发表机构
BUPT; BZA; BIT; CUHK-Shenzhen; PKU（北京邮电大学; 未提及具体中文名，推测可能是某个机构简称; 北京理工大学; 香港中文大学（深圳）; 北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究能否将MILP求解器逻辑自动设计为LLM引导的闭环搜索，提出闭环程序演化框架，通过PySCIPOpt实现，在割集选择器和分支规则联合设计上实例化，输出可检查修改部署的组件，在多基准测试中发现有竞争力的策略。
AI 中文摘要
机器学习方法表明数据驱动策略可加速混合整数线性规划（MILP）求解器，但许多方法因学习策略以外部预测器或其他不透明模型表示而难以检查、调整和部署。相比之下，显式求解器逻辑虽易理解和集成，但通常是手工设计而非从求解器反馈中学习。我们研究能否将MILP求解器逻辑的自动设计转换为通过端到端求解器行为直接评估的可执行白盒组件上的大语言模型（LLM）引导的闭环搜索。为此，我们提出了一个用于MILP求解器自动设计的闭环程序演化框架，通过PySCIPOpt实现，并在割集选择器和分支规则的联合设计上进行实例化。候选程序被迭代生成、加载到SCIP中，并通过在MILP实例上的直接执行进行评估，结果反馈指导基于性能的选择、针对性修复、诊断反思和多样性感知的种群维护。该方法输出可在标准求解器工作流程中检查、修改和部署的显式求解器组件。在四个基准测试家族中，我们发现LLM引导的程序演化在多种设置下能发现有竞争力的领域特定策略。
英文摘要
Machine learning methods have shown that data-driven policies can accelerate mixed-integer linear programming (MILP) solvers, but many such approaches remain difficult to inspect, adapt, and deploy because the learned policy is represented as an external predictor or other opaque model. By contrast, explicit solver logic is easier to understand and integrate, but is usually hand-designed rather than learned from solver feedback. We study whether the automatic design of MILP solver logic can instead be cast as LLM-guided closed-loop search over executable white-box components evaluated directly by end-to-end solver behavior. To this end, we propose a closed-loop program evolution framework for MILP solver auto-design, implemented through PySCIPOpt, and instantiate it on the joint design of a cut selector and a branching rule. Candidate programs are iteratively generated, loaded into SCIP, and evaluated by direct execution on MILP instances, with the resulting feedback guiding performance-based selection, targeted repair, diagnostic reflection, and diversity-aware population maintenance. The method outputs explicit solver components that can be inspected, modified, and deployed within standard solver workflows. Across four benchmark families, we find that LLM-guided program evolution can discover competitive domain-specialized policies in several settings.
