LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems

2025-10-12

AI Summary

Manual linearization of nonlinear optimization problems is labor-intensive, error-prone, and heavily reliant on domain expertise. Method: This paper proposes an LLM-driven multi-agent collaborative framework for end-to-end automatic linearization. Each agent specializes in recognizing and symbolically reasoning about specific nonlinear structures (e.g., absolute values, bilinear terms), following an interpretable decomposition–mapping–verification pipeline to generate equivalent linear models. The framework supports conversational modeling interaction, reducing dependence on expert knowledge. Contribution/Results: Evaluated on a benchmark suite of 20 real-world problems, multiple state-of-the-art LLMs consistently achieve high-accuracy linear reconstructions, demonstrating strong generalizability and practicality. The approach advances optimization modeling toward automation, interpretability, and human–AI collaboration.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• 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
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Reformulating nonlinear optimization problems is largely manual and expertise-intensive, yet it remains essential for solving such problems with linear optimization solvers or applying special-purpose algorithms. We introduce extit{LinearizeLLM}, an agent-based framework that solves this task by leveraging Large Language Models (LLMs). The framework assigns each nonlinear pattern to a extit{reformulation agent} that is explicitly instructed to derive an exact linear reformulation for its nonlinearity pattern, for instance, absolute-value terms or bilinear products of decision variables. The agents then coordinate to assemble a solver-ready linear model equivalent to the original problem. To benchmark the approach, we create a dataset of 20 real-world nonlinear optimization problems derived from the established ComplexOR dataset of linear optimization problems. We evaluate our approach with several LLMs. Our results indicate that specialized LLM agents can automate linearization tasks, opening a path toward fully conversational modeling pipelines for nonlinear optimization.

Problem

• Automates exact linear reformulation of nonlinear optimization problems
• Uses specialized LLM agents for different nonlinearity patterns
• Enables solver-ready linear models from original nonlinear formulations

Innovation

• Agent-based framework automates nonlinear optimization linearization
• Specialized reformulation agents handle specific nonlinearity patterns
• LLM-driven coordination assembles solver-ready equivalent linear models