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

• URL: http://arxiv.org/abs/2602.03318v2
• Date: Wed, 04 Feb 2026 08:04:51 GMT
• Title: MIRROR: A Multi-Agent Framework with Iterative Adaptive Revision and Hierarchical Retrieval for Optimization Modeling in Operations Research
• Abstract summary: MIRROR is a fine-tuning-free, end-to-end multi-agent framework for operations research.<n>It translates natural language optimization problems into mathematical models and solver code.<n>Experiments show that MIRROR outperforms existing methods on standard Operations Research benchmarks.
• Score: 15.28095645151852
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Opti-Agent-Bench: Benchmarking End-to-End Optimization R&D Agents on Real-World Business Problems [1.7689718394104148]
  LLM-based agents are increasingly deployed to solve optimization problems, yet existing benchmarks evaluate them on pre-structured benchmarks.<n>We introduce an end-to-end benchmark that evaluates Large Models (LLMs) from implementation through integer code, descriptions and report generation.
  arXiv  Detail & Related papers  (2026-07-12T13:47:57Z)
• OptiAgent: End-to-End Optimization Modeling via Multi-Agent Iterative Refinement [0.0]
  OptiAgent is a multi-agent framework that is able to output a solver-ready mathematical formulation as well as executable code.<n>Our architecture prioritizes the mathematical modeling step, where dedicated agents extract structures.<n>We introduce a novel multi-loop validation architecture with four specialized feedback mechanisms, each targeting a distinct failure mode.
  arXiv  Detail & Related papers  (2026-07-06T17:27:16Z)
• Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification [53.763212981479455]
  We propose a novel framework with Dual-side Verification (Opt-Verifier) from both structure and solution perspectives.<n> Experiments on popular benchmarks demonstrate that our approach achieves over 20% improvement in accuracy.
  arXiv  Detail & Related papers  (2026-05-28T08:09:52Z)
• FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization [61.43300970020897]
  Large language models (LLMs) are increasingly used for optimization modeling and solver-code generation.<n>Existing benchmarks are limited to small or simplified examples far below real-world scale and complexity.<n>We introduce FrontierOR, among the first benchmarks to evaluate LLM-based efficient algorithm design for realistic large-scale optimization problems.
  arXiv  Detail & Related papers  (2026-05-24T20:10:42Z)
• PEARL: Solver-in-the-Loop Interactive Optimization Modeling from Natural Language [21.03524402280427]
  We introduce PEARL, a system for interactive optimization modeling.<n>PEARL learns when to test partial models, how to revise from solver diagnostics, and when to stop.<n>It operates in a multi-turn tool-integrated setting where intermediate execution results, feasibility signals, and solution checks are used to improve both formulations and solver code before finalization.
  arXiv  Detail & Related papers  (2026-05-14T06:47:20Z)
• FAMA: Failure-Aware Meta-Agentic Framework for Open-Source LLMs in Interactive Tool Use Environments [60.3427704389541]
  Large Language Models are being increasingly deployed as the decision-making core of autonomous agents.<n>Yet, in conversational benchmarks, these agents frequently fail due to the cascading effects of incorrect decision-making.<n>We present the Failure-Aware Meta-Agentic framework to tackle these challenges.
  arXiv  Detail & Related papers  (2026-04-28T02:21:53Z)
• Execution-Verified Reinforcement Learning for Optimization Modeling [49.171122807323634]
  Execution-verified learning framework treats a mathematical programming solver as a deterministic, interactive verifier.<n>Experiments on NL4OPT, MAMO, IndustryOR, and OptiBench across Gurobi, OR-Tools, and COPT show that EVOM matches or outperforms process-supervised SFT.
  arXiv  Detail & Related papers  (2026-04-01T03:39:11Z)
• NEMO: Execution-Aware Optimization Modeling via Autonomous Coding Agents [41.70615840873279]
  We present NEMO, a system that translates Natural-language descriptions of decision problems into formal Executable Mathematical Optimization implementations.<n>NEMO centers on remote interaction with autonomous coding agents (ACAs), treated as a first-class abstraction analogous to API-based interaction with LLMs.<n>Because ACAs execute within sandboxed environments, code produced by NEMO is executable by construction, allowing automated validation and repair.
  arXiv  Detail & Related papers  (2026-01-29T07:57:23Z)
• ComAgent: Multi-LLM based Agentic AI Empowered Intelligent Wireless Networks [62.031889234230725]
  6G networks rely on complex cross-layer optimization.<n> manually translating high-level intents into mathematical formulations remains a bottleneck.<n>We present ComAgent, a multi-LLM agentic AI framework.
  arXiv  Detail & Related papers  (2026-01-27T13:43:59Z)
• Automated Optimization Modeling via a Localizable Error-Driven Perspective [20.591721861026414]
  We propose a novel error-driven learning framework for automated optimization modeling.<n>MIND customized the whole model training framework from data synthesis to post-training.<n>MIND consistently outperforms all the state-of-the-art automated optimization modeling approaches.
  arXiv  Detail & Related papers  (2026-01-17T09:59:01Z)
• Sample-Efficient Online Learning in LM Agents via Hindsight Trajectory Rewriting [92.57796055887995]
  We introduce ECHO, a prompting framework that adapts hindsight experience replay from reinforcement learning for language model agents.<n> ECHO generates optimized trajectories for alternative goals that could have been achieved during failed attempts.<n>We evaluate ECHO on stateful versions of XMiniGrid, a text-based navigation and planning benchmark, and PeopleJoinQA, a collaborative information-gathering enterprise simulation.
  arXiv  Detail & Related papers  (2025-10-11T18:11:09Z)
• CALM Before the STORM: Unlocking Native Reasoning for Optimization Modeling [60.55856973678002]
  Large Reasoning Models (LRMs) have demonstrated strong capabilities in complex multi-step reasoning.<n>Existing domain adaptation methods, originally designed for earlier instruction-tuned models, often fail to exploit the advanced reasoning patterns of modern LRMs.<n>We propose textbfCALM, a framework that progressively refines LRMs within their native reasoning modes for optimization modeling tasks.
  arXiv  Detail & Related papers  (2025-10-05T13:38:31Z)
• Optimization Modeling via Semantic Anchored Alignment [30.047608671041104]
  We propose SAC-Opt, a backward-guided correction framework that grounds optimization modeling in problem semantics rather than solver feedback.<n>At each step, SAC-Opt aligns the original semantic anchors with those reconstructed from the generated code and selectively corrects only the mismatched components.<n> Empirical results on seven public datasets demonstrate that SAC-Opt improves average modeling accuracy by 7.8%, with gains of up to 21.9% on the ComplexLP dataset.
  arXiv  Detail & Related papers  (2025-09-28T12:25:31Z)
• Automated Optimization Modeling through Expert-Guided Large Language Model Reasoning [43.63419208391747]
  We present a novel framework that leverages expert-level optimization modeling principles through chain-of-thought reasoning to automate the optimization process.<n>We also introduce LogiOR, a new optimization modeling benchmark from the logistics domain, containing more complex problems with standardized annotations.
  arXiv  Detail & Related papers  (2025-08-20T04:14:54Z)
• From Natural Language to Solver-Ready Power System Optimization: An LLM-Assisted, Validation-in-the-Loop Framework [1.7136832159667206]
  This paper introduces a novel Large Language Models (LLMs)-assisted agent that automatically converts natural-language descriptions of power system optimization scenarios into compact, solver-ready formulations.<n>The proposed method focuses on discovering a mathematically compatible formulation that can be efficiently solved by off-the-shelf optimization solvers.
  arXiv  Detail & Related papers  (2025-08-11T16:22:57Z)
• ModelingAgent: Bridging LLMs and Mathematical Modeling for Real-World Challenges [72.19809898215857]
  We introduce ModelingBench, a novel benchmark featuring real-world-inspired, open-ended problems from math modeling competitions across diverse domains.<n>These tasks require translating natural language into formal mathematical formulations, applying appropriate tools, and producing structured, defensible reports.<n>We also present ModelingAgent, a multi-agent framework that coordinates tool use, supports structured, creative solutions, and generates well-grounded, creative solutions.
  arXiv  Detail & Related papers  (2025-05-21T03:33:23Z)
• MLE-Dojo: Interactive Environments for Empowering LLM Agents in Machine Learning Engineering [57.156093929365255]
  Gym-style framework for systematically reinforcement learning, evaluating, and improving autonomous large language model (LLM) agents.<n>MLE-Dojo covers diverse, open-ended MLE tasks carefully curated to reflect realistic engineering scenarios.<n>Its fully executable environment supports comprehensive agent training via both supervised fine-tuning and reinforcement learning.
  arXiv  Detail & Related papers  (2025-05-12T17:35:43Z)
• Are Large Language Models Good Prompt Optimizers? [65.48910201816223]
  We conduct a study to uncover the actual mechanism of LLM-based Prompt Optimization. Our findings reveal that the LLMs struggle to identify the true causes of errors during reflection, tending to be biased by their own prior knowledge. We introduce a new "Automatic Behavior Optimization" paradigm, which directly optimize the target model's behavior in a more controllable manner.
  arXiv  Detail & Related papers  (2024-02-03T09:48:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.