GEAKG: Generative Executable Algorithm Knowledge Graphs
This work addresses the challenge of making algorithmic expertise explicit and transferable for researchers and practitioners in AI and optimization, though it builds on existing KG and ACO methods, making it somewhat incremental.
The paper tackles the problem of representing procedural knowledge for algorithm design, which is typically implicit in code, by introducing Generative Executable Algorithm Knowledge Graphs (GEAKG) that store executable operators and learned composition patterns, enabling zero-shot transfer across domains. Results include demonstrations in Neural Architecture Search across 70 cross-dataset transfer pairs and Combinatorial Optimization with zero-shot transfer from the Traveling Salesman Problem to scheduling and assignment domains.
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.