Constrained globalized Nelder-Mead method for simultaneous structural and manufacturing optimization of a composite bracket

The optimized design of composite structures is a difficult task. It requires optimizing simultaneously both structural and manufacturing objectives. The objectives do not have closed form solutions and have multiple local optima that calls for a global search. This paper improves the global search method called GBNM [1], which is based on several restarts of the Nelder-Mead method. Two issues are addressed here. First, the restart procedure is improved by using a one-dimensional probability function and a weighted selection procedure. Second, nonlinear constraints are included by projecting the infeasible points onto the nonlinear constraints. The improved procedure is applied to four mathematical test functions. Numerical results show the proposed approach is more efficient in terms of computational time and probability of finding the global minimum. The improved GBNM[ is then applied to the simultaneous structural and manufacturing design of a Z-shaped composite bracket. The results are compared to those obtained with the genetic algorithm.