A New Concordance Correlation Coefficient based Fitness Function for Genetic Programming for Symbolic Regression

Jizhong Xu, Qi Chen, Bing Xue, Mengjie Zhang

Abstract: Coefficients learning has long been challenging in genetic programming based symbolic regression (GPSR). Recent GPSR methods employ Pearson correlation coefficient for fitness assessment with post-hoc linear scaling for coefficient learning. However, this approach often leads to sub-optimal coefficient learning and inadequate consideration of nonlinear relationships between input variables and outputs. To solve those issues, this study introduces an innovative approach to integrating the Concordance Correlation Coefficient (CCC) into GPSR. Unlike Pearson correlation, CCC can effectively assess both linear and non-linear agreements between two sets of variables. Experimental results on eight regression datasets highlight the potential of CCC as a promising fitness function for GPSR without the need of a more advanced coefficient optimisation method for linear scaling.