Linear Combination of Distance Measures for Surrogate Models in Genetic Programming
This work addresses the problem of reducing expensive function evaluations in genetic programming for researchers in evolutionary computation, but it is incremental as it builds on existing surrogate modeling techniques.
The paper tackled the challenge of surrogate modeling in genetic programming by proposing a linear combination of genotypic and phenotypic distance measures in a Kriging kernel, tested on symbolic regression benchmarks. The results showed improved optimization performance over a model-free algorithm and revealed that phenotypic measures are important early in optimization, while genotypic measures contribute more later.
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.