Optimal Noncollapsing Space-Filling Designs for Irregular Experimental Regions

ABSTRACT

Space-filling and noncollapsing are two important properties in designing computer experiments. We study how the noncollapsing, space-filling designs for irregular experimental regions can be generated efficiently by the proposed metaheuristic methods. We solve this optimal design problem using variants of the discrete particle swarm optimization (DPSO) approaches. Numerical results, including an application in data center thermal management, are used to illustrate the performances of the proposed algorithms. Based on these numerical results, we assert that the most efficient approach is to reformulate the target optimal design problem as a constrained optimization problem and then use a modified DPSO to solve the constrained optimization problem.

KEYWORDS:

• Computer experiment
• Discrete particle swarm optimization
• Space-filling

Acknowledgments

The authors are grateful to the editor, associate editor, and reviewers for their valuable comments and suggestions. The authors also thank Dr. Ping-Yang Chen for his help on the coding.

Funding

The research of Chen was partially supported by the National Science Council under Grant NSC101-2118-M-006-002-MY2 and the Mathematics Division of the National Center for Theoretical Sciences in Taiwan. The research of Wang was partially supported by the Ministry of Science and Technology, the National Center for Theoretical Sciences, and the Taida Institute of Mathematical Sciences in Taiwan. The research of Hung was partially supported by the National Science Foundation under NSF DMS 1349415 and NSF DMS 1660477.