Formulation of the Audze–Eglais Uniform Latin Hypercube design of experiments

Abstract

This paper describes a method for formulating the Audze–Eglais Uniform Latin Hypercube design of experiments (DoE). The formulation of the Audze–Eglais DoE has not been reported in any previous research. The principle of the Audze–Eglais DoE is to distribute experiment points as uniformly as possible within the design variable domain. This is achieved by minimizing the potential energy of the points of a DoE. The DoE for N variables and P experiments is independent of the application under consideration, so once the design is formulated for P points and N design variables, it is stored in a matrix and need not be formulated again. The generation of the Audze–Eglais DoE is time consuming and requires optimization to solve the minimization problem. Therefore, the major aim of the paper is to identify a design variable encoding method for use in optimization. The two methods for encoding the DoE for use in the optimizer are presented. The method adopted in this study uses the co-ordinates of the plan points as design variables. The results for the potential energy are compared to published Audze–Eglais Uniform Latin Hypercube DoE and to random sampling Latin Hypercube DoE. The results indicate that the method works well and improvement over previous results has been achieved.