A First Analysis of Kernels for Kriging-based Optimization in Hierarchical Search Spaces

Many real-world optimization problems require significant resources for objective function evaluations. This is a challenge to evolutionary algorithms, as it limits the number of available evaluations. One solution are surrogate models, which replace the expensive objective. A particular issue in this context are hierarchical variables. Hierarchical variables only influence the objective function if other variables satisfy some condition. We study how this kind of hierarchical structure can be integrated into the model based optimization framework. We discuss an existing kernel and propose alternatives. An artificial test function is used to investigate how different kernels and assumptions affect model quality and search performance.