A Fixed-Budget, Cluster-Aware Standard for LLM-as-a-Judge Evaluation: A Multi-Hop RAG Stress Test

Retrieval-augmented generation (RAG) systems are often compared by asking a large language model (LLM) judge which answer is better. For multi-hop RAG, this has become a measurement problem as much as a modeling problem: the same score can reflect retrieval quality, answer length, lexical overlap, or a statistical test that ignores clustered data. We ask what happens when these choices are made explicit. We propose a minimum measurement standard for LLM-as-a-judge comparisons in RAG. The standard fixes the top-100 candidate pool, evidence budget, answer cap, generator, and prompt; it also requires pre-registered hypotheses, cluster-aware inference, an exact cluster sign-flip check when feasible, and second-judge replication. Clustered benchmarks can overstate progress; the field should adopt this standard. We stress-test it with Genetic Algorithm Decoder for Multi-hop Evidence Composition (GADMEC), an evolutionary evidence selector, on 400 multi-hop questions in computer science/machine learning (CS/ML) and Materials Science. The protocol changes the empirical story. A binomial test makes all four semantic-baseline comparisons look significant; cluster-aware inference leaves only one Bonferroni-significant result. BM25 beats pure semantic GADMEC under the same budget, while a lexical-semantic hybrid recovers in CS/ML and narrows the Materials Science gap.

GEAKG: Generative Executable Algorithm Knowledge Graphs

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.