This paper introduces an inverse problem for crack identification in two-dimensional structures using eXtend Finite Element Method (XFEM) associated with original Grey Wolf Optimization (GWO) and improved GWO using Particle Swarm Optimization (PSO) (IGWO). Static analysis with different boundary conditions and experimental modal analysis of cracked plates with varying crack length, positions, and orientation are used to test the accuracy of IGWO compared with the original GWO. The objective function is based on vertical measured strain and is computed at each iteration. The obtained results indicate that IGWO provides more accurate results than GWO based on convergence study and the error between exact and estimated results. Next, another application based on dynamic experimental cracked plates is used to improve Artificial Neural Network (ANN) parameters using GWO and IGWO. The frequencies and crack lengths are used as input and output for vertical and horizontal cracks in the plates. Thus, the model can be used for the prediction of crack length. IGWO can select the best parameters for better prediction compared with GWO.