Design of robust parameter experiments in a continuous space using an evolutionary optimization algorithm

Abstract

Two common experimental designs used in robust parameter design (RPD) are crossed array and mixed resolution designs. However, the prohibited number of runs, constraints in the design space or special model requirements render some of these designs inadequate. This paper presents the application of an evolutionary strategy to produce nearly optimal design matrices for RPD. The designs are derived by solving a nonlinear optimization problem involving both 𝒟- and 𝒢-efficiency simultaneously. The methodology presented allows the user to obtain new exact designs for a specific number of runs, and a particular experimental region. The combination of 𝒟- and 𝒢-efficiency results in experimental designs that outperform the corresponding benchmarks.

Keywords:

• 𝒟-efficiency
• 𝒢-efficiency
• evolutionary strategy
• RPD designs

AMS Subject Classification :

• 05B99
• 62K05
• 62K25

Acknowledgements

We thank the anonymous referee whose comments and careful examination of our paper greatly improved our presentation. Our thanks also to Dr. del Castillo and Mr. Tom Bowler, whose valuable input was critical to the initial draft and multiple revisions of this paper. Lastly, thanks to Dr. Hansen for his helpful insights on using the CMA-ES algorithm in a hypersphere region.

Additional information

Notes on contributors

Eduardo Santiago

Current affiliation: Minitab, Inc., State College, PA, USA.