Stochastic coordinate-exchange optimal designs with complex constraints

Abstract

The paper provides a method to construct the exact optimal experimental designs for both physical and computer experiments with any regular or irregularly constrained design space. We modify the original greedy coordinate-exchange algorithm into the stochastic version by adding the random selection of the “bad” coordinates that can be exchanged for “better” values to improve the optimal design criterion. More importantly, we adapt it to accommodate the non-convex or disconnected constrained design space. We implement the stochastic coordinate-exchange (SCE) algorithm for D- and linear- (A- and I-) optimal designs for physical experiments, and ${\varphi }_p$-optimal space-filling designs for computer experiments.

Key Words:

• Computer experiment
• coordinate-exchange
• D-optimal design
• linear-optimal design
• nonlinear constraints
• space-filling design

Notes

1 The original formula Eq (9) in Bowman and Woods (2013) has typos. The current one is correct according to the authors.

Additional information

Funding

This research was supported by U.S. National Science Foundation Grant CMMI-1435902.

Notes on contributors

Lulu Kang

Lulu Kang is an Associate Professor of the Department of Applied Math at Illinois Institute of Technology (IIT). She obtained her MS in Operations Research and PhD in Industrial Engineering from the Stewart School of Industrial and Systems Engineering at Georgia Tech in 2010. Dr. Kang's has worked on various areas in Statistics, including uncertainty quantification, statistical design and analysis of experiments, Bayesian computational statistics, etc. To be more specific, Dr. Kang develops theories and implementable algorithms to achieve effective and efficient data collection, data analysis, and optimizations for complex systems in manufacturing, energy, and other engineering fields. Dr. Kang has developed and taught many statistical courses including Statistical Learning, Bayesian Computational Statistics, and Regression and Forecasting, etc. She is also the co-founder and Associate Program Director of the Data Science Program at IIT.