Abstract- Geometric crossover and geometric mutation are representation-independent operators that are welldefined once a notion of distance over the solution space is defined. They were obtained as generalizations of genetic operators for binary strings and real vectors. Our geometric framework has been successfully applied to the permutation representation leading to a clarification and a natural unification of this domain. The relationship between search space, distances and genetic operators for syntactic trees is little understood. In this paper we apply the geometric framework to the syntactic tree representation and show how the wellknown structural distance is naturally associated with homologous crossover and subtree mutation. 1

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