Optimization problems are pervasive in sectors from manufacturing and
distribution to healthcare. However, most such problems are still solved
heuristically by hand rather than optimally by state-of-the-art solvers because
the expertise required to formulate and solve these problems limits the
widespread adoption of optimization tools and techniques. This paper introduces
OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and
solve (mixed integer) linear programming problems from their natural language
descriptions. OptiMUS can develop mathematical models, write and debug solver
code, evaluate the generated solutions, and improve its model and code based on
these evaluations. OptiMUS utilizes a modular structure to process problems,
allowing it to handle problems with long descriptions and complex data without
long prompts. Experiments demonstrate that OptiMUS outperforms existing
state-of-the-art methods on easy datasets by more than $20\%$ and on hard
datasets (including a new dataset, NLP4LP, released with this paper that
features long and complex problems) by more than $30\%$.

OptiMUS 是一种基于大型语言模型（LLM）的代理程序，旨在从自然语言描述中解决（混合整数）线性规划问题。OptiMUS 能够开发数学模型，编写和调试求解器代码，评估生成的解决方案，并根据这些评估改进其模型和代码。在实验证明，对于简单数据集，OptiMUS 的性能超过现有最先进方法 20％以上，对于难以处理的数据集（包括本文随附的英文描述复杂、问题较长的数据集 NLP4LP），性能超过现有最先进方法 30％以上。

OptiMUS: 可扩展的使用 (MI) LP 求解器和大型语言模型的优化建模

OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large  Language Models

Optimization problems are pervasive across various sectors, from
manufacturing and distribution to healthcare. However, most such problems are
still solved heuristically by hand rather than optimally by state-of-the-art
solvers, as the expertise required to formulate and solve these problems limits
the widespread adoption of optimization tools and techniques. We introduce
OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and
solve MILP problems from their natural language descriptions. OptiMUS is
capable of developing mathematical models, writing and debugging solver code,
developing tests, and checking the validity of generated solutions. To
benchmark our agent, we present NLP4LP, a novel dataset of linear programming
(LP) and mixed integer linear programming (MILP) problems. Our experiments
demonstrate that OptiMUS is able to solve 67\% more problems compared to a
basic LLM prompting strategy. OptiMUS code and NLP4LP dataset are available at
\href{https://github.com/teshnizi/OptiMUS}{this https URL}

OptiMUS 是一个基于 LLM 的代理，能够通过自然语言描述来制定和解决 MILP 问题，同时具备开发数学模型、编写和调试求解器代码、开发测试并检查生成的解的有效性的能力。通过与基本 LLM 提示策略的比较，我们的实验表明，OptiMUS 能够解决比基本策略多 67％的问题。

OptiMUS: 利用 MIP 求解器和大型语言模型的优化建模

OptiMUS: Optimization Modeling Using mip Solvers and large language  models

When trained effectively, the Variational Autoencoder (VAE) can be both a
powerful generative model and an effective representation learning framework
for natural language. In this paper, we propose the first large-scale language
VAE model, Optimus. A universal latent embedding space for sentences is first
pre-trained on large text corpus, and then fine-tuned for various language
generation and understanding tasks. Compared with GPT-2, Optimus enables guided
language generation from an abstract level using the latent vectors. Compared
with BERT, Optimus can generalize better on low-resource language understanding
tasks due to the smooth latent space structure. Extensive experimental results
on a wide range of language tasks demonstrate the effectiveness of Optimus. It
achieves new state-of-the-art on VAE language modeling benchmarks. We hope that
our first pre-trained big VAE language model itself and results can help the
NLP community renew the interests of deep generative models in the era of
large-scale pre-training, and make these principled methods more practical.

本研究提出 Optimus 模型，通过大规模预训练和微调，实现了面向各种自然语言生成和理解任务的通用潜在嵌入空间。与 GPT-2 相比，Optimus 可使用潜在向量在抽象层次上进行引导语言生成。与 BERT 相比，由于平滑的潜在空间结构，Optimus 在低资源语言理解任务上具有更好的泛化能力。实验结果表明 Optimus 的有效性，并在 VAE 语言建模基准上实现了新的最佳性能。