A Hybrid GP Approach for Numerically Robust Symbolic Regression

This article introduces a hybrid variant of genetic programming (GP) for doing symbolic regression. Instead of the usual interpretation of a parse tree, all top-level terms are identified and extended by multiplying them with locally optimized factors. These weighted terms are then linearly combined to form the resulting expression. When using the mean square error as fitness function, local optimization of the factors can be done efficiently by applying a robust variant of the method of least squares. Furthermore, the presented hybrid GP uses arbitrary precision arithmetic for evaluating each solution to detect major precision losses, numerical underflows, or overflows. A penalty according to the lost accuracy is added to the objective function to avoid such problems in the final solution. Various experiments indicate that the new hybrid GP finds numerically robust expressions with much smaller approximation errors faster and more reliably than traditional GP.