NLData2Opt: Benchmarking Parameter Derivation and Prediction for Modeling Optimization Problems from Natural Language and Data

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. We introduce Opti-Agent-Bench, an end-to-end benchmark that evaluates Large Language Models (LLMs) across the complete optimization R&D pipeline, from understanding business-language descriptions through mathematical modeling, algorithm selection, and code implementation, to solution report generation. Our design rests on three pillars: (1) businesssemantic authenticity with anti-template traps that defeat pattern matching; (2) modular evaluation with cross-module consistency checking across Problem Understanding, Formal Modeling, Implementation, and Reporting; and (3) the ORAC bi-level validity framework that simultaneously ensures task quality and scoring integrity. Across several industrialscale tasks spanning integer programming, robust optimization, stochastic programming, and non-convex optimization, we expose critical failure modes of current models, including constraint omission, model-code inconsistency, and report-implementation divergence, that remain invisible under conventional single-metric evaluation.

Optimization modeling formulates real-world decision problems as mathematical programs that solvers can use to find optimal decisions. Large language models (LLMs) can automate this process, but the resulting correct formulations can require substantial time and memory to construct and solve, limiting practical scalability. Therefore, we systematically investigate whether LLMs can identify problem structure from natural-language descriptions and apply suitable optimization modeling techniques to generate mathematical models and solver code that solve the problems correctly and efficiently. To this end, we first curate OptTips, a knowledge base of 50 expert modeling techniques in eight families. Using this knowledge, we develop OptDachshund, a multi-agent framework that transforms problems from existing optimization benchmarks into new tasks for evaluating LLMs' use of modeling techniques. It constructs conventional and expert mathematical models with solver code for the same task and data, providing baselines for correctness and computational cost. The resulting EfficientOpt benchmark contains 561 expert-reviewed tasks with paired reference implementations. Evaluation of 11 representative LLMs reveals an efficiency gap on correctly solved tasks with comparable measurements: for every LLM, most generated programs take longer to solve than their expert counterparts. Within the comparable reference-size subset, 57% of programs with correct objective values and fewer variables and linear constraints have longer recorded solver times. Case studies show that different modeling techniques can achieve the same optimal value at similar recorded cost. Faster solving may not reduce execution time if the code takes longer to prepare data and build the model. LLM optimization modeling should therefore be evaluated for both correctness and computational efficiency.

Large language models (LLMs) can translate natural-language optimization problems into solver programs, but reliably producing correct formulations and implementations remains challenging. Existing approaches improve optimization modeling through agentic workflows or task-specific post-training. This raises a practical question: can a lightweight harness using a single model role achieve competitive performance without additional training? We introduce OPTICYCLE and OPTISTATE, two lightweight inference harnesses for optimization modeling, and evaluate them on nine benchmarks comprising 2,634 problems using 11 Qwen variants spanning 0.6B-27B parameters. Our results show that execution-guided revision consistently improves macro accuracy over direct generation for all evaluated models, with gains of up to 49.46 percentage points. Despite their simplicity, both harnesses outperform six adapted agentic workflows in same-model comparisons and four evaluated post-trained optimization models at comparable model sizes, without additional training. Explicit formulation state provides further but model-dependent improvements, suggesting that additional structure is not universally beneficial.