To address the challenges of high-dimensional constrained optimization problems with expensive simulation models, a Surrogate-Assisted Differential Evolution using Manifold Learning-based Sampling (SADE-MLS) is proposed. In SADE-MLS, differential evolution operators are executed to generate numerous high-dimensional candidate points. To alleviate the curse of dimensionality, a Manifold Learning-based Sampling (MLS) mechanism is developed to explore the high-dimensional design space effectively. In MLS, the intrinsic dimensionality of the candidate points is determined by a maximum likelihood estimator. Then, the candidate points are mapped into a low-dimensional space using the dimensionality reduction technique, which can avoid significant information loss during dimensionality reduction. Thus, Kriging surrogates are constructed in the low-dimensional space to predict the responses of the mapped candidate points. The candidate points with high constrained expected improvement values are selected for global exploration. Moreover, the local search process assisted by radial basis function and differential evolution is performed to exploit the design space efficiently. Several numerical benchmarks are tested to compare SADE-MLS with other algorithms. Finally, SADE-MLS is successfully applied to a solid rocket motor multidisciplinary optimization problem and a re-entry vehicle aerodynamic optimization problem, with the total impulse and lift to drag ratio being increased by 32.7% and 35.5%, respectively. The optimization results demonstrate the practicality and effectiveness of the proposed method in real engineering practices.

To deal with the problems of high computational cost and poor global convergence that often exist in discretecontinuous mixed optimization of complex flight vehicle systems, a Sample Mapping and Dynamic Kriging based Discrete-Continuous Mixed Optimization method (SMDK-DC) is proposed. In this method, time-consuming simulation model is replaced by Kriging surrogate model to reduce computational expenses. A sample point mapping mechanism based on generalized Manhattan distance criterion is also proposed to efficiently generate uniformly-distributed real sample points in continuous-discrete domain. Expected improvement criteria is combined with significant sampling space to identify new sample points, update Kriging continuously and dynamically, and guide the rapid convergence of the discrete-continuous optimization process. Benchmark cases show that compared with international methods such as SOMI and NOMAD, SMDK-DC has significant advantages in global convergence and robustness. Finally, SMDK-DC is used for solving a multidisciplinary design optimization problem of solid rocket motor. The method, on the premise of satisfying all the constraints of the combustion chamber and internal ballistic discipline, leads to a total impulse increase of at least 12. 92%, and the optimization yield is 1. 71% higher than that of SOMI, which verifying the effectiveness and engineering practicability of SMDK-DC.