Using Numerical Simplification to Control Bloat 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 process 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 tree, 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 show that simplification results in reductions in expected program size, memory use and computation time. We further show that numerical simplification performs at least as well as algebraic simplification alone, and in some cases will outperform algebraic simplification.