OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling

• URL: http://arxiv.org/abs/2502.11102v2
• Date: Fri, 21 Feb 2025 10:54:36 GMT
• Title: OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling
• Authors: Hongliang Lu, Zhonglin Xie, Yaoyu Wu, Can Ren, Yuxuan Chen, Zaiwen Wen,
• Abstract summary: Lack of high-quality optimization modeling datasets hampers large language models.<n>We propose a scalable framework for synthesizing a high-quality dataset, named OptMATH.<n>We demonstrate that models of various sizes trained on OptMATH achieve superior results on multiple modeling benchmarks.
• Score: 9.617742955894247
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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