Harnessing Language Models as Optimization Modeling Agents

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 generate syntactically valid optimization programs, yet often struggle to reliably choose an effective modeling strategy, leading to incorrect formulations and inefficient solver behavior. We propose SAGE, a strategy-aware framework that makes Modeling Strategy explicit in both data construction and post-training. SAGE builds a solver-verified multi-strategy dataset and trains a student model with supervised fine-tuning followed by Segment-Weighted GRPO using a composite reward over format compliance, correctness, and solver efficiency. Across eight benchmarks spanning synthetic and real-world settings, SAGE improves average pass@1 from 72.7 to 80.3 over the strongest open-source baseline. With multiple generations, SAGE discovers more distinct correct formulations and improves component-level diversity at pass@16 by 19-29%. At the largest scale, SAGE produces more compact constraint systems with 14.2% fewer constraints than the baseline, consistent with solver-efficient modeling. Overall, these results show that making Modeling Strategy explicit improves automated optimization modeling. Code is available at https://github.com/rachhhhing/SAGE.

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.