Estimating the distribution and propagation of genetic programming building blocks through tree compression

Shin et al [19] and McKay et al [15] previously applied tree compression and semantics-based simplification to study the distribution of building blocks in evolving Genetic Programming populations. However their method could only give static estimates of the degree of repetition of building blocks in one generation at a time, supplying no information about the flow of building blocks between generations. Here, we use a state-of-the-art tree compression algorithm, xmlppm, to estimate the extent to which frequent building blocks from one generation are still in use in a later generation. While they compared the behaviour of different GP algorithms on one specific problem -- a simple symbolic regression problem -- we extend the analysis to a more complex problem, a symbolic regression problem to find a Fourier approximation to a sawtooth wave, and to a Boolean domain, odd parity.