A dimensionality reduction and layout optimization scheme for grid-stiffened structures

When directly solving the layout optimization design problem of grid-stiffened structures with large-scale discrete design variables, gradient-based methods and intelligent optimization algorithms are rendered ineffective owing to multilocal optimal traps and the discrete variable space with extremely large dimensionality. A new layout optimization design scheme for grid-stiffened structures is proposed in this study, based on the continuous representation of discrete variables and a dimensionality reduction method. In this method, first, a discrete stiffener layout is described by a bounded field with space correlation and transformed into continuous design variables using material interpolation. Then, to significantly reduce the dimensionality of the design space, a series expansion approach is adopted. Finally, a sequential optimization strategy combined with the kriging surrogate model is used to successfully solve optimization problems. Layout optimization designs, including a stiffened plate and a space-borne antenna reflector, are proposed to demonstrate the validity and applicability of the proposed method.