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...
arXiv:2407. 19633v4 Announce Type: replace Abstract: Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare.
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: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:2609.22987v1 Announce Type: new Abstract: Automated operations research (OR) modeling requires LLMs to translate natural-language decision problems into correct mathematical programs. Existing...
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:2607. 18252v1 Announce Type: new Abstract: Machine learning methods have shown that data-driven policies can accelerate mixed-integer linear programming (MILP) solvers, but many such approaches remain difficult to inspect, adapt, and deploy because the learned policy is represented as an external predictor or other opaque model.
The paper introduces Optimization Modeling from Solver Outcomes (OMSO), a reinforcement learning framework that generates solver‑specific code from natural‑language problem descriptions. OMSO uses a mathematical programming solver as a deterministic environment, executing generated code in a sandbox and converting outcomes into scalar rewards for a closed‑loop generate‑execute‑feedback‑update cycle. Experiments on datasets such as NL4OPT, MAMO, IndustryOR, and OptiBench across solvers like Gurobi, OR‑Tools, and COPT demonstrate that OMSO matches or surpasses process‑supervised fine‑tuning, enables zero‑shot transfer, and improves modeling reasoning and semantic correctness.
The paper introduces two lightweight inference harnesses, OPTICYCLE and OPTISTATE, designed to enable large language models to translate natural-language optimization problems into solver programs without additional training. Evaluated across nine benchmarks and 11 Qwen variants (0.6B–27B parameters), the harnesses consistently improve macro accuracy, with execution-guided revision boosting performance by up to 49.46 percentage points. Despite their simplicity, both harnesses outperform six adapted agentic workflows and four post-trained optimization models of comparable size, though the benefit of explicit formulation state varies by model.
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: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.