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

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.

Figures (7)

• Figure 1: The Nonlinear Semantic Gap in LLM Optimization Modeling
• Figure 2: LLM Nonlinear Optimization Modeling in Existing Methods. (a) Accuracy of 4 categories. Category L (Linear): Linear baselines; Category A (Non-quadratic Powers): Involving high-order power terms; Category B (Fractional/Rational): Introducing complex ratios or average cost constraints; Category C (Logic/Indicator): Containing piecewise functions or conditional costs.(b) Proportion of 3 types of errors: type I: modeling semantic errors, type II: nonlinear code semantic errors, type III: other code writing errors.
• Figure 3: NEDTree framework. Our approach comprises three parts: (a) Sentence-by-Sentence Extraction, (b) Mapping from Modeling Semantic to NED-Tree, and (c) Mapping from NED-Tree to Coding Semantic. The aim is to align modeling semantics with code semantics.
• Figure 4: Ablation study of NEDTree on NEXTOR benchmark. The left line is a line graph showing the difference between the module in the ablation study and NEDTree. The further to the left, the greater the difference.
• Figure 5: NEXTOR’s Statistics. (a) Problem type distribution, where HP, FP and ELP are nonlinear programming involving high-order powers (greater than 2), fractions & fractional powers, and exponentials & logarithms, respectively. (b) Question length distribution. (c) Variable numbers distribution.