让大模型像人一样调试不可行的运筹学问题，自动修复并验证。
ORLoopBench: Solver-in-the-Loop Benchmarks for Self-Correction and Behavioral Rationality in Operations Research
- 构建了带求解器反馈的闭环调试流程，每步操作都触发求解器重运行。
- 在5362个线性/混合整数规划修复任务中，8B模型准确率达95.3%。
- 适合研究可信赖自动化建模与模型自修正的科研人员使用。
运筹学从业者通过迭代诊断不可行模型：检查不可约不可行子系统（IIS）、识别约束冲突、修复模型直至可行。现有大模型基准大多将运筹学视为从问题描述到求解器代码的一次性转换，忽略了这一诊断循环。本文将不可行模型修复形式化为求解器闭环的马尔可夫决策过程，每一步操作均触发求解器重执行和IIS重计算，获得确定性、可验证的反馈。提出ORLoopBench基准套件，包含两个部分：OR-Debug-Bench发布5,362个线性规划（LP）/混合整数规划（MILP）修复实例；OR-Bias-Bench在不同库存设置下评估闭式运营决策的合理性。基于求解器验证的强化学习训练使8B模型在LP修复任务上超越前沿API（RR@5达95.3% vs 92.4%），提升诊断行为，并可迁移至MILP修复。同一评估也揭示了全模型代码再生中的语义漂移：生成的可行MILP可能解决错误问题。通过求解器代理进行过程级评估，可实现针对可靠运筹学自修正的定向训练。
原文摘要 · Abstract (English)
Operations Research practitioners debug infeasible models through an iterative process: inspecting Irreducible Infeasible Subsystems ( IIS), identifying constraint conflicts, and repairing formulations until feasibility is restored. Existing LLM benchmarks mostly treat OR as one-shot translation from problem descriptions to solver code, omitting this diagnostic loop. We formalize infeasible-model repair as a solver-in-the-loop Markov Decision Process in which each action triggers solver re-execution and IIS recomputation, yielding deterministic, verifiable feedback. We introduce ORLoopBench, a benchmark suite with two components: OR-Debug-Bench releases 5,362 LP/MILP repair instances, while OR-Bias-Bench evaluates closed-form operational decision rationality across inventory settings. Solver-verified RLVR training enables an 8B model to surpass frontier APIs on LP repair (95.3% vs 92.4% RR @5), improves diagnostic behavior, and transfers to MILP repair. The same evaluation exposes semantic drift in whole-model code regeneration: feasible regenerated MILPs can solve the wrong problem. Process-level evaluation with solver oracles enables targeted training for reliable OR self-correction.
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