Graph design by graph grammar evolution

Determining the optimal topology of a graph is pertinent to many domains, as graphs can be used to model a variety of systems. Evolutionary algorithms constitute a popular optimization method, but scalability is a concern with larger graph designs. Generative representation schemes, often inspired by biological development, seek to address this by facilitating the discovery and reuse of design dependencies and allowing for adaptable exploration strategies. We present a novel developmental method for optimizing graphs that is based on the notion of directly evolving a hypergraph grammar from which a population of graphs can be derived. A multi-objective design system is established and evaluated on problems from three domains: symbolic regression, circuit design, and neural control. The observed performance compares favorably with existing methods, and extensive reuse of subgraphs contributes to the efficient representation of solutions. Constraints can also be placed on the type of explored graph spaces, ranging from tree to pseudograph. We show that more compact solutions are attainable in less constrained spaces, although convergence typically improves with more constrained designs.