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Optimization Modeling via Semantic Anchored Alignment

Yansen Zhang, Qingcan Kang, Yujie Chen, Yufei Wang, Xiongwei Han, Tao Zhong, Mingxuan Yuan, Chen Ma

TL;DR

The paper addresses semantic gaps in LLM-generated optimization models by introducing SAC-Opt, a backward semantic anchor–driven correction framework that aligns problem semantics with generated code through iterative refinement. It extracts structured problem data, translates it into modular code, reconstructs semantics from the code, and uses semantic consistency checks to selectively correct only mismatched components, followed by solver-based debugging if needed. Empirically, SAC-Opt achieves an average accuracy improvement of 7.8% across seven public datasets, with as much as 21.9% gains on ComplexLP, demonstrating strong generalization across models and tasks. This approach enhances fidelity and robustness in automated optimization modeling without extra supervision, offering a scalable path for reliable real-world deployments.

Abstract

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 7.8\%, 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.

Optimization Modeling via Semantic Anchored Alignment

TL;DR

The paper addresses semantic gaps in LLM-generated optimization models by introducing SAC-Opt, a backward semantic anchor–driven correction framework that aligns problem semantics with generated code through iterative refinement. It extracts structured problem data, translates it into modular code, reconstructs semantics from the code, and uses semantic consistency checks to selectively correct only mismatched components, followed by solver-based debugging if needed. Empirically, SAC-Opt achieves an average accuracy improvement of 7.8% across seven public datasets, with as much as 21.9% gains on ComplexLP, demonstrating strong generalization across models and tasks. This approach enhances fidelity and robustness in automated optimization modeling without extra supervision, offering a scalable path for reliable real-world deployments.

Abstract

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 7.8\%, 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.

Paper Structure

This paper contains 34 sections, 11 equations, 4 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Related Work
  4. LLMs for Optimization
  5. Correction in Optimization
  6. Methodology
  7. Problem Formulation
  8. Structured Data Extraction
  9. Structured Data to Model Translation
  10. Model to Structured Data Reconstruction
  11. Iterative Semantic Alignment and Correction
  12. Model Debugging
  13. Experiments
  14. Dataset
  15. Baselines
  16. ...and 19 more sections

Figures (4)

  • Figure 1: Overview of the SAC-Opt workflow. Semantic anchors, referring to the constraints and objective in the structured data.
  • Figure 2: Comparison of cardinality of the error set and iteration count in SAC-Opt. Here the cardinality of the error set refers to the number of misaligned semantic anchors in the error set.
  • Figure 3: Comparison of average correction and debugging numbers in SAC-Opt.
  • Figure : SAC-Opt: Iterative Correction with Semantic Anchors