# SAC-Opt: Semantic Anchors for Iterative Correction in Optimization Modeling

arXiv: https://arxiv.org/abs/2510.05115 · HTML: https://mlsanity.com/paper/2510.05115/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 43 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [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)
- [Evolution of Semantic Similarity -- A Survey](https://mlsanity.com/paper/2004.13820/) (2020)
- [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://mlsanity.com/paper/2407.09887/) (2024)
- [Large Language Models for Supply Chain Optimization](https://mlsanity.com/paper/2307.03875/) (2023)
- [Can You Trust LLM Judgments? Reliability of LLM-as-a-Judge](https://mlsanity.com/paper/2412.12509/) (2024)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [A Survey on the Optimization of Large Language Model-based Agents](https://mlsanity.com/paper/2503.12434/) (2025)
- [A Theoretical Understanding of Self-Correction through In-context Alignment](https://mlsanity.com/paper/2405.18634/) (2024)
- [Understanding the Dark Side of LLMs' Intrinsic Self-Correction](https://mlsanity.com/paper/2412.14959/) (2024)
- [OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale](https://mlsanity.com/paper/2407.19633/) (2024)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [A Survey of Optimization Modeling Meets LLMs: Progress and Future Directions](https://mlsanity.com/paper/2508.10047/) (2025)
- [Holy Grail 2.0: From Natural Language to Constraint Models](https://mlsanity.com/paper/2308.01589/) (2023)
- [When Large Language Model Meets Optimization](https://mlsanity.com/paper/2405.10098/) (2024)
- [Solving General Natural-Language-Description Optimization Problems with Large Language Models](https://mlsanity.com/paper/2407.07924/) (2024)
- [To the Globe (TTG): Towards Language-Driven Guaranteed Travel Planning](https://mlsanity.com/paper/2410.16456/) (2024)
- [Cardinal Optimizer (COPT) User Guide](https://mlsanity.com/paper/2208.14314/) (2022)
- [Decision Information Meets Large Language Models: The Future of Explainable Operations Research](https://mlsanity.com/paper/2502.09994/) (2025)
- [Self-Correction Makes LLMs Better Parsers](https://mlsanity.com/paper/2504.14165/) (2025)

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

- [ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization](https://mlsanity.com/paper/2602.15983/) (2026)
- [TriVAL: A Tri-Validation Framework for Faithful Automatic Optimization Modeling](https://mlsanity.com/paper/2605.23966/) (2026)
- [StarOR: Synergizing Tree Search and Test-Time Reinforcement Learning for Optimization Modeling](https://mlsanity.com/paper/2606.15197/) (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)
- [EvoOptiGraph: Weakness-Driven Coevolution via Graph-Based Structural Generation for Optimization Modeling](https://mlsanity.com/paper/2606.26578/) (2026)
- [IR2Solve: Structured Intermediate Representations for Cost-Efficient Optimization Autoformulation](https://mlsanity.com/paper/2608.02641/) (2026)
- [Admission Without Answers: Label-Free Certification and Experience Learning for LLM-Based Optimization Modeling](https://mlsanity.com/paper/2608.15565/) (2026)
- [SemOPT: Fixing Semantic Errors in LLM-based Optimization Modeling via Reward-Guided Search](https://mlsanity.com/paper/2609.37361/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have opened new paradigms in optimization modeling by enabling the generation of executable solver code from natural language descriptions. Despite this promise, existing approaches typically remain solver-driven: they rely on single-pass forward generation and apply limited post-hoc fixes based on solver error messages, leaving undetected semantic errors that silently produce syntactically correct but logically flawed models. To address this challenge, we propose SAC-Opt, a backward-guided correction framework that grounds optimization modeling in problem semantics rather than solver feedback. At each step, SAC-Opt aligns the original semantic anchors with those reconstructed from the generated code and selectively corrects only the mismatched components, driving convergence toward a semantically faithful model. This anchor-driven correction enables fine-grained refinement of constraint and objective logic, enhancing both fidelity and robustness without requiring additional training or supervision. Empirical results on seven public datasets demonstrate that SAC-Opt improves average modeling accuracy by 7.7%, with gains of up to 21.9% on the ComplexLP dataset. These findings highlight the importance of semantic-anchored correction in LLM-based optimization workflows to ensure faithful translation from problem intent to solver-executable code.