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

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.