18 Function Stacks, GBEAs, and Crossover for the Parity Problem

Function stacks are a directed acyclic graph representation for genetic programming that subsumes the need for automatically defined functions, substantially reduces the number of operations required to solve a problem, and permits the use of a conservative crossover operator. Function stacks are a generalization of Cartesian genetic programming. Graph based evolutionary algorithms are a method for improving evolutionary algorithm performance by imposing a connection topology on an evolutionary population to strike an efficient balance between exploration and exploration. In this study the parity problems using function stacks for parity on 3, 4, 5, and 6 variables are tested on fifteen graphical connection topologies with and without crossover. Choosing the correct graph is found to have a statistically significant impact on time to solution. The conservative crossover operator for function stacks, new in this study, is found to improve time to solution by 4–9 fold with more improvement in harder instances of the parity problem.