Formulation of the Audze-Eglais uniform Latin hypercube design of experiments for constrained design spaces
Optimal Latin Hypercubes (OLH) created in a constrained design space might produce Design of Experiments (DoE) containing infeasible points if the underlying formulation disregards the constraints. Simply omitting these infeasible points leads to a DoE with fewer experiments than desired and to a set of points that is not optimally distributed. By using the same number of points a better mapping of the feasible space can be achieved. This paper describes the development of a procedure that creates OLHs for constrained design spaces. An existing formulation is extended to meet this requirement. Here. the OLH is found by minimizing the Audze-Eglais potential energy of the points using a permutation genetic algorithm. Examples validate the procedure and demonstrate its capabilities in finding space-filling Latin ypercubes in arbitrarily shaped design spaces. (C) 2011 Elsevier Ltd. All rights reserved.
audze-eglais design of experiments constrained design space optimal latin hypercubes permutation genetic algorithm surrogate based optimization