Geometric Landscape of Homologous Crossover for Syntactic Trees

The relationship between search space, distances and genetic operators for syntactic trees is little understood. Geometric crossover and geometric mutation are representation-independent operators that are well-defined once a notion of distance over the solution space is defined. In this paper we apply this geometric framework to the syntactic tree representation and show how the well-known structural distance is naturally associated with homologous crossover and sub-tree mutation