大尺度複雜系統的設計問題由於整體系統複雜性以及子系統間的耦合，長久以來是一個具有挑戰性的問題，在過往文獻中，針對複雜系統之設計方法主要有兩種：協同最佳化方法( Collaborative Optimization, CO)以及解析目標傳遞法(Analytical Target Cascading, ATC)，此兩種方法皆是利用系統化的拆解方式，將複雜系統拆解成較小的子系統進行求解，在求解過程中，藉由各子系統的協調，可以達到與未拆解前系統的相同最佳值。倘若將焦點轉移至複雜系統之拆解方式，將階層狀架構配合不同的拆解方式並探討其複雜系統的收斂性，我們發現不同的架構對於收斂性也有著不同影響，因此本文旨在針對階層狀架構配合ATC策略發展出一循序暫緩設計方法，嘗試以適當修改架構來解決複雜系統設計問題。在本設計方法的每次迭代計算中，我們利用改良全域敏感度矩陣計算出各子系統間的耦合強度，當子系統擁有較小的耦合強度時，便將其暫時移除並更新架構，同時在下次迭代計算時以新架構進行求解，直到架構再度更新。此外，為進一步減少計算成本，我們也加入active-set 策略--只針對最佳值有貢獻之拘束條件進行計算。本設計方法是經由下列方式來改善計算成本：(i)避免某些結構在數值運算上求解困難；(ii)根據每次迭代結果，可將較不重要的子系統去耦合(移除)，只留下重要的子系統進行計算；(iii)並同時針對單一子系統的計算加以化簡。本論文最後將以一個數學範例、一個固定架設計範例與一個簡易汽車設計範例來展示此設計方法的有效性和效率，並與現有複雜系統最佳化設計方法--解析目標傳遞法中的增廣拉格朗日策略(ATC-AL)做一比較。

Design problems for large-scale systems are challenging to solve due to their overall complexity and the coupling between each subsystems. Methods in the literature, such as collaborative optimization and analytical target cascading (ATC), systematically resolve the problem of large-scale systems by decomposing them into smaller subsystems. By deliberately coordinating between them, these subsystems could reach the same optimum as they were undecomposed. In this work we investigate the impact of hierarchical structure on the convergence of a large-scale system with a dynamic decomposition schemes via ATC. It is found that the impacts of problem structures are major. Therefore we combine the optimal decomposition with ATC to form an iterative suspension and solution strategy. In this strategy, the coupling strengths between subsystems are calculated at each design iteration using modified global sensitivity equations. Subsystems with small coupling strengths are tentatively removed (suspended) and the resulting structure re-evaluated. To further reduce the computation cost, active-set concepts are implemented such that only constraints contributing to the optimum are considered. This new strategy can improve computation cost in several ways : (i) it avoids structures that are numerically difficulty to solve; (ii) it results in a decoupling scenario with only "important" subsystems; (iii) it uses minimal efforts in solving a subsystem. The effectiveness and the efficiency of the proposed method is compared with ATC using augmented Lagrangian via a numerical example and an optimal structural design case study.

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