Phenotype Diversity Objectives for Graph Grammar Evolution

Evolutionary algorithms are a practical means of optimising the topology of graphs. This paper explores the use of phenotype diversity measures as objectives in a graph grammar-based model of multi-objective graph evolution. Since the initial population in this model is exclusively constituted by empty productions, an active promotion of diversity is needed to establish the necessary building blocks from which optimal graphs can be constructed. Six diversity measures are evaluated on problems of symbolic regression, the 6-multiplexer, and neural control of double pole balancing. The highest success rates are obtained by defining diversity as the number of solutions that differ in at least one fitness case and do not Pareto-dominate each other.