Improving the efficiency of GP-GOMEA for higher-arity operators

Deploying machine learning models into sensitive domains in our society requires these models to be explainable. Genetic Programming (GP) can offer a way to evolve inherently interpretable expressions. GP-GOMEA is a form of GP that has been found particularly effective at evolving expressions that are accurate yet of limited size and, thus, promote interpretability. Despite this strength, a limitation of GP-GOMEA is template-based. This negatively affects its scalability regarding the arity of operators that can be used, since with increasing operator arity, an increasingly large part of the template tends to go unused. In this paper, we therefore propose two enhancements to GP-GOMEA: (i) semantic subtree inheritance, which performs additional variation steps that consider the semantic context of a subtree, and (ii) greedy child selection, which explicitly considers parts of the template that in standard GP-GOMEA remain unused. We compare different versions of GP-GOMEA regarding search enhancements on a set of continuous and discontinuous regression problems, with varying tree depths and operator sets. Experimental results show that both proposed search enhancements have a generally positive impact on the performance of GP-GOMEA, especially when the set of operators to choose from is large and contains higher-arity operators.