MIRROR: A Multi-Agent Framework with Iterative Adaptive Revision and Hierarchical Retrieval for Optimization Modeling in Operations Research

2026-02-03

AI Summary

This work addresses the limitations of current large language models in automated optimization modeling, which often lack reliable collaborative error correction and task-relevant retrieval mechanisms, leading to modeling inaccuracies and heavy reliance on expert intervention. The authors propose a fine-tuning-free, end-to-end multi-agent framework that automatically translates natural language problem descriptions into precise mathematical models and solver-ready code. This is achieved through execution-feedback-driven iterative self-correction and a hierarchical, modeling-task-oriented retrieval strategy. Evaluated on standard operations research benchmarks as well as complex industrial datasets—including IndustryOR and Mamo-ComplexLP—the approach significantly outperforms existing methods, offering non-expert users an efficient, robust, and high-precision solution for automated optimization modeling.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Search and Retrieval-Augmented AI: Large language models for search

Abstract

Operations Research (OR) relies on expert-driven modeling-a slow and fragile process ill-suited to novel scenarios. While large language models (LLMs) can automatically translate natural language into optimization models, existing approaches either rely on costly post-training or employ multi-agent frameworks, yet most still lack reliable collaborative error correction and task-specific retrieval, often leading to incorrect outputs. We propose MIRROR, a fine-tuning-free, end-to-end multi-agent framework that directly translates natural language optimization problems into mathematical models and solver code. MIRROR integrates two core mechanisms: (1) execution-driven iterative adaptive revision for automatic error correction, and (2) hierarchical retrieval to fetch relevant modeling and coding exemplars from a carefully curated exemplar library. Experiments show that MIRROR outperforms existing methods on standard OR benchmarks, with notable results on complex industrial datasets such as IndustryOR and Mamo-ComplexLP. By combining precise external knowledge infusion with systematic error correction, MIRROR provides non-expert users with an efficient and reliable OR modeling solution, overcoming the fundamental limitations of general-purpose LLMs in expert optimization tasks.

Problem

• optimization modeling
• Operations Research
• large language models
• error correction
• retrieval

Innovation

• multi-agent framework
• iterative adaptive revision
• hierarchical retrieval
• optimization modeling
• execution-driven correction