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This paper constitutes a first study of the Particle Swarm Optimization (PSO) method in Multiobjective Optimization (MO) problems. The ability of PSO to detect Pareto Optimal points and capture the shape of the Pareto Front is studied through experiments on well-known non-trivial test functions. The Weighted Aggregation technique with fixed or adaptive weights is considered. Furthermore, critical aspects of the VEGA approach for Multiobjective Optimization using Genetic Algorithms are adapted to the PSO framework in order to develop a multi-swarm PSO that can cope effectively with MO problems. Conclusions are derived and ideas for further research are proposed.