LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914300113715200 |
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| author | Kandora, Paul-Niklas Ken Zeller, Simon Caspar Elsing, Aaron Jeremias Kuss, Elena Rebennack, Steffen |
| author_facet | Kandora, Paul-Niklas Ken Zeller, Simon Caspar Elsing, Aaron Jeremias Kuss, Elena Rebennack, Steffen |
| contents | Reformulating nonlinear optimization problems into solver-ready linear optimization problems is often necessary for practical applications, but the process is often manual and requires domain expertise. We propose LinearizeLLM, an agent-based LLM framework that produces solver-ready linear reformulations of nonlinear optimization problems. Agents first detect the nonlinearity pattern (e.g., bilinear products) and apply nonlinearity pattern-aware reformulation techniques, selecting the most suitable linearization technique. We benchmark on 40 instances: 27 derived from ComplexOR by injecting exactly-linearizable operators, and 13 automatically generated instances with deeply nested nonlinearities. LinearizeLLM achieves 73\% mean end-to-end overall success (OSR) across nonlinearity depths (8.3x higher than a one-shot LLM baseline; 4.3x higher than Pyomo). The results suggest that a set of pattern-specialized agents can automate linearization, supporting natural-language-based modeling of nonlinear optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems Kandora, Paul-Niklas Ken Zeller, Simon Caspar Elsing, Aaron Jeremias Kuss, Elena Rebennack, Steffen Machine Learning Artificial Intelligence Reformulating nonlinear optimization problems into solver-ready linear optimization problems is often necessary for practical applications, but the process is often manual and requires domain expertise. We propose LinearizeLLM, an agent-based LLM framework that produces solver-ready linear reformulations of nonlinear optimization problems. Agents first detect the nonlinearity pattern (e.g., bilinear products) and apply nonlinearity pattern-aware reformulation techniques, selecting the most suitable linearization technique. We benchmark on 40 instances: 27 derived from ComplexOR by injecting exactly-linearizable operators, and 13 automatically generated instances with deeply nested nonlinearities. LinearizeLLM achieves 73\% mean end-to-end overall success (OSR) across nonlinearity depths (8.3x higher than a one-shot LLM baseline; 4.3x higher than Pyomo). The results suggest that a set of pattern-specialized agents can automate linearization, supporting natural-language-based modeling of nonlinear optimization. |
| title | LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2510.15969 |