Statistica Sinica Preprint No : SS-2016-0423 . R 2 Title Construction of Maximin Distance Designs via Level Permutation and Expansion

Maximin distance designs as an important class of space-filling designs are widely used in computer experiments, yet their constructions are challenging. We develop an efficient procedure to generate maximin Latin hypercube designs, as well as maximin multi-level fractional factorial designs, from existing orthogonal or nearly orthogonal arrays via level permutation and expansion. We show that the distance distributions of the generated designs are closely connected with the distance distributions and generalized word-length patterns of the initial designs. Examples are presented to show that our method outperforms many current prevailing methods.

[1]  William A. Brenneman,et al.  Optimal Sliced Latin Hypercube Designs , 2015, Technometrics.

[2]  D. Morris Max,et al.  Design of Computer Experiments: Introduction and Background , 2015 .

[3]  George E. P. Box,et al.  The 2 k — p Fractional Factorial Designs Part II. , 1961 .

[4]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[5]  I ScottKirkpatrick.  Optimization by Simulated Annealing: Quantitative Studies , 1984 .

[6]  Boxin Tang.  Orthogonal Array-Based Latin Hypercubes , 1993 .

[7]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[8]  Hegang Chen.  Some projective properties of fractional factorial designs , 1998 .

[9]  V. R. Joseph,et al.  ORTHOGONAL-MAXIMIN LATIN HYPERCUBE DESIGNS , 2008 .

[10]  Boxin Tang,et al.  Construction of orthogonal and nearly orthogonal Latin hypercubes , 2009 .

[11]  Dennis K. J. Lin,et al.  A construction method for orthogonal Latin hypercube designs , 2006 .

[12]  Stephen J. Leary,et al.  Optimal orthogonal-array-based latin hypercubes , 2003 .

[13]  Yong-Dao Zhou,et al.  Space-Filling Fractional Factorial Designs , 2014 .

[14]  Runze Li,et al.  Design and Modeling for Computer Experiments , 2005 .

[15]  Changbao Wu,et al.  Fractional Factorial Designs , 2022 .

[16]  Weng Kee Wong,et al.  Recent developments in nonregular fractional factorial designs , 2008, 0812.3000.

[17]  Hongquan Xu.  Minimum moment aberration for nonregular designs and supersaturated designs , 2001 .

[18]  Hongquan Xu,et al.  An Algorithm for Constructing Orthogonal and Nearly-Orthogonal Arrays With Mixed Levels and Small Runs , 2002, Technometrics.

[19]  Yu Tang,et al.  An effective construction method for multi-level uniform designs , 2013 .

[20]  Dennis K. J. Lin,et al.  Construction of orthogonal Latin hypercube designs with flexible run sizes , 2010 .

[21]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[22]  Dennis K. J. Lin,et al.  Uniform fractional factorial designs , 2012, 1206.0897.

[23]  C. Wu,et al.  Construction of Optimal Multi-Level Supersaturated Designs , 2005, math/0603079.

[24]  Thomas W. Lucas,et al.  Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes , 2007, Technometrics.

[25]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

[26]  Min-Qian Liu,et al.  CONSTRUCTION OF ORTHOGONAL AND NEARLY ORTHOGONAL LATIN HYPERCUBE DESIGNS FROM ORTHOGONAL DESIGNS , 2012 .

[27]  Fred J. Hickernell,et al.  A generalized discrepancy and quadrature error bound , 1998, Math. Comput..