Mixed-integer sequential approximate optimization method for stiffened cylindrical shells in large launch vehicles

A Sequential Approximate Optimization method based on exploitation/exploration Competing Parallel Sampling strategy (SAOCPS) is proposed to conquer the difficulties of coupling multi-mixed-integer variables, high computational cost, and poor optimization convergence in the lightweight design of stiffened cylindrical shells for large launch vehicles. In this method, the Augmented Radial Basis Function (ARBF) approximate model of axial load-carrying capacity is constructed to improve the efficiency of post-buckling analysis for the stiffened cylindrical shells. A dual-elite population evolution-based exploitation strategy is developed to exploit the information in promising regions, thereby enhancing the local optimization performance of SAOCPS. Meanwhile, the new levels are determined according to the one-dimensional projection characteristics of discrete and continuous variables. The combination of element exchange and probabilistic transition is employed to enhance the performance of the permutation optimization method, achieving a uniform coverage of the exploration sample points to the discrete-continuous design space and enhancing the global optimization performance of SAOCPS. Ultimately, the exploration/exploitation competitive mechanism driven by performance gains is introduced for the balance between exploration and exploitation, thereby guiding the rapid convergence of the high-dimensional and time-consuming mixed-integer optimization problems. In applying the lightweight design of large-diameter stiffened cylindrical shells, the optimization results of SAOCPS are still comparable to those of the literature work, even if the initial sample points are greatly reduced by more than 90%. Furthermore, the weight is reduced by 279.8 kg compared with the classical PoF optimization method. The effectiveness and superiority of the proposed method are validated for the prospect of the engineering applications.