We examine the behavior of three classes of evolutionary multiobjective optimization (EMO) algorithms on many-objective knapsack problems. They are Pareto dominance-based, scalarizing function-based, and hypervolume-based algorithms. NSGA-II, MOEA/D, SMS-EMOA, and HypE are examined using knapsack problems with 2–10 objectives. Our test problems are generated by randomly specifying coefficients (i.e., profits) in objectives. We also generate other test problems by combining two objectives to create a dependent or correlated objective. Experimental results on randomly generated many-objective knapsack problems are consistent with well-known performance deterioration of Pareto dominance-based algorithms. That is, NSGA-II is outperformed by the other algorithms. However, it is also shown that NSGA-II outperforms the other algorithms when objectives are highly correlated. MOEA/D shows totally different search behavior depending on the choice of a scalarizing function and its parameter value. Some MOEA/D variants work very well only on two-objective problems while others work well on many-objective problems with 4–10 objectives. We also obtain other interesting observations such as the performance improvement by similar parent recombination and the necessity of diversity improvement for many-objective knapsack problems.