Automated optimization modeling and auditing via dual-team multi-LLM-agent cooperative framework

Abstract

Translating natural language descriptions into solvable mathematical programs utilizing large language models (LLMs) remains a significant challenge in optimization modeling. Traditional approaches often struggle with error propagation between logical modeling and code implementation, while existing evaluation metrics frequently overlook the structural integrity of the mathematical models. This paper presents a dual-team multi-LLM-agent cooperative framework designed to automate optimization modeling and auditing through a decoupled architecture. The proposed system separates the task into a logical abstraction team that formalizes and audits the mathematical model and a physical implementation team that transcribes the audited model into solver code, with an audited mathematical model as their only interface. To improve the reliability of the generated results, we design an automated auditing protocol comprising a model auditor that jointly checks semantic fidelity and variable definitions, together with an execution-based syntax evaluator and a semantic evaluator for the generated program. Furthermore, we employ Graph Edit Distance to provide a structural assessment of model quality without requiring manual annotation on problem texts. Experimental results on the NL4Opt, ComplexOR, and MAMO datasets with (mixed-integer) linear problems demonstrate that our framework effectively reduces implementation failure and enhances the accuracy of both the mathematical formulation and the final solver code.