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Divide, Harmonize, Then Conquer It: Shooting Multi-Commodity Flow Problems with Multimodal Language Models

ICLR 2026 · Multi-agent systems and games › LLM agents · approach: Agent data synthesis and behavior studies · 0 citations (OpenAlex)

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Proposes PRAM, which partitions multi-commodity flow problems by source node and allocates flows with a shared multimodal language model agent (Qwen2.5-VL-7B truncated to 8 layers), adapted via multi-agent RL with counterfactual advantages, LoRA and learned prefix context.

Problem

Multi-commodity flow (MCF) allocation requires balancing solution optimality and computational tractability at scale; LP solvers are slow on large topologies and existing ML/RL methods scale poorly and generalize weakly.

Approach

Partition MCF by source node into subproblems handled in parallel by a shared MLM agent that receives topology as an image and demands as text; coordinate agents with counterfactual multi-agent policy gradients, LoRA communication and reprogrammed context prefix embeddings.

Key results

• On Kdl (754 nodes), PRAM completes allocation in under 25 seconds on average, about 100x faster than LP and 5x faster than POP, while achieving over 90% of the best LP scheme's performance.
• For MLU on CERNET and GEANT, PRAM's configurations are reportedly about 21% and 45% better than LP outputs.
• Under link failures or flow fluctuation, PRAM degradation is reported as under 15% even at alpha=2 in the 90th percentile.

Surprising findings

• PRAM's MLU outputs on CERNET and GEANT are reported to beat the LP solver's outputs, attributed to MLU's convexity properties.
• Without partitioning, the trainable parameter count on Kdl nearly matches full-parameter MLM adaptation.

Limitations

• Fine-tuning PRAM remains resource-intensive even after truncating the backbone.
• Visual encoding of topology may introduce inherent bias.
• Relies on historical demands and predicted demands; performance drops relative to exact-demand LP.

Experimental setup

Datasets: Meta DB Meta WEB Abilene CERNET GEANT GtsCe Colt UsCarrier Cogentco Kdl

Benchmarks: Meta DB Meta WEB Abilene CERNET GEANT GtsCe Colt UsCarrier Cogentco Kdl

Metrics: normalized maximum link utilization normalized total flow normalized concurrent flow computation time

Baselines: LP (Gurobi) POP LP-top DRL HARP Aether

Builds on: LoRA COMA counterfactual baseline Time-LLM POP PPO

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