In this thesis numerical optimization methods for single- and multi-objective design optimization with time-consuming computer experiments are studied in theory and practise. We show that the assistance by metamodeling techniques (or: surrogates) can significantly accelerate evolutionary (multi-objective) optimization algorithms (E(M)OA) in the presence of time consuming evaluations. A further increase of robustness can be achieved by taking confidence information for the imprecise evaluations into account. Gaussian random field metamodels, also referred to as Kriging techniques, can provide such confidence information. The confidence information is used to figure out ‘white spots’ in the functional landscape to be explored. The thesis starts with a detailed discussion of computational aspects related to the Kriging algorithm. Then, algorithms for optimization with single objectives, constraints and multiple objectives are introduced. For the latter, with the S-metric selection EMOA (SMS-EMOA) a new powerful algorithm for Pareto optimization is introduced, which outperforms established techniques on standard benchmarks. The concept of a filter is introduced to couple E(M)OA with metamodeling techniques. Various filter concepts are compared, both by means of deducing their properties theoretically and by experiments on artificial landscapes. For the latter studies we propose new analytical indicators, like the inversion metric and the recall/precision measure. Moreover, sufficient conditions for global convergence in probability are established. Finally the practical benefit of the new techniques is demonstrated by solving several industrial optimization problems, including airfoil optimization, solidification process design, metal forming, and electromagnetic compatibility design and comparing the results to those obtained by standard algorithms.