Numerical simplification for bloat control and analysis of building blocks in genetic programming

In tree-based genetic programming, there is a tendency for the size of the programs to increase from generation to generation, a phenomenon known as bloat. It is standard practice to place some form of control on program size either by limiting the number of nodes or the depth of the program trees, or by adding a component to the fitness function that rewards smaller programs (parsimony pressure). Others have proposed directly simplifying individual programs using algebraic methods. In this paper, we add node-based numerical simplification as a tree pruning criterion to control program size. We investigate the effect of on-line program simplification, both algebraic and numerical, on program size and resource usage. We also investigate the distribution of building blocks within a genetic programming population and how this is changed by using simplification. We show that simplification results in reductions in expected program size, memory use and computation time. We also show that numerical simplification performs at least as well as algebraic simplification, and in some cases will outperform algebraic simplification. We further show that although the two on-line simplification methods destroy some existing building blocks, they effectively generate new more diverse building blocks during evolution, which compensates for the negative effect of disruption of building blocks.