The present work deals with the multi-objective optimization of structures in composite materials using genetic algorithms. This is a nonlinear problem with constraints. Methods based on genetic algorithms are best suited for complex cases with multiple objectives, as they do not require computing derivatives or linearizing the objective functions. The proposed laminate representation method using genetic algorithms is both practical to implement and flexible enough to accommodate further extensions. The optimization process is carried out at two levels: at the macroscopic level, with deformation energy or stiffness as objective functions; and at the material configuration level, focusing on minimizing the weight of the structure. The vector of the optimization parameters concerns the thicknesses and the orientations as well as the material of each ply. The developed code allows generating optimal solutions and leads to a laminate whose stacking sequence best meets a given set of criteria. Simulation results are presented.