Optimization of square-on-square double layer grids is beneficial for design purpose. For this purpose, use of a gradient based optimization algorithm incorporating stochastic feature called static perturbation stochastic approximation (SPSA) has been investigated in this book. Also, a computational procedure for constrained optimization of square-on-square double layer grids combining FEM, SPSA algorithm and neural network has been formulated. This research study shows that the proposed methodology of combining FEM and SPSA algorithm is effective for the purpose of generation of reliable data to train GR and RBF neural network models for use as a practical tool for the prediction of optimal design and maximum deflection of square-on-square double layer grids. This book is especially useful to researchers in the field of optimization of space structures and neural networks and, also, the designers of double layer grids. It is beneficial for postgraduate students majoring in structural engineering.