Isovolumetric adaptations to space-filling design of experiments

A brief review of methods in design of experiments and criteria to determine space-filling properties of a set of samples is given. Subsequently, the so-called curse of dimensionality in sampling is reviewed and used as motivation for the proposal of an adaptation to the strata creation process in Latin hypercube sampling based on the idea of nested same-sized hypervolumes. The proposed approach places samples closer to design space boundaries, where in higher dimensions the majority of the design space volume is located. The same idea is introduced for Monte Carlo considering an affordable number of samples as an a-posteriori transformation. Both ideas are studied on different algorithms and compared using different distance-based space-filling criteria. The proposed new sampling approach then enables more efficient sampling for optimization especially for high-dimensional problems, i.e. for problems with a high number of design variables.