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In traffic and transport a significant portion of research and application is focused on single objective optimization, although there is rarely only one objective that is of interest. The externalities of traffic are of increasing importance for policy decisions related to the design of a road network. The optimization of externalities using dynamic traffic management measures is a multi objective network design problem. The presence of multiple conflicting objectives makes the optimization problem challenging to solve. Evolutionary multi objective algorithms has been proven successful in solving multi objective optimization problems. However, like all optimization methods, these are subject to the free lunch theorem. Therefore, we compare the NSGAII, SPEA2 and SPEA2+ algorithms in order to find a Pareto optimal solution set for this optimization problem. Because of CPU time limitation as a result of solving the lower level using a dynamic traffic assignment model, the performance by the algorithms is compared within a certain budget. The externalities optimized are noise, climate and accessibility. In a numerical experiment the SPEA2+ outperforms the SPEA2 on all used measures. Comparing NSGAII and SPEA2+, there is no clear evidence of one approach outperforming the other.