中文摘要：

针对多目标优化结果排序与选择的多属性决策（Multi-attribute decision making,MADM）问题,将多目标优化与MADM相结合,提出基于MADM的多目标优化方法,并将该方法应用于跨声速前掠翼（Forward-swept wing,FSW）气动隐身多目标优化中,优化结果提高了跨声速FSW的气动和隐身性能。采用类别形状函数变换法（Class-shape function transformation,CST）方法对翼型几何外形进行描述,实现FSW气动和隐身多学科优化设计模型的参数化描述。建立基于N-S方程的计算流体力学方法的FSW气动分析模型和基于矩量法的计算电磁学方法的FSW隐身分析模型。将Pareto多目标遗传算法得到的Pareto非劣解集构成MADM矩阵,采用基于模糊熵权的改进的逼近理想解的排序法（Modified technique for order preference by similarity to ideal solution,M-TOPSIS）方案评价方法进行Pareto非劣解排序,最终确定最佳的Pareto非劣解。研究结果验证了所提出方法的有效性,为多目标优化问题提供了一种新的解决途径。

英文摘要：

In view of multi-attribute decision making（MADM） problems for ranking and selecting of multi-objective optimization results, the multi-objective optimization method based on MADM is proposed by combining the multi-objective optimization with MADM. The multi-objective aerodynamic and stealthy performance of transonic forward-swept wing（FSW） is solved by the proposed method, which can improve the aerodynamic and stealthy performance of transonic FSW effectively. The class-shape function transformation（CST） method is used to describe the parameterized airfoil geometry. The parameterized models for aerodynamic and stealthy performance of FSW are constructed. The aerodynamic analysis model of FSW is constructed by computational fluid dynamics method based on N-S equations. The stealthy performance analysis model of FSW is constructed by computational electromagnetics method based method of moments, The MADM decision matrix is constructed by the Pareto optimal solutions set solved from Pareto multi-objective genetic algorithm, the modified technique for order preference by similarity to ideal solution（M-TOPSIS） approach based on fuzzy entropy weight is employed to rank the Pareto optimal solutions and ultimately to identify the best Pareto solution. The results of the investigation show that the present method is effective, and a new solving approach is provided to the multi-objective optimization problem.