# OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling

arXiv: https://arxiv.org/abs/2502.11102 · HTML: https://mlsanity.com/paper/2502.11102/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Placed in LLM synthetic data generation, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 18 of its 78 references that are in the map.
- First posted on arXiv 16 Feb 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [LLM synthetic data generation](https://mlsanity.com/synth/llm-synthetic-data-generation/)

## Builds on (most cited first, 18 of 18)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [Augmenting Math Word Problems via Iterative Question Composing](https://mlsanity.com/paper/2401.09003/) (2024)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [A Survey on Data Synthesis and Augmentation for Large Language Models](https://mlsanity.com/paper/2410.12896/) (2024)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability](https://mlsanity.com/paper/2310.02807/) (2023)
- [MILP-StuDio: MILP Instance Generation via Block Structure Decomposition](https://mlsanity.com/paper/2410.22806/) (2024)
- [An Improved Analysis of LP-based Control for Revenue Management](https://mlsanity.com/paper/2101.11092/) (2021)
- [DIG-MILP: a Deep Instance Generator for Mixed-Integer Linear Programming with Feasibility Guarantee](https://mlsanity.com/paper/2310.13261/) (2023)

## Built on by (most cited first, 30 of 49)

- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learning](https://mlsanity.com/paper/2511.09092/) (2025)
- [Auto-Formulating Dynamic Programming Problems with Large Language Models](https://mlsanity.com/paper/2507.11737/) (2025)
- [AlphaOPT: Formulating Optimization Programs with Self-Improving LLM Experience Library](https://mlsanity.com/paper/2510.18428/) (2025)
- [Automated Optimization Modeling via a Localizable Error-Driven Perspective](https://mlsanity.com/paper/2602.11164/) (2026)
- [Constructing Industrial-Scale Optimization Modeling Benchmark](https://mlsanity.com/paper/2602.10450/) (2026)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [OptiMind: Teaching LLMs to Think Like Optimization Experts](https://mlsanity.com/paper/2509.22979/) (2025)
- [ORGEval: Graph-Theoretic Evaluation of LLMs in Optimization Modeling](https://mlsanity.com/paper/2510.27610/) (2025)
- [ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization](https://mlsanity.com/paper/2602.15983/) (2026)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization](https://mlsanity.com/paper/2605.25246/) (2026)
- [Toward a Trustworthy Optimization Modeling Agent via Verifiable Synthetic Data Generation](https://mlsanity.com/paper/2508.03117/) (2025)
- [OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scaling](https://mlsanity.com/paper/2601.19924/) (2026)
- [NEMO: Execution-Aware Optimization Modeling via Autonomous Coding Agents](https://mlsanity.com/paper/2601.21372/) (2026)
- [Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification](https://mlsanity.com/paper/2605.29556/) (2026)
- [Strategy-Aware Optimization Modeling with Reasoning LLMs](https://mlsanity.com/paper/2605.02545/) (2026)
- [CALM Before the STORM: Unlocking Native Reasoning for Optimization Modeling](https://mlsanity.com/paper/2510.04204/) (2025)
- [OptiVerse: A Comprehensive Benchmark towards Optimization Problem Solving](https://mlsanity.com/paper/2604.21510/) (2026)
- [From Soliloquy to Agora: Memory-Enhanced LLM Agents with Decentralized Debate for Optimization Modeling](https://mlsanity.com/paper/2604.25847/) (2026)
- [REG: A Regularization Optimizer for Robust Training Dynamics](https://mlsanity.com/paper/2510.03691/) (2025)
- [Canonical Intermediate Representation for LLM-based optimization problem formulation and code generation](https://mlsanity.com/paper/2602.02029/) (2026)
- [MIRROR: A Multi-Agent Framework with Iterative Adaptive Revision and Hierarchical Retrieval for Optimization Modeling in Operations Research](https://mlsanity.com/paper/2602.03318/) (2026)
- [Execution-Verified Reinforcement Learning for Optimization Modeling](https://mlsanity.com/paper/2604.00442/) (2026)
- [ORPilot: A Production-Oriented Agentic LLM-for-OR Tool for Optimization Modeling](https://mlsanity.com/paper/2605.02728/) (2026)
- [TriVAL: A Tri-Validation Framework for Faithful Automatic Optimization Modeling](https://mlsanity.com/paper/2605.23966/) (2026)
- [OptSkills: Learning Generalizable Optimization Skills from Problem Archetypes via Cluster-Based Distillation](https://mlsanity.com/paper/2605.29829/) (2026)
- [Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems](https://mlsanity.com/paper/2606.04816/) (2026)
- [Solver-Independent Automated Problem Formulation via LLMs for High-Cost Simulation-Driven Design](https://mlsanity.com/paper/2512.18682/) (2025)
- [Agentic MIP Research: Accelerated Constraint Handler Generation](https://mlsanity.com/paper/2605.09186/) (2026)

## Abstract (arXiv)

Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language descriptions (NL). This data scarcity also contributes to the generalization difficulties experienced by learning-based methods. To address these challenges, we propose a scalable framework for synthesizing a high-quality dataset, named OptMATH. Starting from curated seed data with mathematical formulations (MF), this framework automatically generates problem data (PD) with controllable complexity. Then, a back-translation step is employed to obtain NL. To verify the correspondence between the NL and the PD, a forward modeling step followed by rejection sampling is used. The accepted pairs constitute the training part of OptMATH. Then a collection of rejected pairs is identified and further filtered. This collection serves as a new benchmark for optimization modeling, containing difficult instances whose lengths are much longer than these of NL4OPT and MAMO. Through extensive experiments, we demonstrate that models of various sizes (0.5B-32B parameters) trained on OptMATH achieve superior results on multiple modeling benchmarks, thereby validating the effectiveness and scalability of our approach. Our dataset is publicly available at https://github.com/AuroraLHL/OptMATH.