NED-Tree: Bridging the Semantic Gap with Nonlinear Element Decomposition Tree for LLM Nonlinear Optimization Modeling

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.