Depth-dependent crossover in genetic programming with frequent trees

One of the most well studied issues in genetic programming is how to make building blocks efficiently. To make building blocks, it is important to find the substructures that appear in the individuals with higher fitness. Recently, a method based on frequent substructures has been proposed, and it has shown good performance; however, the depth of trees is not considered in the method. In this paper, we propose a hybrid crossover that involves the consideration of a combination of frequent trees and the depth of trees and apply the proposed method to symbolic regression problems. We experimentally demonstrate the effectiveness of the proposed method.