AutoOR: Scalably Post-training LLMs to Autoformalize Operations Research Problems

Modern large language models (LLMs) can translate natural-language descriptions into operations research (OR) formulations. Post-training techniques including reinforcement learning and on-policy self-distillation have further improved this capability. However, three limitations remain in training LLMs for OR formulations. First, training commonly relies on synthetic formulations validated by human experts or stronger models, constraining scalable supervision. Second, credit assignment is either coarse or costly: outcome rewards score an entire trajectory without locating the responsible modeling decision, whereas process-level supervision requires an additional evaluator. Third, privileged self-distillation can induce style mismatch by using solver context unavailable at deployment. We find that a model can improve from solver-artifact feedback generated by its own rollouts, making self-distillation a practical, evaluator-free source of dense supervision. Therefore, we propose SOLID: Solver-Informed On-Policy LearnIng through Self-Distillation, a novel framework for self-improving OR language models without verified answers or external evaluators. SOLID executes candidate programs from multiple rollouts, clusters their objectives, and selects a majority-group artifact as a pseudo-reference. The model then performs updates using group-relative advantages and dense self-supervision signals. Across multiple OR benchmarks, SOLID improves solution accuracy for both general-purpose and OR-tuned models over outcome-only group-relative training. These results show that solver artifacts can support scalable self-improvement without trusted answers.

This paper presents ORPilot, an open-source agentic AI system that translates real-world business problems into solver-ready optimization models. Unlike academic LLM-for-OR tools that assume clean problem specifications with preformatted inline data, ORPilot is designed for production conditions: ambiguous descriptions, large-scale raw operational data, and the need for portability across solver backends. The system introduces four novel components: (1) a conversational interview agent to elicit complete problem specifications, (2) a data collection agent that retrieves data independently of prompts, (3) a parameter computation agent to bridge raw tabular data and model-ready parameters, and (4) a solver-agnostic Intermediate Representation (IR) for deterministic, zero-LLM-call recompilation to Gurobi, CPLEX, PuLP, Pyomo, or OR-Tools solvers. Additionally, self-correcting retry loops utilize solver tracebacks for targeted repairs. ORPilot represents the first attempt to target production-level business problems rather than textbook operations research (OR) cases. Evaluation on real-world problems demonstrates promising results. When tested against traditional academic benchmarks: IndustryOR, NL4OPT and NLP4LP, ORPilot outperformed state-of-the-art tools in accuracy on the IndustryOR benchmark and delivered comparable performance on NL4OPT and NLP4LP.

Large language models (LLMs) can translate natural-language optimization problems into solver-ready formulations, but direct code generation is brittle: schema, indexing, and semantic errors can cause compilation failures, infeasible models, or incorrect objectives, while iterative repair, search, and multi-agent workflows increase inference cost. We present IR2Solve, an intermediate-representation-first autoformulation pipeline that uses a single semantic LLM call to produce a schema-constrained ModelIR, followed by two deterministic stages: verification and IR-to-solver compilation. ModelIR explicitly represents sets, parameters, variables, objectives, and constraints using restricted Python-like expression strings. A concrete scalar-constraint convention represents finite per-index constraint families as individual entries, reducing free-index and implicit-quantification errors while simplifying downstream verification and compilation. Across six cleaned optimization benchmarks, IR2Solve achieves strong objective correctness and remains competitive with recent optimization-modeling systems. A controlled ablation on 153 IndustryOR and ComplexLP instances shows sequential gains from the structured IR interface, the scalar-constraint instruction, and deterministic verification. On a matched ten-instance cost panel, IR2Solve uses one semantic call per instance, whereas Chain-of-Experts and SAC-Opt use 8 and 39 calls per instance and consume 3.3 and 22.9 times the token volume of IR2Solve, respectively. These results show that structured intermediate representations, combined with deterministic post-generation processing, provide a practical accuracy-cost trade-off for LLM-based optimization autoformulation.