本研究使用動態族群規模(Dynamic Population Size)方法，結合四種多目標最佳化演算法，包含多目標修正螢火蟲演算法(Multi-Objective Modified Firefly Algorithm)、多目標粒子群最佳化(Multi-Objective Particle Swarm Optimizer)、多目標布穀鳥搜尋(Multi-Objective Cuckoo Search)、非支配排序基因演算法III(Nondominated Sorting Genetic Algorithm III)，進而提出四種動態族群規模最佳化演算法。本研究首先以DTLZ2、DTLZ5、DTLZ6三種測試函數對動態族群規模最佳化演算法及其原始演算法進行測試，測試動態族群規模最佳化演算法在計算時間及族群分布上的優勢，結果顯示可減少7.96%至99.85%的時間，且增加0.68%至48.41%的分布多樣性。本研究選擇分布性及收斂性最佳的多目標修正螢火蟲演算法及動態族群規模多目標修正螢火蟲演算法應用於機構最佳化設計問題。本研究使用六連桿機構Klann Linkage及八連桿機構為路徑產生機構，目標函數則為兩種路徑軌跡及傳力角與90°之偏差，在多個設計變數及限制條件下進行機構最佳化設計，並探討有無時序規定之兩種不同案例。結果顯示動態族群規模多目標修正螢火蟲演算法在達成指定目標函數的要求下，六連桿機構兩種不同案例分別減少97.79%、97.41%的時間，其中增加56.44%、減少10.82%的第三目標函數值；八連桿機構減少99.11%、99.22%的時間，其中減少4.66%、42.55%的第三目標函數值。六連桿及八連桿最佳化機構不但能滿足一定程度的目標軌跡，且具有較佳的傳力角變化，也能夠大幅減少計算時間成本，展現動態族群規模多目標最佳化演算法解決困難的多目標最佳化問題之能力。

This study integrates the dynamic population size method with existing multi-objective optimization algorithms, including Multi-Objective Modified Firefly Algorithm (MOMFA), Multi-Objective Particle Swarm Optimizer (MOPSO), Multi-Objective Cuckoo Search (MOCS) and Nondominated Sorting Genetic Algorithm III (NSGA III). In the dynamic population size method, cell-based rank and density estimation is proposed to efficiently compute the dominance and diversity information. In addition, the population growing and declining strategies are designed to determine whether an individual will survive or be eliminated. To compare the proposed dynamic multi-objective optimization algorithms with original algorithms, three testing problems, DTLZ2, DTLZ5, DTLZ6, are performed. The testing results demonstrate that MOMFA and Dynamic MOMFA (DMOMFA) are superior in terms of converging and distributing ability. Further, it shows that DMOMFA requires less computational time. This study selects MOMFA and DMOMFA to design path generating mechanisms. The six-link and eight-link reconfigurable mechanisms are used in path synthesis problems, and multi-objective functions are the tracking error of two gaits and the deviation of transmission angle to 90°. In the mechanism synthesis, DMOMFA shows competitive result with improved third objective fitness and demands less computational cost under the requirement of achieving the specified first and second objective fitness.

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