OPT2CODE: A retrieval-augmented framework for solving linear programming problems

• Proposes OPT2CODE, an LLM-based framework that translates natural language optimization problems into solver-specific code. • Uses retrieval-augmented generation and prompt chaining to handle complex problem structures. • Evaluates the framework on benchmark linear programming tasks using both open and closed-source language models. • Conducts a comprehensive energy analysis to evaluate the computational efficiency and environmental impact of the OPT2CODE framework. Mathematical optimization drives decisions across domains such as supply chains, energy grids, and financial systems, among others. Linear programming (LP), a tool for optimizing objectives under constraints, requires domain expertise to translate real-world problems into executable models. We explore automating this translation using Large Language Models (LLMs), generating solver-ready code from textual descriptions to reduce reliance on specialized knowledge. We propose OPT2CODE, a Retrieval-Augmented Generation (RAG) framework that utilizes compact LLMs to transform problem descriptions into optimization solver executable code. OPT2CODE utilizes code documentation for document retrieval and incorporates multiple LLM-as-a-Judge components to improve baseline performance. In addition, OPT2CODE is solver flexible and LLM flexible, and it can generate code for a broad range of mathematical optimization problems such as linear, integer linear, and mixed-integer linear, across different solvers as long as the corresponding solver documentation is available. We show empirical results on two datasets, NL4Opt and EOR, and across two solvers, Gurobi and FICO Xpress, using Llama-3.1-8B and Qwen-2.5-Coder-7B. OPT2CODE consistently improves code generation accuracy, reaching up to 67.13 % on NL4Opt with FICO Xpress and 80.00 % on EOR with Gurobi. Finally, our energy analysis shows that these improvements come at reasonable computational cost: OPT2CODE consumes 2,732.91 joules/sample (Llama-3.1-8B) and 1,759.95 joules/sample (Qwen-2.5-Coder-7B).