用多模态大模型解决多商品流问题，兼顾精度与速度。
Divide, Harmonize, Then Conquer It: Shooting Multi-Commodity Flow Problems with Multimodal Language Models
- 将大问题拆解为局部子问题，由大模型代理求解。
- 在真实数据上逼近最优解，速度比线性规划快1-2个数量级。
- 抗干扰能力强，适合部署在实际网络系统中。
多商品流（MCF）问题是网络流与组合优化中的基础课题，广泛应用于交通、通信和物流等领域。随着分配系统规模快速扩张，现有优化引擎在最优性与可计算性之间面临挑战。本文提出Pram，首个基于机器学习的多模态语言模型（MLM）方法，用于应对这一权衡难题。Pram首先将原问题分解为局部子问题，交由MLM驱动的“智能体”快速求解；再通过多智能体强化学习算法对子问题进行协调，确保全局一致性。理论上，Pram学习在上下文中执行梯度下降，可证明收敛至MCF问题族的最优解。实验表明，在真实数据集与公开拓扑上，Pram性能媲美甚至超越线性规划求解器（接近最优解），运行时间显著降低（快1至2个数量级）。同时，其在链路故障或流量突增下表现稳定（性能下降小于10%），展现模型对未见事件的泛化能力。Pram具有目标无关性，可无缝集成至主流分配系统，为未来网络提供实用且可扩展的解决方案。
原文摘要 · Abstract (English)
The multi-commodity flow (MCF) problem is a fundamental topic in network flow and combinatorial optimization, with broad applications in transportation, communication, and logistics, etc. Nowadays, the rapid expansion of allocation systems has posed challenges for existing optimization engines in balancing optimality and tractability. In this paper, we present Pram, the first ML-based method that leverages the reasoning power of multimodal language models (MLMs) for addressing the trade-off dilemma -- a great need of service providers. As part of our proposal, Pram (i) quickly computes high-quality allocations by dividing the original problem into local subproblems, which are then resolved by an MLM-powered "agent", and (ii) ensures global consistency by harmonizing these subproblems via a multi-agent reinforcement learning algorithm. Theoretically, we show that Pram, which learns to perform gradient descent in context, provably converges to the optimum within the family of MCF problems. Empirically, on real-world datasets and public topologies, Pram achieves performance comparable to, and in some cases even surpassing, linear programming solvers (very close to the optimal solution), and substantially lower runtimes (1 to 2 orders of magnitude faster). Moreover, Pram exhibits strong robustness (<10\% performance degradation under link failures or flow bursts), demonstrating MLM's generalization ability to unforeseen events. Pram is objective-agnostic and seamlessly integrates with mainstream allocation systems, providing a practical and scalable solution for future networks.
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