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Formulation of the Optimal Latin Hypercube Design of Experiments Using a Permutation Genetic Algorithm

Stuart J. Bates · Johann Sienz · VASSILI V. TOROPOV

138 citations0/0 files storedAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (SDM)

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Optimal Experimental Design Methods Metaheuristic Optimization Algorithms Research Advanced Multi-Objective Optimization Algorithms

Abstract

The choice of location of the evaluation points is important in response surface generation, especially when the evaluations are expensive. Space-filling designs can be used to specify the points so that as much of the design space is sampled as possible with the minimum number of response evaluations. One popular technique is the optimal Latin hypercube design of experiments. However, its generation is non-trivial, time consuming and is – but for the simplest problems – infeasible to carry out by enumeration. Therefore, solving this problem requires an optimization technique to search the design space. As the problem is discrete, it is ideally suited to the use of discrete optimization techniques such as genetic algorithms. This paper describes a method for generating optimal latin hypercubes using a permutation genetic algorithm and compares it with a standard binary genetic algorithm. The objective of the optimization is based on minimizing a function that is analogous the potential energy of the system of material points. The developed method offers considerable improvements over previous solutions; it generates better solutions and the computational effort in reaching those solutions is significantly reduced.

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References

1996Response Surface Methodology: Process and Product Optimization Using Designed Experiments 2000A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code 1996Response Surface Methodology: Process and Product Optimization Using Designed Experiments 1990Minimax and maximin distance designs 1989Designs for Computer Experiments 1980Small sample sensitivity analysis techniques for computer models.with an application to risk assessment 1987Maximum entropy sampling

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2012Optimizing Latin hypercube designs by particle swarm 2011A novel algorithm of maximin Latin hypercube design using successive local enumeration 2020Machine learning and Design of Experiments: Alternative approaches or complementary methodologies for quality improvement?2016Construction of nested maximin designs based on successive local enumeration and modified novel global harmony search algorithm 2011Formulation of the Audze–Eglais uniform Latin hypercube design of experiments for constrained design spaces 2017

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