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

2026-02-02

AI Summary

This work addresses the challenge large language models face in accurately translating natural language descriptions into optimization models, particularly when handling composite constraints and intricate business rules. To bridge this gap, the authors propose a Canonical Intermediate Representation (CIR) that decouples business rule logic from its mathematical implementation, serving as a semantic intermediary between natural language and formal optimization models. They further introduce a multi-agent R2C framework that parses input text, retrieves domain knowledge, generates CIR specifications, and subsequently instantiates them into mathematical optimization models. The paper establishes the first systematic benchmark for rule-to-constraint reasoning and demonstrates state-of-the-art performance: on a newly curated complex-rule benchmark, their method achieves 47.2% accuracy, matches or exceeds closed-source models like GPT-5 on existing benchmarks, and sets new best results on select tasks through a self-reflection mechanism.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• optimization problem formulation
• large language models
• composite constraints
• operational rules
• code generation

Innovation

• Canonical Intermediate Representation
• constraint archetypes
• rule-to-constraint
• optimization modeling
• LLM-based code generation