Despite the extensive application of multi-objective evolutionary algorithms (MOEAs) to solve multi-objective optimization problems (MOPs), understanding their working principles is still open to research. One of the most popular and successful MOEA approaches is based on Pareto dominance and its relaxed version, Pareto epsilon-dominance. However, such approaches have not been sufficiently studied in problems of increased complexity. In this work, we study the effects of the working mechanisms of the various components of these algorithms on test problems with difficult Pareto set topologies. We focus on separable unimodal and multimodal functions with 2, 3, and 4 objectives, all having difficult Pareto set topologies. Our experimental study provides some interesting and useful insights to understand better Pareto dominance-based MOEAs.