The design optimization of coupled systems requires the implementation of multidisciplinary design optimization techniques in order to obtain consistent and optimal solutions. The associated research topics include the development of optimization algorithms, computational frameworks, and multidisciplinary design optimization formulations. This paper presents a benchmarking of the combination of monolithic formulations and derivative computation techniques. The monolithic formulations include typical literature formulations as well as new normalized variable hybrid formulation. A novel test problem is proposed which consists in the sizing of a space launcher thrust vector control electro-mechanical actuator. Solving the single multidisciplinary coupling present in this problem is complex due to the possibility to face one, two, or no solutions depending on the external load and reducer gear ratio configuration. A larger scale version of this test problem is also proposed and tested by adding a high degree of freedom point-to-point trajectory. The tests are carried out in order to obtain typical performance criteria but also some proposed additional robustness criteria such as variation of the initial conditions or the external load scale. These additional criteria are particularly relevant in an industrial engineering design context where knowledge capitalization and reuse are sought. The most significant findings are the interesting performances of the new formulation in terms of computational cost and the robustness. Furthermore, the effect of the choice of derivative computation strategy on different performance criteria is assessed for the original and larger scale problem, and thus underlines the benefits of full analytic gradient-based optimization.

耦合系统的设计优化需要实现多学科的设计优化技术，以便获得一致且最佳的解决方案。相关的研究主题包括优化算法，计算框架和多学科设计优化公式的开发。本文介绍了整体配方和微分计算技术相结合的基准测试。整体配方包括典型的文献配方以及新的标准化变量混合配方。提出了一种新颖的测试问题，其中包括确定空间发射器推力矢量控制机电致动器的尺寸。解决此问题中存在的单个多学科耦合是复杂的，因为有可能面对一，二，还是没有解决方案，具体取决于外部负载和减速器齿轮比配置。还建议并通过添加高度自由的点对点轨迹来测试此测试问题的更大规模版本。为了获得典型的性能标准，还进行了测试，还提出了一些其他的稳健性标准，例如初始条件的变化或外部负载规模。这些附加标准在寻求知识资本化和再利用的工业工程设计环境中特别重要。最重要的发现是就计算成本和鲁棒性而言，新配方的有趣性能。此外，