AI 中文总结
针对现有优化建模框架过度依赖MILP的缺陷，提出以DSL为核心的OptiDSL框架，通过LLM实现自然语言到标准化DSL的映射，在44种COP类型基准测试中显著优于MILP框架，建模准确率和效率大幅提升。
AI 中文摘要
求解组合优化问题（COP）不仅需要高效算法，还需要精心设计的建模形式。尽管近期研究利用大语言模型（LLM）实现了优化建模自动化，但当前框架大多依赖刚性的混合整数线性规划（MILP）范式。本文指出，并非所有问题都最适合建模为MILP，因为将复杂领域强行转化为线性约束会导致极高的建模复杂度，并严重限制求解器的灵活性。为解决这一问题，我们提出OptiDSL框架，该框架将重点从刚性MILP建模形式转移到特定领域语言（DSL）表示。通过利用LLM将自然语言映射到标准化、领域认可的结构，OptiDSL将问题建模与执行解耦。该范式支持与多样化的专用求解器库无缝集成，涵盖从传统启发式方法到现代基于学习的方法。在包含44种COP类型的综合基准测试中，实验结果显示OptiDSL显著优于基于MILP的流程，建模准确率提升51.66%，建模时间缩短91.71%；在现有基准测试中，它同样优于基于MILP的流程，建模准确率提升23.09%。我们的代码可在该https地址获取。
英文摘要
Solving combinatorial optimization problems (COPs) requires not only efficient algorithms but also carefully crafted formulations. While recent works have leveraged LLMs to automate optimization modeling, current frameworks predominantly rely on a rigid mixed-integer linear programming (MILP) paradigm. In this paper, we argue that not all problems are best modeled as MILP, as forcing complex domains into linear constraints can induce prohibitive modeling complexity and severely restrict solver flexibility. To address this, we propose OptiDSL, a framework that shifts the focus from rigid MILP formulations to domain-specific language (DSL) representations. By utilizing LLMs to map natural language onto standardized, domain-accepted structures, OptiDSL decouples problem formulation from execution. This paradigm enables seamless integration with a diverse library of specialized solvers, ranging from traditional heuristics to modern learning-based methods. Experimental results on the comprehensive benchmark of 44 COP types show that OptiDSL significantly surpasses MILP-based pipelines, yielding a 51.66% gain in formulation accuracy and a 91.71% decrease in modeling time. Notably, it also outperforms MILP-based pipelines on the existing benchmark, achieving a 23.09% higher formulation accuracy. Our code is available at https://anonymous.4open.science/r/OptiDSL.
