  Surrogate models are a well established approach to reduce the number of
expensive function evaluations in continuous optimization. In the context of
genetic programming, surrogate modeling still poses a challenge, due to the
complex genotype-phenotype relationships. We investigate how different
genotypic and phenotypic distance measures can be used to learn Kriging models
as surrogates. We compare the measures and suggest to use their linear
combination in a kernel.
  We test the resulting model in an optimization framework, using symbolic
regression problem instances as a benchmark. Our experiments show that the
model provides valuable information. Firstly, the model enables an improved
optimization performance compared to a model-free algorithm. Furthermore, the
model provides information on the contribution of different distance measures.
The data indicates that a phenotypic distance measure is important during the
early stages of an optimization run when less data is available. In contrast,
genotypic measures, such as the tree edit distance, contribute more during the
later stages.
