OptiMind: Teaching LLMs to Think Like Optimization Experts

TL;DR

OptiMind tackles the challenge of translating natural language problem descriptions into executable MILP formulations by integrating optimization-domain knowledge into both training and inference. The framework uses a class-based error analysis to generate targeted hints, cleans training data to reduce ground-truth noise, and employs inference-time prompts with self-consistency and multi-turn refinement to reduce output errors. Empirical results show 13–21 percentage-point accuracy gains over a base 20B model across challenging MILP benchmarks, with further improvements from hints and test-time scaling, approaching frontier-model performance while remaining open-source. The work demonstrates that domain-informed data and prompting strategies substantially improve reliability and scalability of LLM-assisted optimization formulation, with broad implications for democratizing access to optimization capabilities. It also provides a rigorous evaluation protocol via careful benchmark cleaning and multi-turn inference analysis, and plans to release datasets and methods to benefit the research community.

Abstract

Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise. Recent advances in large language models for complex reasoning have spurred interest in automating this task, translating natural language into executable optimization models. Current approaches, however, achieve limited accuracy, hindered by scarce and noisy training data without leveraging domain knowledge. In this work, we systematically integrate optimization expertise to improve formulation accuracy for mixed-integer linear programming, a key family of mathematical programs. Our OptiMind framework leverages semi-automated, class-based error analysis to guide both training and inference, explicitly preventing common mistakes within each optimization class. Our resulting fine-tuned LLM significantly improves formulation accuracy by 20.7% across multiple optimization benchmarks, with consistent gains under test-time scaling methods such as self-consistency and multi-turn feedback, enabling further progress toward robust LLM-assisted optimization formulation.

Figures (14)

• Figure 1: OptiMind high-level overview.
• Figure 2: From problem description to solution.
• Figure 3: An overview of our training data cleaning and multi-turn inference pipeline.
• Figure 4: Sample hint for a problem type (Traveling Salesman Problem, TSP) and comparison of the model's response before and after applying hints.
• Figure 5: Average accuracy for different models without majority voting. Models colored in blue are open-sourced models under 32B parameters, and models in purple are closed-sourced frontier models. OptiMind outperforms open-source baselines and performs comparably to O4-Mini in the single-turn setting and to GPT-5 with multi-turn self-corrections.