Recently, it has repeatedly been reported that the search ability of Pareto dominance-based multi-objective evolutionary algorithms severely deteriorates with the increase in the number of objectives. In this paper, we examine the generality of the reported observations through computational experiments on a wide variety of test problems. First, we generate 18 types of test problems by combining various properties of Pareto fronts and feasible regions. Next, we examine the performance of a frequently-used Pareto dominance-based evolutionary algorithm called NSGA-II on the generated test problems in comparison with four decomposition-based algorithms. We observe that the performance of NSGA-II severely degrades for three types of many-objective test problems which are similar to frequently-used DTLZ1-4 test problems with triangular Pareto fronts. However, better results are obtained by NSGA-II than all the examined decomposition-based algorithms for nine types of test problems even when they have ten objectives. Then, we discuss why NSGA-II does not work well on DTLZ type test problems whereas it works well on other test problems.