化工製程的設計在傳統上是只以經濟效益作為評估的標準，然而在實際操作情形下，系統中可能有某些參數因為不確定外部因素的干擾而導致系統逐漸偏離原先的設計，甚至致使系統無法操作。因此，除了經濟面的考量外，確保實際化工製程的操作彈性也是十分重要的設計考量。在過往的研究當中，已經針對動態系統定義了動態彈性指標(dynamic flexibility index, FId)，作為參數不確定情況下動態系統的操作彈性評估標準，使設計者能以此指標作為設計衡量的依據。然而傳統的計算方法較無法有效率地計算動態彈性指標問題，因此本研究中開發了新的數值求解策略，即透過蒙地卡羅樹搜索演算法(monte-carlo tree search algorithm, MCTS)輔助傳統頂點法的頂點窮舉步驟，得到更佳的計算效率。本研究中藉由Python與GAMS撰寫程式，開發並實作新型求解策略。另外在過往的研究中尚未對具偏微分方程動態模式的動態系統之彈性分析有進一步的研究，因此將延伸所開發的新求解策略應用於該類動態系統，並對數個動態系統案例進行分析。而透過案例結果，驗證了新求解策略較過往計算策略具有更好的計算效率。

The chemical processes are traditionally designed to maximize economic benefits according to nominal operating conditions and model parameters. However, in realistic processes, some parameters may deviate from their original design values due to uncertain external disturbances and/or inaccurate model formulations. These deficiencies may result in off-spec products and even cause the operation infeasible. Therefore, other than the economic criteria, it is equally important to consider the operational flexibility in process design. Although the dynamic flexibility index ({
m FI}_d) has often been adopted as a performance index, the existing calculation methods are not efficient enough for practical applications. Therefore, a novel numerical strategy has been developed in this study to address this important issue. In particular, the Monte Carlo tree search algorithm (MCTS) is utilized to speed up the vertex enumeration step. Then, the variable neighborhood search (VNS) algorithm could be utilized to approach the exact solution form the results of MCTS. In this study, Python and GAMS were used to construct the code to implement the proposed numerical strategies. It should be noted that these strategies are applicable for flexibility analysis of dynamic systems formulated with either ordinary or partial differential equations. Four (4) case studies are presented in this thesis to demonstrate the accuracy and efficiency achieved with the proposed computation algorithms.

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