Composite structures offer a practical approach for many engineering applications, but their design is complex and can result in excessive sizing due to limitations in current modeling techniques. BTDs minimize the number of unknown variables in a kinematic theory for desired accuracy or for a fixed error in the Carrera Unified Formulation. This paper presents a method for computing Best Theory Diagrams (BTDs) for laminated composite plates using Genetic Algorithms (GA). As reported in previous papers by the authors, a multi-objective optimization technique using a GA is applied to build BTDs for a given structural problem. The plate models stresses and displacements are compared to those of a reference solution, and a plate model performance is quantified in terms of the number of unknown variables, the mean error and standard deviation of the stresses and displacements. Also, with the objective of reducing the computational time, a Neural-Networks (NN) was trained to reproduce the mean error and standard deviation of the stresses and displacements for any plate model refined from a reference plate model is addressed. Numerical simulations were computed for laminated composite plates with previously uninvestigated boundary conditions and compare computational time for BTD calculation. The preliminary results show that the use of multi-objective GA plus NN method reduces considerably the computation time to build BTDs.