How the Combinatorics of Neutral Spaces Leads Genetic Programming to Discover Simple Solutions

For various evolutionary systems it was found that the abundance of phenotypes in a search space, defined as the size of their respective neutral networksNeutral networks, is key to understanding the trajectory an evolutionary process takes from an initial to a target solution. In this chapter we use a Linear Genetic Programming system to demonstrate that the abundance of phenotypes is determined by the combinatorics offered in its neutral components. This translates into the size of the neutral space available to a phenotype and also can explain the beautiful and rather curious observation that the abundance of phenotypes is dependent on their complexity in a negative exponential fashion.