A novel tree differential evolution using inter-symbol distance

Differential Evolution (DE) is one of the evolutionary algorithm that was developed to handle optimization problems over continuous domains. It´s a population-based stochastic search technique with simple concept and high efficient. In recent year, many DE variants were proposed and have been applied for solving various problems. In addition, some DE based techniques are modified to handle discrete optimization problems. One of them, Tree based DE (TreeDE), which maps full trees to vectors and represents discrete symbols by points in a real-valued vector space, is a new DE-based tree discovering algorithm. TreeDE directly can apply differential operation of DE to individual vectors. However, since the search space of genotypes in the TreeDE does not correspond to the solution space of phenotypes (program tree), the mutation operation will not always work effectively. Therefore, we explicitly handle the distance of programming tree and propose new TreeDE which optimizes tree structure based on DE. In the proposed method, each individual has two types of genes: one express the neighborhood structure between the symbols, the other represents a full tree structure of the program. By evolving both genes simultaneously, effective mutation operation and optimization of the tree structure by DE engine are realized. The proposed TreeDE is compared with Genetic Programming (GP) on standard benchmark problems, and experimental results showed the effectiveness of the proposed TreeDE.