Most conventional optimization approaches are deterministic and based on the derivative information of a problem's function. On the other hand, nature-inspired and evolution-based algorithms have a stochastic method for finding the optimal solution. They have become a more popular design and optimization tool, with a continually growing development of novel algorithms and new applications. Flexibility, easy implementation, and the capability to avoid local optima are significant advantages of these algorithms. In this study, shapes, and shape perturbation limits of a bracket part, which is used in aviation, have been set using the hypermorph tool. The objective function of the optimization problem is minimizing the volume, and the constraint is maximum von Mises stress on the structure. The grey wolf optimizer (GWO) and the moth-flame Optimizer (MFO) have been selected as nature-inspired evolution-based optimizers.