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

2026-04-01

AI Summary

This work addresses the semantic misalignment and unstable information extraction that arise when large language models automatically translate natural language descriptions of nonlinear operations research optimization problems into executable code. To tackle these challenges, the authors propose the NED-Tree framework, which enhances parameter mapping robustness through sentence-level information extraction and recursively decomposes complex nonlinear terms into solver-compatible subcomponents using an adaptive tree structure, thereby aligning modeling semantics with code semantics. As the first approach to incorporate an element decomposition mechanism to guide large models in nonlinear modeling, this study also introduces NEXTOR, a new benchmark tailored to complex nonlinear, multi-constraint operations research problems. Experimental results demonstrate that the proposed method achieves an average accuracy of 72.51% across ten benchmarks, significantly outperforming existing approaches.

Abstract

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.

Problem

• Nonlinear Optimization
• Semantic Gap
• Large Language Models
• Operations Research
• Natural Language to Code

Innovation

• NED-Tree
• nonlinear optimization
• semantic alignment
• element decomposition
• LLM-based modeling