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 Hypercubes in arbitrarily shaped design spaces.