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In evolutionary computuation, there are lots of applications and methods of study where it's useful to have a concept of distance or dissimilarity between individuals. In genetic programming, this often means calculating a syntactic distance between tree structures. In this project we aim to understand distance in terms of transition probability via operators, and approximate this type of graph-based distance using syntactic distances.


McDermott, O'Reilly, Vanneschi, and Veeramachaneni, "How Far Is It From Here to There? A Distance that is Coherent with GP Operators", EuroGP 2011, Springer.

The distance between pairs of individuals is a useful concept in the study of evolutionary algorithms. It is particularly useful to define a distance which is coherent with, i.e. related to, the action of a particular operator. We present the first formal, general definition of this operator-distance coherence. We also propose a new distance function, based on the multi-step transition probability (MSTP), that is coherent with any GP operator for which the one-step transition probability (1STP) between individuals can be defined. We give an algorithm for 1STP in the case of subtree mutation. Because MSTP is useful in GP investigations, but impractical to compute, we evaluate a variety of means to approximate it. We show that some syntactic distance measures give good approximations, and attempt to combine them to improve the approximation using a GP symbolic regression method. We conclude that 1STP itself is a sufficient indicator of MSTP for subtree mutation.


A library of code used in the experiments for the above paper is available here. A theorem omitted from the paper to save space is available here. Slides from the EuroGP presentation are available here.