This study commences with the application of an efficient artificial neural network (ANN)-balancing composite motion optimization (BCMO) algorithm for finding the optimal material distribution of bi-directional functionally graded nanocomposite (FGN) plates accounting for geometrical nonlinearity. The method integrates ANN into the framework of BCMO to improve the computational efficiency of the iteration-based optimization process. In this strategy, the ANN-based surrogate model is used to replace the high-fidelity structural responses obtained by a geometrically nonlinear NURBS-based isogeometric analysis. Whilst BCMO is employed as an optimizer for solving optimization problems without complex sensitivity analyses. To enhance the possibility to explore the complex distribution of optimal material profiles, the optimal in-plane volume fraction function of FGN plates is modeled by a two-dimensional non-uniform rational B-spline (NURBS) basis function which is separate from the NURBS analysis meshes. Accordingly, its unknown control point values are selected as the continuous design variables. The effectiveness and accuracy of the proposed algorithm are illustrated via selected numerical examples. Results show a significant reduction in the computational effort over the conventional approach based on BCMO-IGA scheme.