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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。
In order to solve the multi-attribute decision making (MADM) problem of multi-objective optimization results sorting and selection, a multi-objective optimization method based on MADM is proposed by combining multi-objective optimization with MADM. The proposed method is applied to multi- In the aerodynamic stealth multi-objective optimization of Forward-swept wing (FSW), the optimization results improve the aerodynamic and stealth behavior of trans-FSW. The airfoil geometric shape is described by using the Class-shape function transformation (CST) method, and the parametric description of multi-disciplinary optimization design model of aerodynamic and stealth FSW is realized. FSW aerodynamic analysis model based on Computational Fluid Dynamics method based on N-S equation and FSW stealth analysis model based on moment method for calculating electromagnetism are established. The Pareto non-inferior solution set obtained by Pareto multi-objective genetic algorithm is used to construct the MADM matrix. The modified technique for order preference by similarity to ideal solution (M-TOPSIS) Perform Pareto non-inferiority rankings to finalize the best Pareto non-inferiority solution. The results verify the effectiveness of the proposed method and provide a new solution to the multi-objective optimization problem.