Crossover-Based Tree Distance in Genetic Programming

In evolutionary algorithms, distance metrics between solutions are often useful for many aspects of guiding and understanding the search process. A good distance measure should reflect the capability of the search: if two solutions are found to be close in distance, or similarity, they should also be close in the search algorithm sense, i.e., the variation operator used to traverse the search space should easily transform one of them into the other. This paper explores such a distance for genetic programming syntax trees. Distance measures are discussed, defined and empirically investigated. The value of such measures is then validated in the context of analysis (fitness-distance correlation is analyzed during population evolution) as well as guiding search (results are improved using our measure in a fitness sharing algorithm) and diversity (new insights are obtained as compared with standard measures).