Hierarchical semantic cluster operator for automatic empirical modeling

This study proposed a new semantic-based library and operator to improve the convergence of genetic programming (GP) in symbolic regression. The suggested library (hierarchical semantic cluster library, HSCL) is a program set in which programs form hierarchical clusters based on their semantics, through which the proposed operator (hierarchical semantic cluster operator, HSCO) performs a hierarchical search to derive an offspring. The validity of HSCO was verified at both the operator and algorithm levels. The percentile rank of HSCO’s offspring was in the top 0.3% when compared to exhaustive search (EX)’s offspring, and the computation time of HSCO was only approximately 5% of EX. In a benchmark test using 11 types of algorithms, the algorithm employing HSCO (Iterated local search using HSCO, ILSH) showed the third, second, and fourth best performance in training error, testing error, and program size, respectively.