Metamodel-based optimization of stochastic computer models for engineering design under uncertain objective function

Abstract

Stochastic computer models are prevailingly used to help the design engineer to understand and optimize analytically intractable systems. A frequently encountered, but often ignored problem is that the objective function representing system performance may contain some uncertain parameters. Due to lack of computationally efficient tools, rational procedures for dealing with the problem such as finding multiple Pareto-optimal solutions or conducting sensitivity analysis on the uncertain parameters require the stochastic computer model to be optimized many times, which would incur extensive computational burden. In this work, we provide a computationally efficient metamodel-based solution to capture this uncertainty. This solution first constructs a Cartesian product design over the space of both design variables and uncertain parameters. Thereafter, a radial basis function metamodel is used to provide a smooth prediction surface of the objective value over the space of both design variables and uncertain parameters. Based on the Cartesian product design structure, a fast fitting algorithm is also derived for fitting the metamodel. To illustrate the effectiveness of the developed tools in solving practical problems, they are applied to seek a robust optimal solution to a drug delivery system with uncertain desirability function parameters based on a criterion that we propose.

Keywords:

• Stochastic computer models
• Cartesian product design
• objective function uncertainty
• radial basis function
• sensitivity analysis

Acknowledgments

The authors thank two referees for comments that helped improve the article.

Notes on Contributors

Guilin Li is currently a postdoctoral research fellow in the School of Data Science at City University of Hong Kong. She received a B.S. degree in statistics from Nankai University, China, and a Ph.D. degree in industrial systems engineering and management from the National University of Singapore. Her research interests, which lie broadly in the area of engineering statistics, including regression analysis, experimental design and uncertainty quantification.

Matthias Hwai Yong Tan is an assistant professor in the School of Data Science at City University of Hong Kong. He received his B.Eng. degree in mechanical-industrial engineering from the Universiti Teknologi Malaysia, an M.Eng. degree in industrial and systems engineering from the National University of Singapore and a Ph.D. degree in industrial and systems engineering from Georgia Institute of Technology. His research interests include uncertainty quantification, design and analysis of computer experiments, and applied statistics.

Szu Hui Ng is an associate professor in the Department of Industrial Systems Engineering & Management at the National University of Singapore. She holds B.S., M.S. and Ph.D. degrees in industrial and operations engineering from the University of Michigan. Her research interests include computer simulation modeling and analysis, design of experiments and quality and reliability engineering. She is a member of IEEE and INFORMS, and a senior member of IISE.

Additional information

Funding

Matthias Tan’s research was supported by General Research Fund projects 11226716 and 11201117 funded by the Research Grants Council of Hong Kong. Guilin Li’s research was supported by project T32-101/15-R funded by the Research Grants Council of Hong Kong