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An algorithm for fast optimal Latin hypercube design of experiments
Author(s) -
Viana Felipe A. C.,
Venter Gerhard,
Balabanov Vladimir
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2750
Subject(s) - latin hypercube sampling , curse of dimensionality , algorithm , monte carlo method , computer science , genetic algorithm , point (geometry) , mathematical optimization , hypercube , simple (philosophy) , optimal design , mathematics , artificial intelligence , philosophy , statistics , geometry , epistemology , machine learning , parallel computing
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.