NED-Tree: Bridging the Semantic Gap with Nonlinear Element Decomposition Tree for LLM Nonlinear Optimization Modeling
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911562433822720 |
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| author | Hu, Zhijing Deng, Yufan Liu, Haoyang Fan, Changjun |
| author_facet | Hu, Zhijing Deng, Yufan Liu, Haoyang Fan, Changjun |
| contents | Automating the translation of Operations Research (OR) problems from natural language to executable models is a critical challenge. While Large Language Models (LLMs) have shown promise in linear tasks, they suffer from severe performance degradation in real-world nonlinear scenarios due to semantic misalignment between mathematical formulations and solver codes, as well as unstable information extraction. In this study, we introduce NED-Tree, a systematic framework designed to bridge the semantic gap. NED-Tree employs (a) a sentence-by-sentence extraction strategy to ensure robust parameter mapping and traceability; and (b) a recursive tree-based structure that adaptively decomposes complex nonlinear terms into solver-compatible sub-elements. Additionally, we present NEXTOR, a novel benchmark specifically designed for complex nonlinear, extensive-constraint OR problems. Experiments across 10 benchmarks demonstrate that NED-Tree establishes a new state-of-the-art with 72.51% average accuracy, NED-Tree is the first framework that drives LLMs to resolve nonlinear modeling difficulties through element decomposition, achieving alignment between modeling semantics and code semantics. The NED-Tree framework and benchmark are accessible in the anonymous repository https://anonymous.4open.science/r/NORA-NEXTOR. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01588 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | NED-Tree: Bridging the Semantic Gap with Nonlinear Element Decomposition Tree for LLM Nonlinear Optimization Modeling Hu, Zhijing Deng, Yufan Liu, Haoyang Fan, Changjun Artificial Intelligence Automating the translation of Operations Research (OR) problems from natural language to executable models is a critical challenge. While Large Language Models (LLMs) have shown promise in linear tasks, they suffer from severe performance degradation in real-world nonlinear scenarios due to semantic misalignment between mathematical formulations and solver codes, as well as unstable information extraction. In this study, we introduce NED-Tree, a systematic framework designed to bridge the semantic gap. NED-Tree employs (a) a sentence-by-sentence extraction strategy to ensure robust parameter mapping and traceability; and (b) a recursive tree-based structure that adaptively decomposes complex nonlinear terms into solver-compatible sub-elements. Additionally, we present NEXTOR, a novel benchmark specifically designed for complex nonlinear, extensive-constraint OR problems. Experiments across 10 benchmarks demonstrate that NED-Tree establishes a new state-of-the-art with 72.51% average accuracy, NED-Tree is the first framework that drives LLMs to resolve nonlinear modeling difficulties through element decomposition, achieving alignment between modeling semantics and code semantics. The NED-Tree framework and benchmark are accessible in the anonymous repository https://anonymous.4open.science/r/NORA-NEXTOR. |
| title | NED-Tree: Bridging the Semantic Gap with Nonlinear Element Decomposition Tree for LLM Nonlinear Optimization Modeling |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2604.01588 |