on graph data, where multimodal large language models (MLLMs) are employed as evolutionary operators. The authors further incorporate the proposed framework with the following techniques for improvements:\n\n-  Applying graph sparsification techniques to prune complex networks while preserving essential structural properties. \n-  Utilizing a master-slave framework to distribute networks across multiple sparsified views, mitigating the biases produced by only viewing a single sparsified graph.\n\nThe experimental results on real-world networks validate the effectiveness of the proposed framework.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The paper proposes an innovative algorithm that leverages MLLMs as evolutionary operators in the optimization process on graph data.\n- The framework, which utilizes multiple sparsification views and various layouts to improve solution quality, is theoretically sound and effective, as evidenced by its better performance in ablation studies.\n- The paper is well-organized, and the formulations of the entire framework are comprehensive and easy to follow.\n\nWeaknesses:\n- While the method is designed for combinatorial graph optimization, the experiments focus exclusively on the influence maximization task, which limits the insights into its generalizability. Including additional combinatorial optimization tasks in the experimental analysis would strengthen the evidence for its generalizability.\n- The paper lacks comparisons with other state-of-the-art methods involving different modalities, such as the GNN-based methods GLIE [1] and AutoGNP [2], which are designed for combinatorial graph optimization.\n\nReferences:\n\n[1] Maximizing Influence with Graph Neural Networks\n\n[2] Combinatorial Optimization with Automated Graph Neural Networks\n\nQUESTIONS:\n- The paper applies a consensus voting mechanism among MLLMs. Have the authors considered a weighted voting variant, where the weights are proportional to the fitness scores of the best solutions produced by each MLLM?\n\n- While the ensemble approach with image-based MLLMs helps mitigate layout sensitivity, it would be interesting to explore whether a single graph-based MLLM could achieve similar robustness without requiring multiple layout representations. Have the authors considered this alternative in the study?\n\n- See Weaknesses for further comparisons on different combinatorial graph optimization tasks and SOTA methods with different modalities.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-18"}

comments: SUMMARY:
The paper proposes a new evolutionary optimization approach to graph influence maximization by leveraging the reasoning capabilities of vision language models. More specifically, the proposed approach uses vision language models in an evolutionary loop and in a pointwise / pairwise fashion to update the selected nodes in a graph that might improve the overall fitness function. The authors conduct a variety of experiments to ablate various design choices in their approach over eight small/medium-sized graph datasets.

STRENGTHS AND WEAKNESSES:
Strengths:

1. The paper proposes a novel cross-disciplinary approach for influence maximization
2. The paper is well written and easy to follow along

Weaknesses:

1. The paper might have a narrow scope with regards to the NeurIPS community / line of work
2. Though the paper ablates the various design choices of their framework to a good extent, it is only limited to one task (influence maximization) when the technique is trivially generalizable to other tasks
3. Only small datasets are used in experiments which might limit the generality of the technique in larger & complex scenarios
4. Inference calls to large vision language models is expensive and the proposed approach will scale poorly to large graphs / datasets

QUESTIONS:
Following up from the listed weaknesses above:

1. Why have the experiments been restricted to only influence maximization? Section 2.1 of the paper lists numerous other tasks, including which would have increased the robustness of the empirical results.
2. How does the proposed approach scale as a function of the number of nodes / edges in a dataset (e.g., in terms of # of LLM calls).
3. Any reasons to restrict to only small-medium scale datasets for this paper?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-23