Lévy-flight genetic programming: Towards a new mutation paradigm

Abstract

Lévy flights are a class of random walks inspired directly by observing animal foraging habits, in which the stride length is drawn from a power-law distribution. This implies that the vast majority of the strides will be short. However, on rare occasions, the stride are gigantic. We use this technique to self-adapt the mutation rate used in Linear Genetic Programming. We apply this original approach to three different classes of problems: Boolean regression, quadratic polynomial regression, and surface reconstruction. We find that in all cases, our method outperforms the generic, commonly used constant mutation rate of 1 over the size of the genotype. We compare different common values of the power-law exponent to the regular spectrum of constant values used habitually. We conclude that our novel method is a viable alternative to constant mutation rate, especially because it tends to reduce the number of parameters of genetic programing. © 2012 Springer-Verlag.