The particle swarm optimizer (PSO), originally proposed for single-objective optimization problems, has been widely extended to other areas. One of them is multiobjective optimization. Recently, using the PSO to handle many-objective optimization problems (MaOPs) (i.e., problems with more than three objectives) has caught increasing attention from the evolutionary multiobjective community. In the design of a multiobjective/many-objective PSO algorithm, the selection of leaders is a crucial issue. This paper proposes an effective many-objective PSO where the above issue is properly addressed. For each particle, the leader is selected from a certain number of historical solutions by using scalar projections. In the objective space, historical solutions record potential search directions, and the leader is elected as the solution that is closest to the Pareto front in the direction determined by the nadir point and the point constructed by the objective vector of this particle. The proposed algorithm is compared with eight state-of-the-art many-objective optimizers on 37 test problems in terms of four performance metrics. The experimental results have shown the superiority and competitiveness of our proposed algorithm. The new algorithm is free of a set of weight vectors and can handle Pareto fronts with irregular shapes. Given the high performance and good properties of the proposed algorithm, it can be used as a promising tool when dealing with MaOPs.