A schema theory analysis of mutation size biases in genetic programming with linear representations

Understanding operator bias in evolutionary computation is important because it is possible for the operator's biases to work against the intended biases induced by the fitness function. In recent work we showed how developments in GP schema theory can be used to better understand the biases induced by the standard subtree crossover when genetic programming is applied to variable length linear structures. In this paper we use the schema theory to better understand the biases induced on linear structures by two common GP subtree mutation operators: FULL and GROW mutation. In both cases we find that the operators do have quite specific biases and typically strongly oversample shorter strings.