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: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:2608. 07040v1 Announce Type: new Abstract: Solving combinatorial optimization problems (COPs) requires not only efficient algorithms but also carefully crafted formulations.
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: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:2605. 25246v3 Announce Type: replace Abstract: Large language models (LLMs) are increasingly used for optimization modeling and solver-code generation, yet practical operations research and optimization problems often require a harder capability: designing scalable algorithms that exploit problem structure and outperform direct formulation-and-solve baselines.
arXiv:2608.23353v1 Announce Type: new Abstract: Mixed-integer programming (MIP) lies at the core of operations research and industrial optimization. While large language models (LLMs) have recently s...
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.
The paper introduces OptTips, a knowledge base of 50 expert optimization modeling techniques, and OptDachshund, a multi‑agent framework that generates mathematical models and solver code from natural‑language problem descriptions. Using these tools, the authors create the EfficientOpt benchmark, comprising 561 expert‑reviewed tasks with paired reference implementations, to evaluate large language models (LLMs) on both correctness and computational efficiency. Their experiments with 11 LLMs show a consistent efficiency gap: even when LLMs produce correct solutions, the resulting programs often take longer to solve than expert‑crafted counterparts, highlighting the need to assess both accuracy and runtime performance in LLM‑based optimization modeling.
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:2407. 19633v4 Announce Type: replace Abstract: Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare.
Mixed-integer programming (MIP) lies at the core of operations research and industrial optimization. While large language models (LLMs) have recently shown promise in automated MIP modeling from natur...
NextEval introduces an agent-based derivative-free optimization solver that leverages a large language model to guide the sequential selection of evaluation points. The system couples an LLM agent with a numerical environment, allowing the agent to choose tools, configure parameters, and allocate a limited evaluation budget while the environment maintains shared history and state across method switches. A benchmark protocol, NextEval Bench, is also presented to compare different agent configurations on shared DFO tasks under matched budgets and information constraints, and numerical experiments show that NextEval outperforms state-of-the-art baselines in function-evaluation efficiency.