Complexity Drift in Evolutionary Computation with Tree Representations
Justinian P. Rosca, Dana H. Ballard · UR Research (University of Rochester) · 1996
One serious problem of standard Genetic Programming (GP) is that evolved expressions appear to drift towards large and slow forms on average. This report presents a novel analysis of the role played by variable complexity in the selection and survival of GP expressions. It defines a particular property of GP representations, called rooted tree-schema, that sheds light on the role of variable complexity of evolved representations. A tree-schema is a relation on the space of tree-shaped structures which provides a quantifiable partitioning of the search space. The present analysis answers questions such as: What role does variable complexity play in the selection and survival of evolved expressions? What is the influence of a parsimony penalty? How heavy should parsimony penalty be weighted or how should it be adapted in order to preserve the underlying optimization process? Are there alternative approaches to simulating a parsimony penalty that do not result in a change of the fitness landscape? The present report provides theoretical answers to these questions, interpretation of these results, and an experimental perspective.