Laminated composites are highly in demand for the applications where high strength and stiffness are required at less weight. They generally fail due to buckling, as they are modeled as thin plates and are loaded compressively. Therefore, the design parameters of the laminated composite plates are to be optimized for the multiple-conflicting objectives buckling strength and weight. However, the composite plates, which are used in real world applications, are to be made with cut-outs and finite element analysis is required to analyze them. As it makes the optimization process more complex, a methodology is proposed in this paper to carry out a multiobjective optimization for the rectangular composite plate made with a central elliptical cut-out. The nondominated solutions are obtained using nondominated sorting genetic algorithm (NSGA-II) in which the multilayer feed-forward neural network is used to replace the time consuming finite element analysis. The numerical results show that the proposed method finds the nondominated solutions efficiently and reduces the computational cost prominently. © 2016 Mathematical Sciences Publishers.