Personalized optimization and its implementation in computer experiments

Abstract

Optimization problems with both control variables and environmental variables often arise in quality engineering. This article introduces a personalized optimization strategy to handle such problems when the environmental variables can be observed or measured. Unlike traditional robust optimization, personalized optimization aims to find the values of control variables that yield the optimal value of the objective function for given values of environmental variables. Therefore, the solution from personalized optimization, which consists of optimal surfaces defined on the domain of environmental variables, is more reasonable and better than that from robust optimization. The implementation of personalized optimization for expensive black-box computer models is discussed. Based on statistical modeling of computer experiments, we provide two algorithms to sequentially design input values for approximating the optimal surfaces. Numerical examples including a real application show the effectiveness of our algorithms.

Keywords:

• Environmental variable
• expected improvement
• Kriging
• personalized decision
• robust optimization
• sequential design

Acknowledgments

We thank the Editors and referees for constructive comments which lead to a significant improvement of this paper.

Additional information

Funding

This work is supported by Funding from Chinese Ministry of Science and Technology (Grant No. 2016YFF0203801), the National Natural Science Foundation of China (Grant No. 11671386, 11871033), and Key Laboratory of Systems and Control, CAS.

Notes on contributors

Shifeng Xiong

Shifeng Xiong is is an associate professor at Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He received his Ph.D. degree (2005) in statistics from Chinese Academy of Sciences. His research interests are industrial statistics and mathematical statistics.