Canonical Intermediate Representation for LLM-based optimization problem formulation and code generation

TL;DR

This paper introduces the Canonical Intermediate Representation (CIR) schema and the rule-to-constraint (R2C) framework to improve LLM-based formulation of complex optimization problems, achieving state-of-the-art accuracy.

Contribution

The paper proposes CIR as a novel schema for explicit problem modeling and R2C as a multi-agent pipeline, advancing LLM-based optimization problem formulation.

Findings

R2C achieves 47.2% accuracy on the new benchmark.

R2C performs competitively on existing benchmarks.

Reflection mechanism improves R2C's performance.

Abstract

Automatically formulating optimization models from natural language descriptions is a growing focus in operations research, yet current LLM-based approaches struggle with the composite constraints and appropriate modeling paradigms required by complex operational rules. To address this, we introduce the Canonical Intermediate Representation (CIR): a schema that LLMs explicitly generate between problem descriptions and optimization models. CIR encodes the semantics of operational rules through constraint archetypes and candidate modeling paradigms, thereby decoupling rule logic from its mathematical instantiation. Upon a newly generated CIR knowledge base, we develop the rule-to-constraint (R2C) framework, a multi-agent pipeline that parses problem texts, synthesizes CIR implementations by retrieving domain knowledge, and instantiates optimization models. To systematically evaluate rule-to-constraint reasoning, we test R2C on our newly constructed benchmark featuring rich operational rules, and benchmarks from prior work. Extensive experiments show that R2C achieves state-of-the-art accuracy on the proposed benchmark (47.2% Accuracy Rate). On established benchmarks from the literature, R2C delivers highly competitive results, approaching the performance of proprietary models (e.g., GPT-5). Moreover, with a reflection mechanism, R2C achieves further gains and sets new best-reported results on some benchmarks.