1 An Algorithm for Fast Optimal Latin Hypercube Design of Experiments

This paper presents the Translational Propagation algorithm; a new method for obtaining optimal or near optimal Latin hypercube designs without using formal optimization. The procedure requires minimal computational effort with results virtually provided in real time. The algorithm exploits patterns of point locations for optimal Latin hypercube designs based on the pφ criterion (a variation of the maximum distance criterion). Small building blocks, consisting of one or more points each, are used to recreate these patterns by simple translation in the hyperspace. Monte Carlo simulations were used to evaluate the performance of the new algorithm for different design configurations where both the dimensionality and the point density were studied. The proposed algorithm was also compared against three formal optimization approaches (namely random search, genetic algorithm, and enhanced stochastic evolutionary algorithm). It was found that (i) the distribution of the pφ values tends to lower values as the dimensionality is increased; and (ii) the proposed translational propagation algorithm represents a computationally attractive strategy to obtain near optimum Latin hypercube designs up to medium dimensions