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

TL;DR

MIRROR is a multi-agent framework that enhances natural language to optimization model translation in operations research by integrating iterative error correction and hierarchical retrieval, outperforming existing methods on standard benchmarks.

Contribution

It introduces a fine-tuning-free, end-to-end multi-agent system with adaptive revision and hierarchical retrieval for more accurate OR modeling from natural language.

Findings

Outperforms existing methods on OR benchmarks

Achieves notable results on IndustryOR and Mamo-ComplexLP datasets

Provides reliable modeling for non-expert users

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.