本研究將萊維飛行與隨機漫步結合至螢火蟲演算法，提出結合萊維飛行與隨機漫步之改良式螢火蟲演算法，並使用十二個最佳化測試函數為範例，比較螢火蟲演算法、萊維飛行之螢火蟲演算法、修正螢火蟲算法、結合萊維飛行與隨機漫步之改良式螢火蟲演算法等四種演算法的最佳化結果。結果顯示，本研究所提出的結合萊維飛行與隨機漫步之改良式螢火蟲演算法在中低維度的搜索空間中，具有較佳的搜索能力。本研究同時針對四連桿機構與八連桿Jansen機構之模型，將其剛性旋轉接頭替換成由兩段直線與一段圓弧所組成的撓性關節，並提出一套設計具有撓性關節的路徑產生機構的最佳化方法，此方法結合演算法與有限元素分析軟體ANSYS，將機構進行尺寸最佳化，藉此設計出符合特定目標軌跡的撓性關節連桿機構。其中，撓性關節四連桿機構範例根據設計變數的不同分成兩個案例，而撓性關節八連桿機構範例則根據撓性關節的數量區分成一組、三組、五組撓性關節之八連桿機構。結果顯示此方法可有效的設計出符合目標軌跡的撓性關節連桿機構。

This study proposes a new algorithm that combines Lévy flight and random walk into the firefly algorithm, and uses twelve test functions to evaluate the optimization results from four algorithms, including the firefly algorithm (FA), the Lévy-flight firefly algorithm (LFA), the modified firefly algorithm (MFA), and the modified firefly algorithm with Lévy flight and random walk (LMFA). The results show that the proposed modified firefly algorithm with Lévy flight and random walk has superior search capabilities in low and medium-dimensional search space. In addition, this study replaces the revolute joint with a compliant joint, which consists of two straight lines and a circular arc, for the four-bar linkage and the eight-bar Jansen's linkage. This study also proposes a method to synthesize path-generation mechanisms with compliant joints. The method combines the proposed heuristic algorithm and the finite element analysis software ANSYS, to design linkage mechanisms with compliant joints that conform to a specific target path. The four-bar linkage with a compliant joint is divided into two cases according to different design variables. The eight-bar linkage with compliant joints is divided into three cases according to the number of compliant joints, including one compliant joint, three compliant joints, and five compliant joints. The results show that the proposed method can effectively design linkage mechanisms with compliant joints that conform to the target paths.

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