Optimization and Constraint Modeling using LLMs with a Retrieval Augmented Generation Process

Abstract

Both optimization modeling and constraint modeling are non-trivial problems requiring deep domain expertise and proficiency in modeling formalism languages. Despite their importance across logistics, healthcare, and supply chain management, current large language models regularly produce structurally inconsistent or incomplete optimization formulations, particularly in combinatorial settings. This paper evaluates whether a Retrieval-Augmented Generation pipeline built on a curated synthetic dataset can meaningfully improve LLM optimization modeling performance. A total of 500 optimization problems were synthesized using seed descriptions from the Text2Zinc dataset and professional personas created using an LLM, specified in JSON and associated with validated Python solver scripts. These problems were encoded in a Chroma vector database. For each inference problem, semantically similar problems were retrieved and used as contextual guidance for a LangChain LLM agent. Three benchmark testbeds were used to evaluate the proposed pipeline under the Qwen 3 30B Instruct model. Accuracy rose from 40% to 72% on NL4OPT, 40% to 56% on MAMO Easy, and 32% to 56% on MAMO Complex. The use of semantically validated synthetic examples greatly improves both solution accuracy and structure. The combination of synthetic dataset generation with retrieval augmentation provides an effective alternative to fine-tuning, suggesting that domain-specific synthetic corpora paired with retrieval augmentation can serve as a practical pathway for deploying LLM-based optimization tools in real-world decision-support contexts without costly model retraining.