Design of experiment and response surface modeling methods are applied to the problem of constructing Pareto fronts for computationally expensive multiobjective design optimization problems. The work presented combines design of experiment methods with kriging (Gaussian process) models to enable the parallel evolution of multiobjective Pareto sets. This is achieved via the use of updating schemes based on new extensions of the expected improvement criterion commonly applied in single-objective searches. The approaches described provide a statistically coherent means of solving expensive multiobjective design problems using single-objective search tools. They are compared to the use of nondominaled sorting genetic algorithm (NSGA-ii) based multiobjective search, both with and without response surface support. The new approaches are shown to give more exact, wider ranging, and more evenly populated Pareto fronts than the genetic algorithm based searches at reduced or similar cost.