Maximin Strong Orthogonal Arrays

Date created: 
Strong Orthogonal Array
Maximin Distance
Search Algorithm

As space-filling designs, orthogonal arrays have been widely used either directly or via OA-based Latin hypercubes in computer experiments. He and Tang (2013) introduced and constructed a new class of arrays, strong orthogonal arrays, for computer experiments. Strong orthogonal arrays of strength t enjoy better space-filling properties than comparable orthogonal arrays of strength t in all dimensions lower than t. Given a single orthogonal array, many strong orthogonal arrays can be generated using the method of He and Tang (2013). We examine the selection of better strong orthogonal arrays using the maximin distance, which is a criterion attempting to place points in a design region so that no two points are too close. In this project, we focus on maximin strong orthogonal arrays of strength three. For small designs, we apply the method of complete search. For large designs, the complete search is infeasible and we propose a search algorithm, which greatly reduces the computation time compared with the complete search approach. The performance of the algorithm is examined and it is found that the algorithm performs almost as well as the complete search.

Document type: 
Graduating extended essay / Research project
Copyright remains with the author. The author granted permission for the file to be printed and for the text to be copied and pasted.
Boxin Tang
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.