# ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization

arXiv: https://arxiv.org/abs/2602.15983 · HTML: https://mlsanity.com/paper/2602.15983/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [LEVER: Learning to Verify Language-to-Code Generation with Execution](https://mlsanity.com/paper/2302.08468/) (2023)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Metamorphic Testing: A New Approach for Generating Next Test Cases](https://mlsanity.com/paper/2002.12543/) (2020)
- [OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling](https://mlsanity.com/paper/2502.11102/) (2025)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [OptiChat: Bridging Optimization Models and Practitioners with Large Language Models](https://mlsanity.com/paper/2501.08406/) (2025)
- [SAC-Opt: Semantic Anchors for Iterative Correction in Optimization Modeling](https://mlsanity.com/paper/2510.05115/) (2025)

## Built on by (most cited first, 8 of 8)

- [OptiLoop: Coordination-in-the-Loop Verification and Repair for LLM-Generated Optimization Agents](https://mlsanity.com/paper/2605.27630/) (2026)
- [StarOR: Synergizing Tree Search and Test-Time Reinforcement Learning for Optimization Modeling](https://mlsanity.com/paper/2606.15197/) (2026)
- [Falsification-Based Verification of LLM-Generated Optimization Models: Sound Test Batteries and Their Detection Limits](https://mlsanity.com/paper/2607.16646/) (2026)
- [Is Vibe Coding the Future? An Empirical Assessment of LLM Generated Codes for Construction Safety](https://mlsanity.com/paper/2604.12311/) (2026)
- [Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontiers](https://mlsanity.com/paper/2606.15577/) (2026)
- [Admission Without Answers: Label-Free Certification and Experience Learning for LLM-Based Optimization Modeling](https://mlsanity.com/paper/2608.15565/) (2026)
- [OptiSkill: A Hierarchical and Evolving SkillBank for LLM-Based Optimization Modeling](https://mlsanity.com/paper/2609.22987/) (2026)
- [OR for AI That Does OR: Routing LLMs up the Escalator inside the OSCAR Framework](https://mlsanity.com/paper/2610.00912/) (2026)

## Abstract (arXiv)

Large language models (LLMs) can translate natural-language problem descriptions into optimization code, but the code is prone to silent failures: it executes and returns a solver-feasible solution while encoding a semantically incorrect formulation. On compositional problems, the resulting feasibility-correctness gap reaches 90 percentage points. We introduce ReLoop, which combines two mechanisms. Structured generation decomposes code production into a four-stage reasoning chain (understand, formalize, synthesize, verify) to reduce formulation errors during generation. Behavioral verification detects the errors that remain by testing whether the formulation responds correctly to solver-based parameter perturbation, a signal that comes from the solver rather than from LLM self-review and requires no ground truth. The two mechanisms address different error structures: structured generation gives the largest gain on compositional problems (+8.5pp accuracy on RetailOpt-190 with Claude Opus 4.6), and behavioral verification gives its largest gain on localized defects (+4.4pp on MAMO-ComplexLP). With diagnostic execution recovery, ReLoop reaches 100% executable code on Claude Opus 4.6, and relative to direct generation it raises or preserves every reported metric of the three chat-tuned foundation models on all three benchmarks. For the narrowly fine-tuned SFT model we test, the chain-of-thought prompt conflicts with its learned output format and lowers its accuracy on MAMO-ComplexLP; we document and analyze this interaction. We release RetailOpt-190, 190 compositional retail optimization scenarios in which several constraints interact.