In this work, we improve upon two frequently used mutation algorithms and therefore introduce three rened mutation strategies for Cartesian Genetic Programming. At rst, 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 predened 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 dierent classication, regression and boolean regression benchmarks that all methods lead to better tness values. This is then further supported by probabilistic comparison methods such as the Bayesian comparison of classiers 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 dier from the second mutation strategy listed.

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This work presents and evaluates a novel modification to existing mutation operators for Cartesian Genetic Programming (CGP). We discuss and highlight a so far unresearched limitation of how CGP explores its search space which is caused by certain nodes being inactive for long periods of time. Our new mutation operator is intended to avoid this by associating each node with a dynamically changing weight. When mutating a connection between nodes, those weights are then used to bias the probability distribution in favour of inactive nodes. This way, inactive nodes have a higher probability of becoming active again. We include our mutation operator into two variants of CGP and benchmark both versions on four Boolean learning tasks. We analyse the average numbers of iterations a node is inactive and show that our modification has the intended effect on node activity. The influence of our modification on the number of iterations until a solution is reached is ambiguous if the same number of nodes is used as in the baseline without our modification. However, our results show that our new mutation operator leads to fewer nodes being required for the same performance; this saves CPU time in each iteration. CCS CONCEPTS• Computing methodologies → Genetic programming.