Multicast routing algorithms have recently been intensively investigated due to the increment over the last years in the use of new point-to-multipoint applications. In this work, three formulations for the routing problem are investigated, considering 3, 4 and 5 objectives related to Quality of Service and Traffic Engineering requirements. A multiobjective evolutionary model is proposed to tackle this problem, using the well-known SPEA2 scheme as the underlying search. The key investigation performed here is about the incorporation of two strategies to help SPEA2 convergence to Pareto solutions, namely, filtering to reduce repeated individuals, and a mating selection based on neighborhood crossover. Results indicate that the adequacy of the strategies depends on the dynamics of currently non-dominated set over the generations. A new adaptive environment is proposed in which this information is considered periodically to decide what kind of strategy will be used in each situation.