本研究參考螢火蟲演算法與布穀鳥搜尋演算法，結合螢火蟲的生物特性，提出修正螢火蟲演算法。本研究將修正螢火蟲演算法應用在路徑產生機構最佳化尺寸合成，首先以六個基準最佳化測試函數為範例，比較螢火蟲演算法與修正螢火蟲演算法，證明修正螢火蟲演算法的最佳化結果優於螢火蟲演算法。再以三個機構尺寸最佳化的範例，分別為四連桿機構、六連桿機構、八連桿機構，說明修正螢火蟲演算法於機構尺寸最佳化的可行性。並依據此三個範例將修正螢火蟲演算法與五個啟發式演算法做比較，其中包含：布穀鳥搜尋演算法、螢火蟲演算法、花朵授粉演算法、基因遺傳演算法、帝國主義競爭演算法。於六連桿機構範例尺寸最佳化範例中，本研究以Klann Linkage機構繪出的軌跡為此範例的目標軌跡，因此已知的最佳解為Klann Linkage機構尺寸，以此範例來驗證修正螢火蟲演算法最佳化結果的正確性。於八連桿機構尺寸最佳化範例中，本研究採用Theo Jansen機構，並以人類爬梯軌跡為目標軌跡，最佳化出一組最接近人類爬梯軌跡的八連桿機構。

This study combines firefly algorithm and cuckoo search to form a modified firefly algorithm. The proposed modified firefly algorithm is applied to synthesize path generating mechanisms. Six test functions are used as test examples. These examples compare the result from firefly algorithm and the modified firefly algorithm, and the results show that the optimal solution of the modified firefly algorithm is better than the firefly algorithm. Three analysis cases including four-bar linkage, six-bar linkage, and eight-bar linkage, are used to illustrate the feasibility of using the modified firefly algorithm for optimum synthesis of path generating mechanisms. These examples compare the result from the modified firefly algorithm, cuckoo search, flower pollination algorithm, genetic algorithm, and imperialist competitive algorithm. In the six-bar linkage example, this study uses Klann linkage’s locus as the target locus, so the best solution is the dimension of Klann linkage. Therefore, this example validates the result of the modified firefly algorithm. In the eight-bar linkage example, this study uses Theo Jansen linkage, and uses human foot trajectory when climbing stairs as the target locus. The results show the proposed method can synthesize path generating mechanisms successfully.

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