Using Genetic Programming to Learn Probability Distributions as Mutation Operators with Evolutionary Programming

The mutation operator is the only source of variation in Evolutionary Programming. In the past these have been human nominated and have included the Gaussian distribution in Classical Evolutionary Programming, the Cauchy distribution in Fast Evolutionary Programming, and the Lévy distribution. In this paper, we automatically design the mutation operators (probability distributions) using Genetic Programming. This is done by using random number generators (uniformly distributed in the range 0 to 1) and using them as terminals in Genetic Programming. In other words, a random number generator is a function of a uniformly generated random number passed through a function generated by Genetic Programming. Rather than attempting to develop mutation operator for arbitrary benchmark functions drawn from the research literature, we have taken existing benchmark functions and included them in a function class, which is a probability distribution over a set of problem instances (functions). The mutation probability distribution is trained on a set of problems instances, and then tested on a second independent test set of instances to confirm that the evolved probability distribution has indeed generalized to the problem class. Initial results are highly encouraging; on each of the problem classes the probability distributions generated using Genetic Programming outperforms both the Gaussian and Cauchy distributions.