SOVER: Formal Certification of Optimization Reformulations via LLM-Assisted SMT Verification

2026-09-01

AI Summary

为解决优化问题转换验证不可靠的问题，提出SOVER框架，结合LLM与SMT技术进行形式化验证，确保转换准确性。

Abstract

Large Language Models (LLMs) have shown remarkable promise in translating and reformulating complex mathematical optimization problems across modeling languages. However, validating such transformations through empirical solver executions alone is unreliable, as solver outcomes may be affected by local minima, structural timeouts, numerical artifacts, and subtle semantic divergence between formulations. We introduce SOVER, an LLM-assisted SMT framework that separates semantic mapping from formal certification: Z3 checks domain cross-feasibility and global objective-order preservation for mixed-integer linear formulations, while dReal provides tolerance-aware feasibility/range and $ε$-argmin checks for continuous nonlinear formulations. We also introduce NLEquiv-150, a public benchmark of 100 equivalent and 50 deliberately hard non-equivalent nonlinear reformulation pairs. With LLM-extracted mappings, SOVER classifies 149/150 pairs (99.33%) correctly, including all 50 hard negatives; the sole error is an incomplete mapping extraction.

Problem

• Large Language Models
• Mathematical Optimization
• Formulation Reformulation
• Semantic Divergence
• Solver Execution

Innovation

• LLM-assisted SMT
• formal certification
• optimization reformulations
• cross-feasibility
• global objective-order preservation