Maintaining Population Diversity in Deterministic Geometric Semantic Genetic Programming by ε-Lexicase Selection

Genetic Programming (GP) is an evolutionary method for automatic programming. In recent years, crossover operators based on the semantics of programs have attracted much attention for improving the search efficiency. We have previously proposed a semantics-based crossover that deterministically generates an optimal offspring by utilizing the target semantics explicitly in symbolic regression problems. The GP method using this crossover is called Deterministic Geometric Semantic GP (D-GSGP). However, this operation may cause rapid convergence of the population. One of the ways to maintain diversity is to use an improved selection method. epsilon-Lexicase Selection is a method to select individuals based on their responses to a part of fitness cases. D-GSGP has a high affinity with epsilon-Lexicase Selection because the responses to a part of fitness cases are components of the semantics of the program. Therefore, in this research, we combine D-GSGP and epsilon-Lexicase Selection to maintain the diversity of the population. To verify the effectiveness of our proposed method, we applied the method to a practical symbolic regression problem, the Boston Housing Dataset.