On the search space of genetic programming and its relation to nature's search space

The size of the search space has been analyzed for genetic programming and genetic algorithms. It is highly unlikely to find any single individual in this huge search space. However, genetic programming with variable length structures differs from standard genetic algorithms where fixed size bit strings are used in that usually many different individuals show the same pheno-typical behavior due to introns. Therefore, finding any given behavior is not as difficult as the size of the search space suggests. A quantitative analysis is presented for the number of individuals that code for the identity function. The identity function is important in the analysis of the search space because it can be used to construct individuals showing the same behavior as any given individual. Finally, an analogy is drawn to nature's sequence space which suggests possible directions for future research. The representation should be chosen such that all possible behaviors are reachable within a comparatively small number of steps from any given behavior and the individuals coding for any given behavior should be distributed randomly in the search space. In addition, long paths of neutral mutations should lead to individuals which code for the same behavior.