In the context of algorithms for problem solving, procedural knowledge -- the know-how of algorithm design and operator composition -- remains implicit in code, lost between runs, and must be re-engineered for each new domain. Knowledge graphs (KGs) have proven effective for organizing declarative knowledge, yet current KG paradigms provide limited support for representing procedural knowledge as executable, learnable graph structures. We introduce \textit{Generative Executable Algorithm Knowledge Graphs} (GEAKG), a class of KGs whose nodes store executable operators, whose edges encode learned composition patterns, and whose traversal generates solutions. A GEAKG is \emph{generative} (topology and operators are synthesized by a Large Language Model), \emph{executable} (every node is runnable code), and \emph{transferable} (learned patterns generalize zero-shot across domains). The framework is domain-agnostic at the engine level: the same three-layer architecture and Ant Colony Optimization (ACO)-based learning engine can be instantiated across domains, parameterized by a pluggable ontology (\texttt{RoleSchema}). Two case studies -- sharing no domain-specific framework code -- provide concrete evidence for this framework hypothesis: (1)~Neural Architecture Search across 70 cross-dataset transfer pairs on two tabular benchmarks, and (2)~Combinatorial Optimization, where knowledge learned on the Traveling Salesman Problem transfers zero-shot to scheduling and assignment domains. Taken together, the results support that algorithmic expertise can be explicitly represented, learned, and transferred as executable knowledge graphs.

翻译：在问题求解的算法背景下，程序性知识——即算法设计与算子组合的“技法”——仍然隐式地存在于代码中，在不同运行之间丢失，并且必须为每个新领域重新构建。知识图谱已被证明能有效组织陈述性知识，但当前知识图谱范式对将程序性知识表示为可执行、可学习的图结构的支持有限。我们引入生成式可执行算法知识图谱，这是一类知识图谱，其节点存储可执行算子，边编码学习得到的组合模式，遍历图即可生成解决方案。一个GEAKG是生成式的（拓扑与算子由大型语言模型合成）、可执行的（每个节点均为可运行代码）以及可迁移的（学习到的模式可零样本泛化至跨领域）。该框架在引擎层面是领域无关的：相同的三层架构与基于蚁群优化的学习引擎可跨领域实例化，并通过可插拔本体（`RoleSchema`）参数化。两项案例研究（未共享任何特定领域的框架代码）为该框架假设提供了具体证据：（1）在两个表格基准上的70个跨数据集迁移对上的神经架构搜索，以及（2）组合优化——在旅行商问题上学习到的知识可零样本迁移至调度和分配领域。综合而言，这些结果支持了算法专长可以被显式地表示为可执行知识图谱、进行学习并迁移的观点。