This paper proposes a general multi-objective particle swarm optimizer based on R2-indicator and decomposition (called R2-MOPSO) to deal with multi-objective optimization problems and then to solve many-objective optimization problems. R2-MOPSO makes use of the R2 contribution of the archived solutions to select global best leaders and update the swarm. R2-MOPSO uses decomposition method for selecting the personal best leaders and updates them for each particle in the population. In order to enhance the diversity of the particles, elitist-learning strategy and gaussian learning strategy are used. Our proposed algorithm is evaluated adopting benchmark test problems and indicators reported in the specialized literature, comparing is results with respect to those obtained by the state-of-the-art multi-objective evolutionary algorithms. Our preliminary results indicate that our proposal is competitive with respect to state-of-the-art multi-objective evolutionary algorithms, being particularly suitable for solving multi-objective and many-objective optimization problems.