Particle swarm exchange algorithms with applications in generating optimal model-discrimination designs

Abstract

Exchange-type algorithms have been commonly used to construct optimal designs. As these algorithms may converge to a local optimum, the typical procedure requires the use of several randomly chosen initial designs. Thus, the search for the optimal design can be conducted by performing several independent optimizations. We propose a general framework that combines exchange algorithms with particle swarm intelligence techniques. The main strategy is to represent each initial design as a particle and make the algorithm share information from various converging paths from those initial designs. This amounts to conducting one coordinated optimization instead of several independent optimizations. The proposed general algorithm is called the particle swarm exchange (PSE) algorithm. We compare the performance of PSE with those of two commonly used exchange algorithms – the columnwise-pairwise (CP) exchange algorithm of Li and Wu (1997) for designs with structural requirements and the coordinate exchange algorithm of Meyer and Nachtsheim (1995) for designs without such requirements. In the context of model-robust discriminating designs, we demonstrate that PSE typically performs as well as or, very often, better than the corresponding pure exchange algorithms.

Keywords:

• Columnwise-pairwise exchange algorithm
• coordinate exchange algorithm
• exchange algorithm
• model-discrimination design
• swarm intelligence

Additional information

Funding

This work was supported by Ministry of Science and Technology, Taiwan.

Notes on contributors

Ping-Yang Chen

Dr. Ping-Yang Chen is currently a postdoctoral research fellow in the Department of Statistics, National Cheng Kung University. He received his B.Sc. in Applied Mathematics from National Chengchi University in Taiwan and both his Master and Ph.D. degrees in Statistics from National Cheng Kung University in Taiwan. His contribution to this article includes optimizing and publishing the PSE codes, conducting the performance comparison among the optimal design generating algorithms, and building a website to catalog the model-discrimination designs.

Ray-Bing Chen

Professor Ray-Bing Chen is Professor in the Department of Statistics and Institute of Data Science, National Cheng Kung University. He received his Ph.D. in Statistics from the University of California, Los Angeles. His research interests include statistical and machine learning, statistical modeling, computer experiment, and optimal design. Prof. Chen’s papers are published in the field of computational statistics and industrial statistics, like, Journal of Computational and Graphical Statistics and Technometrics. He was elected as Elected Member of the International Statistical Institute in 2020.

Jui-Pin Li

Mr. Jui-Ping Li received his Master’s degree in Statistics from University of Cheng Kung University in 2014. His mater thesis is related to develop numerical algorithms for generating optimal designs.

William Li

Professor William Li is Professor of Management at Shanghai Institute of Finance of Shanghai Jiao Tong University and Emeritus Professor in the Carlson School of Management at the University of Minnesota. He is an elected Fellow of the American Statistical Association. His research articles have appeared in journals such as Journal of American Statistics Association, Technometrics, Journal of Quality Technology, INFORMS on Computing, and Neural Computation. He has served on editorial board of several journals including Technometrics.