We consider a symmetric composite multilayered plate whose fiber orientation varies from a layer to another. The plate model used is that of Mindlin. We are interested in determining the optimal fiber orientations that optimize, in the same time, two criteria: minimizing the compliance and maximizing the smallest eigenfrequency of vibration or minimizing both of the compliance and the smallest eigenfrequency or maximizing both of the smallest eigenfrequency and the smallest buckling load. In order to optimize one of the above criteria, a metaheuristic algorithm of Simulated Annealing type is used. While, in the case of optimizing two objectives, the Pareto front method is used. Numerical results are presented for a rectangular eight-layered plate.