In this paper we discuss two statistical techniques for achieving computational economy during the optimization process. The first, the use of approximization methods is often applied when optimizing expensive computational models of complex engineering systems: the idea is to replace the expensive analysis code by a cheap surrogate model for the purposes of optimization. There are many approximation methods available in the literature, we focus here on kriging. Teh second, screening experiments, has received much attention in the statistics community. This statistical tool has been applied to the problem of structural optimization her. Indeed, one purpose of this paper is to increase awareness of these tools in the structural optimization community. In particular, a focus here is on screening multiple responses, as a structural optimization problem typically requires optimization of at least one objective subject to at least one constraint. Finally, both approaches are combined in order to provide an algortihm which appears very efficient for large dimensional strucutral optimization problems. A structural optimization case study of industrial interest demonstrates the approach.