Improved Augmented Lagrangian Relaxation-Assisted Analytical Target Cascading for Multidisciplinary Design Optimization

Abstract

Analytical target cascading (ATC) is an optimization strategy designed for multilevel and multidisciplinary design optimization (MDO) problems. Its core aim is to enhance the overall convergence of the system by reducing the inconsistency between different levels. In previous studies, although the augmented Lagrangian relaxation method can achieve rapid and accurate positioning of the optimal solution, it is highly sensitive to the penalty parameters, which can easily cause instability in numerical calculation. In contrast, the Lagrangian duality theory effectively reduces the numerical instability by adaptively adjusting the parameters, but this method is at the expense of increasing the computational time and the number of iterations. This study proposes an analytical target cascading combined with the Maclaurin series method (ATC-MAC), which aims to reduce parameter sensitivity and accelerate convergence to the optimal solution. The method uses the Maclaurin series to approximate the cross terms in the augmented Lagrangian function to reduce its interference with the main function. Meanwhile, the step size updating strategy is optimized by combining the duality theory and the multiplier method. Through the application in three numerical cases and one engineering case, the effectiveness and practicability of the ATC-MAC method are verified.