Linear Combination of Distance Measures for Surrogate Models in Genetic Programming

TL;DR

This paper explores combining different genotypic and phenotypic distance measures to improve surrogate modeling in genetic programming, leading to better optimization performance and insights into measure contributions over time.

Contribution

It introduces a linear combination of distance measures for Kriging surrogate models in genetic programming, demonstrating improved optimization and interpretability.

Findings

Phenotypic distance is crucial early in optimization.

Genotypic distance becomes more important later.

The combined model outperforms model-free approaches.

Abstract

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.