发表机构
Institute of Automation, Chinese Academy of Sciences; School of Artificial Intelligence, University of Chinese Academy of Sciences; Shandong University（中国科学院自动化研究所; 中国科学院大学人工智能学院; 山东大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对MILP分支定界中策略搜索成本高的问题，提出BiFE框架，用低保真模仿得分预筛选、高保真实例评估精英候选，在CPU上发现优于SCIP及部分GPU神经策略的分支规则。
AI 中文摘要
在混合整数线性规划（MILP）的分支定界（B&B）中，分支变量选择对效率有着关键影响。现有的神经分支策略通常需要GPU推理，而CPU高效的符号表达式则缺乏表示复杂逻辑的能力。大语言模型（LLM）生成的代码为设计具有多样化算法逻辑的轻量级分支规则提供了灵活的搜索空间。为了在基于LLM的进化框架中发现有效规则，一个核心挑战随之而来：在真实实例上进行完整的B&B评估代价过高，而离线模仿学习则面临分布偏移问题。为解决这一问题，我们提出了一个双保真度进化框架（BiFE）。它采用低保真度模仿得分作为快速预筛选器，并仅对精英候选者选择性地应用高保真度的实例内评估，从而有效平衡搜索效率与性能可靠性。实验验证了BiFE的搜索效率及其发现规则的竞争力，这些规则在CPU上优于SCIP求解器和其他基线，甚至超越了某些基于GPU的神经策略。
英文摘要
In branch-and-bound (B&B) for mixed-integer linear programming (MILP), branching variable selection critically impacts efficiency. Existing neural branching policies often require GPU inference, while CPU-efficient symbolic expressions lack the representational capacity for complex logic. Large Language Model (LLM)-generated code provides a flexible search space for designing lightweight branching rules with diverse algorithmic logic. To discover effective rules within LLM-based evolutionary frameworks, a core challenge arises: full B&B evaluation on real instances is prohibitively expensive, whereas offline imitation learning suffers from distribution shift. To address this, we introduce a Bi-Fidelity Evolutionary framework (BiFE). It employs low-fidelity imitation scores as a rapid pre-screener and selectively applies high-fidelity on-instance evaluation only to elite candidates, effectively balancing search efficiency with performance reliability. Experiments validate both the search efficiency of BiFE and the competitiveness of its discovered rules, which outperform the SCIP solver and other baselines on CPUs, and even surpass certain GPU-based neural policies.
