This work analyzes the dynamics of dominance based multi-objective evolutionary algorithms and extends a many-objective evolutionary algorithm so that it can also work effectively in multi-objective problems. The many-objective algorithm incorporates in its selection mechanism a density sampling approach based on epsilon-dominance and performs recombination within neighborhoods created by another epsilon-dominance based procedure. The many-objective algorithm works well during the stage of the search where there are too many non-dominated solutions and dominance is not capable of ranking solutions. Here we modify the selection mechanism of the algorithm to also work effectively during the early stage of the search where dominance can be used to bias selection. This allows the algorithm to solve multi- or many-objective problems formulations using the same framework.