An algorithm for fast optimal Latin hypercube design of experiments

TLDR

The study introduces the translational propagation algorithm, a new method for generating optimal or near‑optimal Latin hypercube designs without formal optimization. The algorithm constructs Latin hypercube designs by translating small building‑block patterns derived from the φ_p criterion across hyperspace, and its performance was evaluated through Monte Carlo simulations and compared with random search, genetic algorithm, and enhanced stochastic evolutionary algorithm approaches. The translational propagation algorithm achieves near‑optimal Latin hypercube designs with minimal computational effort, delivering real‑time results and outperforming formal optimization methods in medium‑dimensional settings. © 2009 John Wiley & Sons, Ltd.

Abstract

Abstract This paper presents the translational propagation algorithm, a new method for obtaining optimal or near optimal Latin hypercube designs (LHDs) 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 LHDs based on the ϕ p 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 ϕ p 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 LHDs up to medium dimensions. Copyright © 2009 John Wiley & Sons, Ltd.