The paper introduces SOVER, a framework that uses Large Language Models (LLMs) to extract semantic mappings between optimization reformulations and then formally verifies these mappings with SMT solvers. Z3 is employed to check domain cross-feasibility and objective-order preservation for mixed-integer linear problems, while dReal handles tolerance-aware feasibility and ε-argmin checks for continuous nonlinear problems. The authors also present NLEquiv-150, a benchmark of 150 nonlinear reformulation pairs, and report that SOVER correctly classifies 149 out of 150 pairs, including all 50 hard negatives, with the single error due to incomplete mapping extraction.
arXiv:2608.28725v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly used as graders, verifiers, and process auditors, but most mathematical evaluations still emphasize final...
The paper examines large language models (LLMs) as tools for numerical optimization, focusing on their ability to exploit mathematical problem structures and generate near‑optimal solutions. An evaluation framework is introduced to separate solution quality from execution failures such as numerical inaccuracies, constraint violations, and formatting errors. Experiments on convex optimization, fractional programming, and constrained projection problems show that LLMs can capture useful optimization structures, but reliability decreases with higher dimensionality and depends on the problem’s structure. An iterative refinement mechanism that provides targeted feedback on feasibility and solution quality significantly improves reliability and extends the dimensional range where LLMs produce valid solutions, though persistent numerical and structural errors limit their use as standalone optimizers.
arXiv:2602. 15983v3 Announce Type: replace-cross Abstract: Large language models (LLMs) can translate natural language into optimization code, but silent failures pose a critical risk: code that executes and returns solver-feasible solutions may encode semantically incorrect formulations---a feasibility--correctness gap reaching 90 percentage points on compositional problems.
arXiv:2607. 10768v1 Announce Type: new Abstract: LLM-based agents are increasingly deployed to solve optimization problems, yet existing benchmarks evaluate them on pre-structured mathematical formulations that bypass the most critical challenge: translating complex business requirements into correct models and solve efficiently.
arXiv:2608. 07040v1 Announce Type: new Abstract: Solving combinatorial optimization problems (COPs) requires not only efficient algorithms but also carefully crafted formulations.
arXiv:2608. 02641v1 Announce Type: cross Abstract: 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.
arXiv:2607. 18256v1 Announce Type: new Abstract: Optimization modeling is the process of translating real-world decision problems, often described in natural language, into formal mathematical formulations and executable solver code.
arXiv:2607. 20474v1 Announce Type: new Abstract: Natural language interfaces can greatly benefit the accessibility and usability of optimization modeling, and recent advances in large language models (LLMs) show promise in automatically translating textual problem descriptions into executable solver formulations.
arXiv:2606. 15577v1 Announce Type: new Abstract: Large Language Models (LLMs) are increasingly involved in complex mathematical optimization, even if the pragmatic user who triggers them is unaware of it.
arXiv:2609.38434v1 Announce Type: cross Abstract: Real-world optimization problems are difficult to model accurately because many objectives and constraints reside in domain experts' tacit knowledge,...
ORSMT is a tool that uses Satisfiability Modulo Theories to verify and repair artifacts produced by large language models when automating optimization modeling from natural language. It provides a typed semantic interface, exact SMT relation queries, and mechanisms to align decisions, project auxiliary variables, and reconstruct artifacts, thereby improving model-code match rates across thousands of problems. The system demonstrates significant gains in correctness and matching rates compared to existing methods such as ReLoop and Opt‑Verifier.
arXiv:2607. 14818v1 Announce Type: cross Abstract: We report on CoreForge, an experience in using large language models (LLMs) to build an unweighted MaxSAT solver from research papers rather than from an existing solver codebase.