Construction and Efficient Implementation of Adaptive Objective-Based Designs of Experiments

This work is devoted to the development of a new and efficient procedure for the construction of adaptive model-based designs of experiments. This work couples kriging theory with design of experiments optimization techniques and its originality relies on two main ingredients: (i) the definition of a general criterion in the objective function that allows one to take into account the analyst’s choices in order to explore critical regions, and (ii) an efficient numerical implementation including a stabilization step to avoid numerical problems due to kriging matrix inversion and a computational cost reduction strategy that allows for the model’s use in industrial applications. After a full description of these key points, the resulting efficient algorithm is applied to extend over a territory in France a network of probes for environmental monitoring. This study leads to a final design of experiments where the new probes are located in undersampled regions of high population density. Moreover, it can be performed with an affordable computational cost, which is not the case with classical approaches based on an optimization over the whole domain.