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

arXiv: https://arxiv.org/abs/1807.01011 · HTML: https://mlsanity.com/paper/1807.01011/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2018.

## Built on by (most cited first, 3 of 3)

- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)
- [Surrogate-based optimization of system architectures subject to hidden constraints](https://mlsanity.com/paper/2504.08721/) (2025)

## Abstract (arXiv)

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.