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The performance of the Particle Swarm Optimization method in coping with Constrained Optimization problems is investigated in this contribution. In the adopted approach a non {stationary multi {stage assignment penalty function is incorporated, and several experiments are performed on well {known and widely used benchmark problems. The obtained results are reported and compared with those obtained through different evolutionary algorithms, such as Evolution Strategies and Genetic Algorithms. Conclusions are derived and directions of future research are exposed.