Positional Bias Does Not Influence Cartesian Genetic Programming with Crossover

Henning Cui, Michael Heider, Jörg Hähner

Abstract: The recombination operator plays an important role in many evolutionary algorithms. However, in Cartesian Genetic Programming (CGP), which is part of the aforementioned category, the usefulness of crossover is contested. In this work, we investigate whether CGP’s positional bias actually influences the usefulness of the crossover operator negatively. This bias describes a skewed distribution of CGP’s active and inactive nodes, which might lead to destructive behaviours of standard recombination operators. We try to answer our hypothesis by employing one standard CGP implementation and one without the effects of positional bias. Both versions are combined with one of four standard crossover operators, or with no crossover operator. Additionally, two different selection methods are used to configure a CGP variant. We then analyse their performance and convergence behaviour on eight benchmarks taken from the Boolean and symbolic regression domain. By using Bayesian inference, we are able to rank them, and we found that positional bias does not influence CGP with crossover. Furthermore, we argue that the current research on CGP with standard crossover operators is incomplete, and CGP with recombination might not negatively impact its evolutionary search process. On the contrary, using CGP with crossover improves its performance.