基于流形结构重建的多目标气动优化算法

在多目标优化中，Pareto解集是一个分段连续的k维流形，这一规律被传统进化算法所忽略。本文提出了一种基于流形结构重建的多目标优化算法，首先利用流形结构重建方法完成解集分布从目标空间到设计空间的映射，建立解集的概率分布，并在目标空间中扩展流形结构，从而借助解集在目标空间的推进来指导优化算法的快速演化。数值算例表明本文算法对于具有不同特征的Pareto前沿具有很好的适应性，能够极大提高算法的收敛效率。多目标气动优化算例验证，本文算法相比于常规多目标进化算法能够减少约80%的计算量，极大程度缩短了气动设计的周期。

Multi-objective aerodynamic optimization algorithm based on manifold reconstruction

The Pareto set of a multi-objective design problem is a piecewise continuous k-dimensional manifold, and this fact has always been neglected by traditional multi-objective genetic algorithms. A multi-objective optimization algorithm based on manifold reconstruction is proposed in this paper. The manifold reconstruction algorithm is employed for building the mapping between the design space and the objective space, and the probability distribution of the solution set is built. Then the manifold structure in the objective space is extended, enabling the advancing of the solution set in the objective space to optimize the algorithm. The analytic design cases show that the proposed algorithm is adaptive to problems with diverse Pareto structure features, and the optimization efficiency is improved significantly. The proposed algorithm is also verified by multi-objective aerodynamic design problems. The results demonstrated that about 80% computational cost can be saved compared with traditional multi-objective genetic algorithms. The proposed algorithm has the ability to significantly shorten the aerodynamic design cycle.