The externalities of traffic are increasingly important for policy decisions related to design of a road network. Optimization of externalities with dynamic traffic management measures influencing the supply of infrastructure is a multiobjective network design problem, which in turn is a bi-level optimization problem. The presence of conflicting objectives makes the solution to the optimization problem a challenge. Evolutionary multiobjective algorithms have proved successful in solving such problems. However, like all optimization methods, these are subject to the no-free-lunch theorem. Therefore, this paper compares the nondominated sorting genetic algorithm II (NSGA-II), the strength Pareto evolutionary algorithm 2 (SPEA2), and the strength Pareto evolutionary algorithm 2+ (SPEA2+) to find a Pareto optimal solution set for this problem. Because incorporation of traffic dynamics is important, the lower level should be solved through a dynamic traffic assignment model, which increases needed CPU time. Therefore, algorithm performance is compared within a certain budget. The approaches are compared in a numerical experiment through different metrics. The externalities optimized are noise, climate, and congestion. The results show that climate and congestion are aligned and that both are opposed to noise in the case study. On average, SPEA2+ outperforms SPEA2 in this problem on all used measures. Results of NSGA-II and SPEA2+ are inconclusive. A larger population results on average in a larger space coverage, while a smaller population results in higher performance on spacing and diversity. Most performance measures are relatively insensitive for the mutation rate.