In the field of engineering design and optimization, metamodels are widely used to replace expensive simulation models in order to reduce computing costs. To improve the accuracy of metamodels effectively and efficiently, sequential sampling designs have been developed. In this article, a sequential sampling design using the Monte Carlo method and space reduction strategy (MCSR) is implemented and discussed in detail. The space reduction strategy not only maintains good sampling properties but also improves the efficiency of the sampling process. Furthermore, a local boundary search (LBS) algorithm is proposed to efficiently improve the performance of MCSR, which is called LBS-MCSR. Comparative results with several sequential sampling approaches from low to high dimensions indicate that the space reduction strategy generates samples with better sampling properties (and thus better metamodel accuracy) in less computing time.

Some adaptive sampling approaches have been developed to efficiently and accurately build global metamodels for the deterministic single-response problems. Most complex engineering problems, however, yield multiple responses during one simulation. This article adjusts the framework of the CV-Voronoi adaptive sampling approach for a multi-response system. In the proposed multi-response CV-Voronoi (mCV-Voronoi) sampling approach, a new strategy that combines a weighted-sum term and an extreme term is presented to properly estimate the cell errors by simultaneously considering the characteristics of multiple responses. The performance of this approach is investigated on 57 multi-response systems and two engineering design problems. The results show that mCV-Voronoi is very promising for global metamodeling of deterministic multi-response systems.