Refining Mutation Variants in Cartesian Genetic Programming

Abstract

In this work, we improve upon two frequently used mutation algorithms and therefore introduce three refined mutation strategies for Cartesian Genetic Programming. At first, we take the probabilistic concept of a mutation rate and split it into two mutation rates, one for active and inactive nodes respectively. Afterwards, the mutation method Single is taken and extended. Single mutates nodes until an active node is hit. Here, our extension mutates nodes until more than one but still predefined number n of active nodes are hit. At last, this concept is taken and a decay rate for n is introduced. Thus, we decrease the required number of active nodes hit per mutation step during CGP’s training process. We show empirically on different classification, regression and boolean regression benchmarks that all methods lead to better fitness values. This is then further supported by probabilistic comparison methods such as the Bayesian comparison of classifiers and the Mann-Whitney-U-Test. However, these improvements come with the cost of more mutation steps needed which in turn lengthens the training time. The third variant, in which n is decreased, does not differ from the second mutation strategy listed.