  Large language models (LLMs) have exhibited their problem-solving ability in
mathematical reasoning. Solving realistic optimization (OPT) problems in
industrial application scenarios requires advanced and applied math ability.
However, current OPT benchmarks that merely solve linear programming are far
from complex realistic situations. In this work, we propose E-OPT, a benchmark
for end-to-end optimization problem-solving with human-readable inputs and
outputs. E-OPT contains rich optimization problems, including linear/nonlinear
programming with/without table data, which can comprehensively evaluate LLMs'
solving ability. In our benchmark, LLMs are required to correctly understand
the problem in E-OPT and call code solver to get precise numerical answers.
Furthermore, to alleviate the data scarcity for optimization problems, and to
bridge the gap between open-source LLMs on a small scale (e.g., Llama-2-7b and
Llama-3-8b) and closed-source LLMs (e.g., GPT-4), we further propose a novel
data synthesis method namely ReSocratic. Unlike general data synthesis methods
that proceed from questions to answers, ReSocratic first incrementally
synthesizes optimization scenarios with mathematical formulations step by step
and then back-translates the generated scenarios into questions. In such a way,
we construct the ReSocratic-29k dataset from a small seed sample pool with the
powerful open-source large model DeepSeek-V2. To demonstrate the effectiveness
of ReSocratic, we conduct supervised fine-tuning with ReSocratic-29k on
multiple open-source models. The results show that Llama3-8b is significantly
improved from 13.6% to 51.7% on E-OPT, while DeepSeek-V2 reaches 61.0%,
approaching 65.5% of GPT-4.
