Structural versus evaluation based solutions similarity in genetic programming based system identification

Estimating the similarity of solution candidates represented as structure trees is an important point in the context of many genetic programming (GP) applications. For example, when it comes to observing population diversity dynamics, solutions have to be compared to each other. In the context of GP based system identification, i.e., when mathematical expressions are evolved, solutions can be compared to each other with respect to their structure as well as to their evaluation. Obviously, structural similarity estimation of formula trees is not equivalent to evaluation based similarity estimation; we here want to see whether there is a significant correlation between the results calculated using these two approaches. In order to get an overview regarding this issue, we have analyzed a series of GP tests including both similarity estimation strategies; in this paper we describe the similarity estimation methods as well as the test data sets used in these tests, and we document the results of these tests. We see that in most cases there is a significant positive linear correlation for the results returned by the evaluation based and structural methods. Especially in some cases showing very low structural similarity there can be significantly different results when using the evaluation based similarity methods.