An isotropic mechanical structure cannot withstand shocks, accidents, and mechanical loading. In this perspective, composite structures have been introduced to improve the performance of mechanical structures. We are interested in the study of laminates with the aim to find an optimal structure resistant to vibrations and buckling. To remedy the problem of vibrations and buckling, we use artificial intelligence methods to optimize the design of composite structures. As it is a typical method of artificial intelligence adapted to this studied problem, we use genetic algorithms based on a new genetic operator. In the present article, an optimization procedure based on the new genetic operator called genetic immigration operator is developed to determine the maximum buckling load and fundamental frequency of the laminated plate with plies oriented at -45•/45• ,0•, and 90•. The aim of this paper is the use of two different methods for their effectiveness. These optimization works consist of first maximizing the buckling load factor with UGA (Uniform Genetic Algorithm) and a new evolutionary search strategies called Immigration Genetic: SIG (Standard Immigration Genetic Algorithm) and AIG (Improved Genetic Immigration Algorithm) and second of solving a multi-objective problem with minimizing the cost and weight of the hybrid laminate made of the fibers of two composite materials. The resolution of this problem by the proposed genetic immigration approach is reinforced by the optimization of the CPU computation time which is due to the exploitation of the parallel architecture based on the multi-processor parallel computation.