This paper proposes a method, based on a genetic algorithm, to generate smoth manipulator trajectories in a multi-objective perspective. The method uses terms proportional to the integral of the squared displacements in order to eliminate the jerk movement. In this work, the algorithm, based on NSGA-II and maximin sorting schemes, considers manipulators of two, three and four rotational axis (2R, 3R, 4R). The efficiency of the algorithm is evaluated, namely the extension of the front and the dispersion along the front. The effectiveness and capacity of the proposed approach are shown through simulations tests.