This work presents a genetic algorithm combining two types of computational parallelization methods, resulting in a hybrid shared/distributed memory algorithm based on the island model using both OpenMP and MPI libraries. In order to take further advantage of the island configuration, different genetic parameters are used in each one, allowing the consideration of multiple evolution environments concurrently. To specifically treat composite structures, a three-chromosome variable encoding and special laminate operators are used. The resulting gains in execution time due to the parallel implementation allow the use of high fidelity analysis procedures based on the Finite Element Method in the optimization of composite laminate plates and shells. Two numerical examples are presented in order to assess the performance and reliability of the proposed algorithm.