To improve the analysis and optimization efficiency of stiffened composite cylindrical shells, a novel fast modeling method for the Augmented Radial Basis Function (ARBF) approximate model is proposed by fusing sample clustering and improved K-fold cross-validation. The K-means clustering algorithm is used to determine the optimal sample clustering, and the reference shape parameters of the samples are determined based on the local density of the samples. The scaling coefficient is introduced into each cluster to adjust the shape parameters adaptively, which effectively balance the optimization efficiency and accuracy of the shape parameters. The ARBF auxiliary approximation model is established by sample subset, and then the evaluation criteria of ARBF auxiliary approximation model generalization performance is established based on bias-variance decomposition, addressing the problem of insufficient utilization of traditional K-fold cross-validation sample information. Based on the block matrix inversion technique, a fast inversion method of the high-order coefficient matrix of the ARBF auxiliary approximation model is derived, and the scaling coefficient optimization method based on the improved K-fold cross-validation is proposed, which greatly reduces the computational complexity of determining the optimal shape parameters and improves the efficiency and accuracy of ARBF approximation modeling. Numerical and engineering examples validate that the optimal sample clustering and fast cross-validation have significant contributions to the approximate modeling efficiency and accuracy, and reduce the sensitivity of modeling efficiency to sample size and problem dimension. Moreover, using the same number of training samples, the modeling accuracy of the proposed method is significantly superior to that of other typical methods. The results verifies the effectiveness, advancemen and practical engineering value of the proposed method.

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.