LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems
This work addresses the problem of automating nonlinear optimization reformulation for researchers and practitioners in operations research and optimization, representing an incremental step toward conversational modeling pipelines.
The authors tackled the manual and expertise-intensive task of reformulating nonlinear optimization problems into linear forms by introducing LinearizeLLM, an agent-based framework that uses Large Language Models (LLMs) to automate this process, achieving results that indicate specialized LLM agents can handle such tasks effectively.
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 \textit{LinearizeLLM}, an agent-based framework that solves this task by leveraging Large Language Models (LLMs). The framework assigns each nonlinear pattern to a \textit{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.