Investigation of simplification threshold and noise level of input data in numerical simplification of genetic programs

In tree based Genetic Programming (GP) there is a tendency for program sizes to increase as the run proceeds without a corresponding improvement in fitness. This increases resource usage, both memory and CPU time, and may result in over-fitting the training data. Numerical simplification is a method for removing redundant code from the program trees as the run proceeds. Compared with the canonical genetic programming method, numerical simplification can generate much smaller programs, use much shorter evolutionary training times and achieve comparable effectiveness performance. A key parameter of this method is the simplification threshold. This paper examines whether there exists any relationship between the noise level in the input data and the optimum value for the simplification threshold and, if it exists, what that relationship is. Our results suggest that there is a relationship between the optimum value of the simplification threshold and the level of noise in the input data and that a lower bound for the optimum simplification threshold is equal to the noise level and an upper bound is five times the noise level.