Structure-Based Constants in Genetic Programming

Abstract

Evolving constants in Genetic Programming is still an open issue. As real values they cannot be integrated in GP trees in a direct manner, because the nodes represent discrete symbols. Present solutions are the concept of ephemeral random constants or hybrid approaches, which have additional computational costs. Furthermore, one has to change the GP algorithm for them. This paper proposes a concept, which does not change the GP algorithm or its components. Instead, it introduces structure-based constants realized as functions, which can be simply added to each function set while keeping the original GP approach. These constant functions derive their constant values from the tree structures of their child-trees (subtrees). That is, a constant is represented by a tree structure being this way under the influence of the typical genetic operators like subtree crossover or mutation. These structure-based constants were applied to symbolic regression problems. They outperformed the standard approach of ephemeral random constants. Their results together with their better properties make the structure-based constant concept a possible candidate for the replacement of the ephemeral random constants.