Roman Kalkreuth

Duy Long Tran, Anja Jankovic, Marie Anastacio et al.

Cartesian Genetic Programming has traditionally been using mutation as its main and often sole genetic operator to drive evolutionary search. Despite advancements in recent years, recombinationbased approaches have long been avoided, due to apparent lack of performance gains. This study examines two recently suggested recombination-based operators, subgraph crossover and discrete phenotypic recombination on SRBench, a benchmarking platform for symbolic regression. Using the implementations provided in the TinyverseGP framework, we perform hyperparameter optimisation of the respective representations with these two operators. Our work demonstrates that hyperparameter optimisation can lead to improvements in performance for recombination-based Cartesian Genetic Programming.

Duc-Cuong Dang, Roman Kalkreuth, Andre Opris

Cartesian Genetic Programming (CGP) is among the practical and popular forms of Genetic Programming as it uses a graph-based representation of programs. This paper presents a first runtime analysis of CGP in evolving Boolean functions using complete training sets. We prove an asymptotic bound $O(n D^5)$ for the expected number of fitness evaluations of CGP to construct a conjunction of $n$ inputs using at most $D \geq n-1$ binary gates, a minimal function set, and even with a strict survival selection. When the non-strict selection is used, the bound is improved to $O(n D^4)$. Our analysis reveals interesting characteristics of CGP induced search, which have been only observed empirically. In particular, enabling the acceptance of equally good solutions, including those with connected gates non-contributing to fitness, can lead to a speedup, and consequently a better asymptotic time bound. In contrast to conjunctions, we also prove a negative result which shows that CGP requires exponential time to evolve an exclusive disjunction. Experiments evolving conjunctions complement our theoretical findings. The use of incomplete training sets is found to further reduce the average number of fitness evaluations while maintaining a good level of generalisation.