Preserving Optimization Algorithm Expertise by means of Executable Algorithm Knowledge Graphs: A Worked Example on the TSP

Abstract

Procedural knowledge and expertise in algorithm design are usually hidden in source code and reproduced for each new optimization problem. In this work, we deal with the important question of how to store and encode this expertise in a reusable way. This is done by so-called Generative Executable Algorithm Knowledge Graphs (GEAKGs), which store expertise as a typed, executable graph: nodes are algorithmic roles that hold validated operators, edges encode admissible compositions, learned pheromone weights record effective sequences, and a deterministic Symbolic Executor produces solutions by traversal with no runtime language-model calls. This paper is a worked example. We construct a GEAKG for the Traveling Salesman Problem step by step-deriving an eleven-role schema, generating and validating executable operators, assembling an ontology-constrained topology, and learning edge weights with the MAX-MIN Ant System-and then run it. The frozen snapshot returns feasible solutions across three model scales, including a fully local model, and reaches single-digit-percent optimality gaps at zero deployment tokens. A controlled check confirms that the ontology constraint lowers the search gap by concentrating it on valid transitions. The cross-domain transfer study is deferred to the companion full version; the goal here is a reproducible recipe for building and executing this representation on a single domain.