用执行验证提升大模型优化建模能力，无需繁琐标注即可跨求解器通用。
Execution-Verified Reinforcement Learning for Optimization Modeling
- 将求解器当作可执行的验证器，通过生成-执行-反馈闭环训练
- 在多个数据集上表现优于有监督微调方法，支持零样本求解器迁移
- 低成本适配新求解器，适合需要快速部署的工业优化场景
用自然语言自动化优化建模是实现可扩展决策智能的可行路径，但现有方法或依赖高延迟的闭源大模型代理流程，或需昂贵的过程监督微调小模型，常过度拟合单一求解器API。受可验证奖励强化学习启发，我们提出执行验证优化建模（EVOM），将数学规划求解器视为确定性交互式验证器。给定自然语言问题与目标求解器，EVOM生成特定求解器代码，在沙盒环境中执行，并将执行结果转化为标量奖励，通过GRPO和DAPO在闭环生成-执行-反馈-更新过程中优化。该仅基于结果的设定无需过程级监督，通过切换验证环境即可实现跨求解器泛化。在NL4OPT、MAMO、IndustryOR和OptiBench上，针对Gurobi、OR-Tools和COPT的实验表明，EVOM性能匹配或超越过程监督微调模型，支持零样本求解器迁移，并可通过在目标求解器后端继续训练实现有效低成本适配。
原文摘要 · Abstract (English)
Automating optimization modeling with LLMs is a promising path toward scalable decision intelligence, but existing approaches either rely on agentic pipelines built on closed-source LLMs with high inference latency, or fine-tune smaller LLMs using costly process supervision that often overfits to a single solver API. Inspired by reinforcement learning with verifiable rewards, we propose Execution-Verified Optimization Modeling (EVOM), an execution-verified learning framework that treats a mathematical programming solver as a deterministic, interactive verifier. Given a natural-language problem and a target solver, EVOM generates solver-specific code, executes it in a sandboxed harness, and converts execution outcomes into scalar rewards, optimized with GRPO and DAPO in a closed-loop generate-execute-feedback-update process. This outcome-only formulation removes the need for process-level supervision, and enables cross-solver generalization by switching the verification environment rather than reconstructing solver-specific datasets. Experiments on NL4OPT, MAMO, IndustryOR, and OptiBench across Gurobi, OR-Tools, and COPT show that EVOM matches or outperforms process-supervised SFT, supports zero-shot solver transfer, and achieves effective low-cost solver adaptation by continuing training under the target solver backend.
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