Enhanced Nonhierarchical Analytical Target Cascading Decomposition for Multidisciplinary Design Optimization Integrating Global Sensitivity Analysis and K-Means Clustering

Abstract Multidisciplinary design optimization (MDO) is devoted to address the coupled problems among different disciplines in a complex system. Analytical target cascading (ATC) is a distributed algorithm within multidisciplinary design optimization that utilizes hierarchical formulations to decompose the problem into multiple levels, adjusting inconsistencies between levels to converge to an optimal solution. However, when dealing with nonhierarchical MDO problems, there are many coupled variables that make the problem difficult to decompose or decompose ineffectively. This is because there is a lack of characterization of the coupling degree between different objective functions and constraints, which leads to an inability to decompose them reasonably. To solve this problem, we propose a new decomposition method for the nonhierarchical ATC. This method uses global sensitivity analysis to represent the degree of coupling between variables with sensitivity indices, then simplifies the problem by fixing variables with small sensitivity indices in the constraints, and finally uses the K-means algorithm to cluster constraints or objective functions with high coupling degrees. In a numerical benchmark and an engineering benchmark problem, the proposed method achieves similar accuracy and convergence with less computational cost compared to two published nonhierarchical ATC methods. In addition, to demonstrate the practicality of the proposed method, the modified problem of the total cost per flight for a simple mission of an electric vertical take-off and landing (eVTOL) aircraft was optimized using this method.