An algorithm for fast optimal Latin hypercube design of experiments

A Simulated Annealing Based Optimization Algorithm

“…the above metamodel becomes mðxÞ ¼β þ rðxÞ T R −1 ðf −1βÞ (17) whereβ is the estimated drift coefficient, R is the symmetric matrix of correlations between all interpolation vectors, f is the vector of objective values and 1 is a vector with all elements equal to 1. r T is the correlation vector between a new vector x and the sample vectors, namely, r T ¼ ½cðθ;x;x 1 Þ, …;cðθ;x;x n Þ…”

“…Initialization: The algorithm begins by generating an initial sample of vectors based on the optimal Latin hypercube design (OLHD) method [17]. The method ensures that the resultant sample is space-filling, namely, adequately covers the search space, which in turn improves the prediction accuracy of the metamodels.…”

Generating Sequential Space-Filling Designs Using Genetic Algorithms and Monte Carlo Methods

“…The ultimate goal of this experiment is to develop highly efficient sequential space-filling algorithms that can compete with proven and popular one-shot experimental design techniques such as the optimized Latin hypercube [1,11]. These methods will use Monte Carlo methods as the optimization method of choice, as opposed to global optimization methods.…”

Model assisted qualification of NDE techniques

“…m-1 therefore brute force optimization of a design rapidly becomes impractical as the number of parameters and number of sample points increases, for example 41 points for two parameters has 3.35x10 49 possible designs. The method used in this work to generate highly optimal designs is the Translational Propagation Algorithm [4] which uses the propagation of a small initial seed design to generate the final design. An example of the outcome of this algorithm is shown in Fig.…”

“…They indicate that the perpendicular position is a more significant factor than the lateral position as there is a larger variation in the probability of detection for that parameter. This can also be assessed by casting the fitted model in the form of Equation 4 and performing an ANOVA decomposition. The result (a) (b)…”