本研究參考螢火蟲演算法(Multi-Objective Modified Firefly Algorithm)，結合ℇ-支配法，提出一個多目標修正螢火蟲演算法，並將多目標修正螢火蟲演算法應用在路徑產生機構的最佳化尺寸合成。本研究首先以七個最佳化測試函數為範例，並與其他多目標演算法進行比較，藉由檢視多目標修正螢火蟲演算法的收斂與分散能力，證明多目標修正螢火蟲演算法優於其他多目標演算法。其中用以比較的多目標演算法包含 : 多目標粒子群演算法(Multiple Objective Particle Swarm Optimizer)、多目標蟻獅演算法(Multi-Objective Ant Lion Optimization)、分解式多目標進化演算法(Multi-Objective Evolutionary Algorithm Based on Decomposition) 以及非支配排序基因演算法III (Nondominated Sorting Genetic Algorithm III)。再以兩個機構尺寸最佳化問題做測試，分別為八連桿以及六連桿問題，說明本演算法於路徑產生機構的最佳化尺寸合成問題的可行性。在八連桿的問題中，本研究以現有的機構軌跡作為目標軌跡，因此已知最佳解，藉此驗證演算法的正確性。於六連桿的問題當中，本研究以三個不同的人為設計軌跡作為目標軌跡，並最佳化出最接近的六連桿機構。經過結果比較，本研究提出之多目標修正螢火蟲演算法結果優於其他演算法。

A new multi-objective algorithm, Multi-Objective Modified Firefly Algorithm (MOMFA), is proposed in the study. The new algorithm combines the convergence operator by using Modified Firefly Algorithm with the distributing method modifying ℇ-dominance method. To demonstrate the converging and distributing ability, seven testing problems are performed. By comparing the new algorithm with four other multi-objective algorithms that include Multiple Objective Particle Swarm Optimizer, Multi-Objective Ant Lion Optimization, Multi-Objective Evolutionary Algorithm Based on Decomposition and Nondominated Sorting Genetic Algorithm III, several features for algorithms could be distinguished and summarized. In the mechanism synthesis problems, three gaits that are generated from one existing eight-bar reconfigurable mechanism set to demonstrate the effectiveness of the proposed MOMFA. Further, the study uses three manually designed gaits on six-bar mechanism synthesis problem to identify the searching ability for the proposed algorithm with unknown mechanism’s dimension. The results show that MOMFA is able to produce better solutions regarding convergence and distribution compared to other algorithms.

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