Optimization problems arise in many application areas such as engineering, transportation planning, and climate modeling. Often, several conflicting objectives must be optimized simultaneously. For example, in airfoil design the goals may be to minimize the drag and maximize the lift coefficient. For these multi-objective problems, there does not exist a single solution that optimizes all objective functions. Rather, a set of trade-off (Pareto-optimal) solutions must be identified. We consider optimization problems whose objective function evaluations require computationally expensive black-box simulations and for which derivative information is not available. The computational expense arising from doing a single function evaluation, which may range from several hours to days, restricts the total number of evaluations that can be done in many cases to few hundred. This poses a problem for applying widely used solution algorithms such as scalarizing or evolutionary strategies, which generally require thousands of function evaluations for finding an approximation of the Pareto front. Hence, our goal is to devise new algorithms that find (near-) Pareto-optimal solutions within only very few expensive objective function evaluations. In this talk, we will present a new solution approach that employs computationally cheap surrogate models to approximate the expensive objective functions and guide the search for improved solutions.