Genetic programming convergence

Abstract

We study both genotypic and phenotypic convergence in GP floating point continuous domain symbolic regression over thousands of generations. Subtree fitness variation across the population is measured and shown in many cases to fall. In an expanding region about the root node, both genetic opcodes and function evaluation values are identical or nearly identical. Bottom up (leaf to root) analysis shows both syntactic and semantic (including entropy) similarity expand from the outermost node. Despite large regions of zero variation, fitness continues to evolve and near zero crossover disruption suggests improved GP systems.

Genetic programming convergence

“…But the goal of GP should also be to solve problems which cannot be solved by other methods. Recently Rich Lenski [15] has confounded the Biological establishment and overturned conventional wisdom by showing that natural evolution can continue to produce fitter organisms even after tens of thousands of generations (see Section 1.5 in [11]). Perhaps a way to open up GP to more adventurous applications, will require that the GP population evolves for far longer?…”

“…For all other uses, contact the owner/author(s). To support this we have made a series of traditional and automatic software improvements [4][5][6][7][8][9]12] such that the run shown in [11,Fig. 3] which was cut short after 5 weeks due to a neigbourhood wide external power failure, can now be repeated in 5 days.…”

“…After many thousands of generations, GP populations are typically composed of trees of random shape, neither balanced and full nor deep and straggly but somewhat fractal, self similar, between the two extremes[2,14]. We also see again sub-quadratic bloat[2] (e.g [11,. Fig.…”

Failed Disruption Propagation in Integer Genetic Programming

“…(For visualisation small x-direction noise added.) Top: in ten 1000 generations runs GP tends to converge [28] making the speed up of incremental evaluation [26] more effective. Note top (single core) data are spread out horizontally for visualisation only.…”

A Trillion Genetic Programming Instructions per Second

“…Information theory suggests what we have described for floating point [48,51] and now integer genetic programming [47] will hold where there aren't side effects to carry information long distances through program code or GP trees (see Figure 4, page 6). Essentially the argument is: for a mutation, change, bug, transient error, etc., to have an effect it must give rise to a change of state and that change of state must propagate from the error to the program's output [65].…”