Latin Hypercube Designs

Computer experiments involve a large numbers of variables, but only a few of them have no negligible influence on the response. Unfortunately, randomly generated Latin Hypercube Designs (LHDs) almost always show poor space-filling properties. When numbers of factors as well as number of experimental points are large, the heuristic approaches also require a couple of hours or even more to find out a simulated optimal design. Specially for the need of real time solution, the time complexity of the ILS approaches is analyzed. After analyzing, the time complexity model of the algorithms for two optimal criterion namely Opt (D1, J1) as well as Opt() has been developed. More over some experiments have been performed for higher dimension namely dimensions k >10. Some new maximin LHDs value are obtained from these experiments, as there are few maximin LHDs value available in the literatures for higher dimension, k >10. From these experiments, multi-collinearity property, maximin LHDs in Rectangular distance, mimimal values, maximum pair-wise distance value of LHDs etc. are represented in this book.