Semantic tournament selection for genetic programming based on statistical analysis of error vectors

The selection mechanism plays a very important role in the performance of Genetic Programming (GP). Among several selection techniques, tournament selection is often considered the most popular. Standard tournament selection randomly selects a set of individuals from the population and the individual with the best fitness value is chosen as the winner. However, an opportunity exists to enhance tournament selection as the standard approach ignores finer-grained semantics which can be collected during GP program execution. In the case of symbolic regression problems, the error vectors on the training fitness cases can be used in a more detailed quantitative comparison. In this paper we introduce the use of a statistical test into GP tournament selection that utilizes information from the individual's error vector, and three variants of the selection strategy are proposed. We tested these methods on twenty five regression problems and their noisy variants. The experimental results demonstrate the benefit of the proposed methods in reducing GP code growth and improving the generalisation behaviour of GP solutions when compared to standard tournament selection, a similar selection technique and a state of the art bloat control approach.