Using schema theory to explore interactions of multiple operators

In the last two years the schema theory for Genetic Programming (GP) has been applied to the problem of understanding the length biases of a variety of crossover and mutation operators on variable length linear structures. In these initial papers, operators were studied in isolation. In practice, however, they are typically used in various combinations, and in this paper we present the first schema theory analysis of the complex interactions of multiple operators. In particular we apply the schema theory to the use of standard subtree crossover, full mutation, and grow mutation (in varying proportions) to variable length linear structures in the one-then-zeros problem. We then show how the results can be used to guide choices about the relative proportion of these operators in order to achieve certain structural goals during a run.