Optimization of externalities and accessibility using dynamic traffic management measures on a strategic level is a specific example of solving a multi-objective network design problem. Solving this optimization problem is time consuming, because heuristics like evolutionary multi objective algorithms are needed and solving the lower level requires solving the dynamic user equilibrium problem. Using function approximation like response surface methods (RSM) in combination with evolutionary algorithms could accelerate the determination of the Pareto optimal set. Three algorithms in which RSM are used in different ways in combination with the Strength Pareto Evolutionary Algorithm 2+ (SPEA2+) are compared with employing the SPEA2+ without the use of these methods. The results show that the algorithms using RSM methods accelerate the search considerably at the start, but tend to converge more quickly, possibly to a local optimum, and therefore loose their head start. Therefore, usage of function approximation is mainly of interest if a limited number of exact evaluations can be done or this can be used as a pre phase in a hybrid approach.