In this study, Genetic Algorithms (GAs) combined with the proposed neural networks were implemented to the free vibration analysis of an adhesively bonded double containment cantilever joint with a functionally graded plate. The proposed neural networks were trained and tested based on a limited number of data including the natural frequencies and modal strain energies calculated using the finite element method. GA evaluates a value generated iteratively by an objective function and this value is calculated by the finite element method. The iteration process restricts us apparently to use directly the finite element method in our multi-objective optimisation problem in which the natural frequency is maximised and the corresponding modal strain energy is minimised. The proposed neural networks were used accurately to predict the natural frequencies and modal strain energies instead of calculating directly them by using the finite element method. Consequently, the computation time and efforts were reduced considerably. The adhesive joint was observed to tend vertical bending modes and torsional modes. Therefore, the multi-objective optimisation problem was limited to only the first mode which appeared as a bending mode. The effects of the geometrical dimensions and the material composition variation through the plate thickness were investigated. As the material composition of the horizontal plate becomes ceramic rich, both natural frequency and modal strain energy of the adhesive joint increased regularly. The plate length and plate thickness were more effective geometrical design parameters whereas the support length and thickness were less effective. However, the adhesive thickness had a small effect on the optimal design of the adhesive joint as far as the natural frequencies and modal strain energies are concerned. The distributions of optimal solutions were also presented for the adhesive joints with fundamental joint lengths and material compositions in reference to their natural frequencies and corresponding modal strain energies.