Gene-pool Optimal Mixing in Cartesian Genetic Programming

Genetic Programming (GP) can make an important contribution to explainable artificial intelligence because it can create symbolic expressions as machine learning models. Nevertheless, to be explainable, the expressions must not become too large. This may, however, limit their potential to be accurate. The re-use of subexpressions has the unique potential to mitigate this issue. The Genetic Programming Gene-pool Optimal Mixing Evolutionary Algorithm (GP-GOMEA) is a recent model-based GP approach that has been found particularly capable of evolving small expressions. However, its tree representation offers no explicit mechanisms to re-use subexpressions. By contrast, the graph representation in Cartesian GP (CGP) is natively capable of re-use. For this reason, we introduce CGP-GOMEA, a variant of GP-GOMEA that uses graphs instead of trees. We experimentally compare various configurations of CGP-GOMEA with GP-GOMEA and find that CGP-GOMEA performs on par with GP-GOMEA on three common datasets. Moreover, CGP-GOMEA is found to produce models that re-use subexpressions more often than GP-GOMEA uses duplicate subexpressions. This indicates that CGP-GOMEA has unique added potential, allowing to find even smaller expressions than GP-GOMEA with similar accuracy.