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Multi-Objective Particle Swarm Optimization (MOPSO) is a population based multi-objective meta-heuristic inspired on animal swarm intelligence. It is used to solve several Multi-Objective Optimization Problems (MOPs), problems with more than one objective function. However, Multi-Objective Evolutionary Algorithms (MOEAs), including MOPSO, have some limitations when the number of objective grows. Many-Objective Optimization research methods to decrease the negative effect of applying MOEAs into problems with more than three objective functions. In this context, the goal of this work is to explore several archiving methods from the literature used by MOPSO to store the selected leaders into Many-Objective Problems. Moreover, new archiving methods are proposed specially for these problems. The use of the archiving methods into MOPSO is evaluated through an empirical analysis aiming to observe the impact of these methods in the convergence and the diversity to the Pareto front, in Many-Objective scenarios.