Large-Scale Optimization Model Auto-Formulation: Harnessing LLM Flexibility via Structured Workflow

2026-01-14

AI Summary

This work addresses the complexity and limited automation in large-scale optimization modeling by proposing LEAN-LLM-OPT, a novel lightweight multi-agent framework. The approach decomposes modeling into standardized subtasks: an upstream agent dynamically constructs the modeling pipeline, while a downstream agent generates structured optimization formulations. Leveraging few-shot learning, tool invocation, and collaborative reasoning capabilities of large language models (e.g., GPT-4.1 and gpt-oss-20B), the framework introduces the first large-scale automated modeling benchmark, Large-Scale-OR, along with a real-world airline revenue management scenario, Air-NRM. Evaluated on both synthetic and Singapore Airlines case studies, the system achieves state-of-the-art performance, demonstrating strong effectiveness and generalization across diverse optimization contexts.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Learning to Search
• Natural Language Processing: (Large) Language Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Large-scale optimization is a key backbone of modern business decision-making. However, building these models is often labor-intensive and time-consuming. We address this by proposing LEAN-LLM-OPT, a LightwEight AgeNtic workflow construction framework for LLM-assisted large-scale OPTimization auto-formulation. LEAN-LLM-OPT takes as input a problem description together with associated datasets and orchestrates a team of LLM agents to produce an optimization formulation. Specifically, upon receiving a query, two upstream LLM agents dynamically construct a workflow that specifies, step-by-step, how optimization models for similar problems can be formulated. A downstream LLM agent then follows this workflow to generate the final output. The agentic workflow leverages common modeling practices to structure the modeling process into a sequence of sub-tasks, offloading mechanical data-handling operations to auxiliary tools. This reduces the LLM's burden in planning and data handling, allowing us to exploit its flexibility to address unstructured components. Extensive simulations show that LEAN-LLM-OPT, instantiated with GPT-4.1 and the open source gpt-oss-20B, achieves strong performance on large-scale optimization modeling tasks and is competitive with state-of-the-art approaches. In addition, in a Singapore Airlines choice-based revenue management use case, LEAN-LLM-OPT demonstrates practical value by achieving leading performance across a range of scenarios. Along the way, we introduce Large-Scale-OR and Air-NRM, the first comprehensive benchmarks for large-scale optimization auto-formulation. The code and data of this work is available at https://github.com/CoraLiang01/lean-llm-opt.

Problem

• large-scale optimization
• auto-formulation
• LLM
• workflow construction
• optimization modeling

Innovation

• LLM agents
• optimization auto-formulation
• few-shot learning
• workflow decomposition
• large-scale optimization