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Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models
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Uses multimodal LLMs (GPT-4o) as evolutionary crossover/mutation/initialization operators on image-encoded graph sparsifications, with a master-worker cooperative multi-sparsification framework and layout-ensemble consensus voting, evaluated on influence maximization and toy tasks.
Problem
Traditional EA encodings (binary/numerical) fail to capture network topology in graph-structured combinatorial problems such as influence maximization; large network visualizations are cluttered and MLLMs are sensitive to layout.
Approach
Encode graph and candidate solution jointly as an image, use MLLMs as evolutionary operators on degree- and community-sparsified networks, cooperate across sparsified domains via a master-worker elite pool with projection/injection mappings, and ensemble multiple graph layouts by consensus voting.
Key results
- Co-MLLM(KK) achieves the best average ranking (1.38) among compared methods on influence maximization over eight networks, e.g., Netscience 17.6 vs 16.8 for CoeCo.
- MLLM-Ensemble ranks first (avg rank 1.13) against single-layout MLLM variants (KK, FR, GraphOpt) and vanilla EO, e.g., Polblogs 196.3 vs 190.0 for vanilla EO.
- Heuristic-based injection filling slightly outperforms random filling across all eight graphs (e.g., Rutgers89 753.12 vs 732.9).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use knowledge transfer between degree-based and community-based sparsified domains instead of a single-domain evolutionary optimizer | Co-EO · Influence maximization across eight real-world networks | fitness | Helped |
| Use MLLM-guided operators with multiple layouts and consensus voting rather than the strongest single-layout MLLM variant | MLLM-based evolutionary optimization · Influence maximization across eight real-world networks | fitness | Mixed |
| Set knowledge-transfer interval to 2 rather than 5 (ablation) | Cooperative evolutionary optimization · Influence maximization across eight real-world networks | fitness | Helped |
| Use heuristic-based filling rather than random filling for injected candidates (ablation) | Cooperative evolutionary optimization · Influence maximization across eight real-world networks | fitness | Helped |
Surprising findings
- Degree-based sparsification and community-based sparsification each yield different MLLM validation rates, with Spars-D producing more mutation repetition errors on several networks.
- Layout choice alone shifts MLLM initialization fitness substantially, with no single layout dominating across networks.
Limitations
- Plotting beyond roughly 200 nodes produces cluttered images, so subset-selection tasks need sparsification to a fixed 50 nodes/100 edges.
- Sparsification cannot be applied to permutation problems such as TSP, so the method is limited for them.
- Results rely on a single proprietary MLLM (GPT-4o) and API calls, with MLLM outputs needing fidelity checks.
Experimental setup
Datasets: USAir Netscience Polblogs Facebook WikiVote Rutgers89 MSU24 Texas84 Dolphins Lesmis
Benchmarks: USAir Netscience Polblogs Facebook WikiVote MSU24 Texas84 Rutgers89 Dolphins Lesmis TSP
Metrics: expected diffusion value (fitness) AUC of largest connected component tour length average rank validation rate API running time
Baselines: SAEP CoeCo SSR Vanilla EO Spars-D-EO Spars-C-EO Co-EO
Builds on: SAEP CoeCo SSR
Closest papers by meaning
- $\texttt{STRCMP}$: Integrating Graph Structural Priors with Language Models for Combinatorial Optimization (NeurIPS 2025 · similarity 0.88)
- EvoOptiGraph: Weakness-Driven Coevolution via Graph-Based Structural Generation for Optimization Modeling (NeurIPS 2026 · similarity 0.87)
- GraphChain: Large Language Models for Large-scale Graph Analysis via Tool Chaining (NeurIPS 2025 · similarity 0.85)
- ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution (NeurIPS 2024 · similarity 0.85)
- From Sequence to Structure: Uncovering Substructure Reasoning in Transformers (NeurIPS 2025 · similarity 0.84)
- Divide, Harmonize, Then Conquer It: Shooting Multi-Commodity Flow Problems with Multimodal Language Models (ICLR 2026 · similarity 0.84)
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