Optimization modeling and verification from problem specifications using a multi-agent multi-stage LLM framework
Bibliographic record
Abstract
This paper explores the use of Large Language Models (LLMs) in modeling real-world optimization problems. We concretely define the task of translating natural language descriptions into optimization models (NL2OPT) and provide criteria for classifying optimization problems for the NL2OPT task. Our novel multi-agent modeling framework leverages relations identifier agents and a multi-agent verification mechanism, eliminating the need for solver execution. Additionally, we introduce a straightforward and practical evaluation framework, offering a more effective assessment method compared to traditional execution-based evaluations. We have created a unique dataset tailored for optimization modeling, featuring Problem Specifications as a structured representation of optimization problems. Through comprehensive experiments, our study compares our modeling framework with existing LLM reasoning strategies, highlighting their relative effectiveness in optimization modeling tasks. We also perform ablation studies to explore the effect of different components of our modeling framework. Experimental results demonstrate that our multi-agent framework outperforms many common LLM prompting strategies.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".