Adaptive-region sequential design with quantitative and qualitative factors in application to HPC configuration

Abstract

Motivated by the need of finding optimal configuration in the high-performance computing (HPC) system, this work proposes an adaptive-region sequential design (ARSD) for optimization of computer experiments with qualitative and quantitative factors. Experiments with both qualitative and quantitative factors are also encountered in other applications. The proposed ARSD method considers a sequential design criterion under the additive Gaussian process to deal with both qualitative and quantitative factors. Moreover, the adaptiveness of the proposed sequential procedure allows the selection of next design point from the adaptive design region achieving a meaningful balance between exploitation and exploration for optimization. Theoretical justification of the adaptive design region is provided. The performance of the proposed method is evaluated by several numerical examples in simulations. The case study of HPC performance optimization further elaborates the merits of the proposed method.

Keywords:

• Adaptive design
• design of experiment
• exploitation and exploration
• Gaussian process
• optimal configuration

Acknowledgement

We are grateful to the editor and the referees for their constructive comments that have helped improve the article significantly.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work by Cai is supported by the National Natural Science Foundation of China (Grant No. 12001155), and the Natural Science Foundation of Hebei Province of China (Grant No. A2022208001). The work by Lin is supported by the Natural Sciences and Engineering Research Council of Canada.

Notes on contributors

Xia Cai

Xia Cai is an Associate Professor in the School of Science at the Hebei University of Science and Technology. Her email address is [email protected].

Li Xu

Li Xu is a PhD candidate in the Department of Statistics at the Virginia Tech. His email address is [email protected].

C. Devon Lin

Chunfang Devon Lin is a Professor in the Department of Mathematics and Statistics at the Queen’s University. Her email address is [email protected]

Yili Hong

Yili Hong is a Professor in the Department of Statistics at the Virginia Tech. His email address is [email protected].

Xinwei Deng

Xinwei Deng is a Professor in the Department of Statistics at the Virginia Tech. His email address is [email protected].