傳統上，程序設計大多都是依據經濟效益作為評量標準，但在現實應用中存在不確定隨機變化的外界干擾，設計過程中採用的參數值可能會在極端狀況下改變，以致使系統無法操作，因此在設計過程中除了考慮成本以外，還需要確保操作的可行性。此外，一般認為程序設計與控制應在製程開發初期就須同時考慮，以便獲得同時具有操作彈性與經濟效益的實際系統。在過去的研究中，雖然已有學者分析在參數不確定情況下動態系統的操作彈性，使設計者能夠以此性能指標作為設計衡量依據。但是，由於傳統頂點法的頂點數量過於龐大，造成難以負荷的計算量。而在傳統活性約束法的數學規劃模型中由於KKT 條件包含大量的限制式和二元變數以致於相應最適化計算難以收斂。另外，值得注意的是，在計算FId的傳統方法中允許瞬時和連續的控制調整也是不切實際的，因此我們在本研究中假設可調控變數可以分段且常數形式表示。我們參考基因演算法及兩種傳統的計算方式，發展出周嚴的動態彈性指標計算流程。具體步驟可描述如下：
1. 使用活性約束法、GA頂點法或窮舉頂點法來尋找可能的頂點區域。
2. 使用較細的時間區間離散化窮舉頂點法中的限制式，針對可能的頂點區域進行搜尋與計算出精確的動態彈性指標。
3. 最後，利用較細的時間區間離散化活性約束法的限制式，並且代入上一步所得結果，以此驗證結果的正確性。
我們藉由商用軟體Matlab及GAMS，可以有效地執行上述最適化問題。而該計算流程不僅保留了傳統頂點法和活性約束法的優點，更避免了它們的缺點。在本論文中，我們研究並討論幾個案例所得到的結果，以證明解決策略的可行性和準確性。

The chemical processes, designed on the basis of nominal operating conditions and parameters, have traditionally been evaluated according to economic criteria. This approach often ends up with a plant which may become inoperable in realistic environment if some of the conditions/parameters significantly deviate from their nominal values. Thus, in addition to the financial feasibility, it is equally important to consider the operational flexibility in a practical design. The dynamic flexibility index (FId) have already been well defined to characterize the batch or unsteady operations, and the corresponding dynamic programming models have also be rigorously derived for computing such metrics. However, at the present time, it is still very difficult to apply the traditional vertex method or the active set method to numerically compute FId for even moderately complex systems. This is often due to an overwhelmingly large number of vertices in the former case. On the other hand, since the Karush–Kuhn–Tucker conditions must be included into the mathematical programming model in the latter case, the huge number of real and binary variables usually causes convergence failure. In addition, notice that it is really impractical to allow instantaneous and continuous control adjustments in computing the original version of FId. It is actually more realistic to assume that the manipulated variables are piecewise constant.
Together with the above assumption and constraints for incorporating additional insights, the above two traditional solution methods are integrated with the genetic algorithm in this work to overcome the aforementioned numerical difficulties. Specifically, the following three-step compotation strategy is proposed:
1.Identify the approximate region(s) of candidate vertexes by using the dynamic active-set method, the dynamic vertex method solved with genetic algorithm, or the dynamic vertex method solved with exhaustive enumeration.
2.Use a refined time interval to discretize the constraints in vertex method and carry out the corresponding computation procedure by fixing the identified regions of candidate vertexes.
3.Use a refined time interval to discretize the constraints in KKT conditions and fix the time profiles of control variables and uncertain parameters identified in the previous step to carry out dynamic active set method again
The above optimization computations can be readily implemented with MATLAB and GAMS. This strategy not only retains the advantages from traditional vertex method and the active set method but also avoid their shortcomings .The numerical results obtained in several case studies are reported in this thesis to demonstrate the feasibility and accuracy of the solution strategy.

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