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

TL;DR

This paper investigates how different kernels can improve Kriging-based surrogate models for hierarchical search spaces in resource-intensive optimization problems, enhancing model accuracy and search efficiency.

Contribution

It introduces alternative kernels for hierarchical variables in Kriging models and evaluates their impact on optimization performance using an artificial test function.

Findings

Certain kernels improve model quality in hierarchical spaces

Kernel choice significantly affects search performance

Hierarchical structure integration enhances surrogate modeling

Abstract

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.