本文將力法分析應用於和聲搜尋(Harmony Search, HS)與離散拉格朗日法(Discrete Lagraingian Method, DLM)組成之混合演算法進行桁架拓樸結構輕量化設計，並比較力法與位移法之輕量化設計搜尋效率的快慢。 位移法分析時需求解方程式大小是由系統自由度的數量決定，具有高度通用性與自動化分析條件，被廣泛用於現今最佳化設計，而力法分析所需求解的方程式大小是系統贅餘度的數量決定，因此，當超靜定結構的贅餘度數量小於系統自由度數量時，力法在方程式求解的速度上佔有優勢，此外，力法分析中的力平衡矩陣，在結構拓樸與形狀相同下不會改變，因此不需重複將平衡矩陣拆解成對應贅力桿件的贅力矩陣和基元靜定結構的靜定矩陣。本文利用上述之力法分析上的優勢，結合HS隨機搜尋的能力在全域選定一個固定拓樸結構後，利用DLM健全的局部搜尋能力找出局部最佳解，在HS-DLM反覆的搜尋後，本文中所有算例皆可找出與文獻相同或是更好的解，證明了HS-DLM有不錯的搜尋能力，跟位移法分析結果比較後，也證明了力法分析較位移法有速度上的優勢。 This paper is study the efficiency between force method and displacement method applied to hybrid metaheuristic algorithm, namely HS-DLM,for topology optimization design of truesses wiht continuous and discrete variables. Most structural optimization algorithms published in the literature were developed based on the displacement method of analysis which is incorporated inside the optimization routine. In the displacement method, the number of equations needed to be solved is the number of degrees of freedom for the system whereas that for the force method is the number of redundant forces.If the number of degrees of freedom is greater than the number of redundant in a structural system, the displacement method requires much more computer time than the force method does. Furthermore, the equilibrium matrix in the force method does not change when the topology and shape of truss is fixed in the redesign process making this method attractive and efficient.Using the HS(Harmony Search) global searching ability to find a fixed topology of truss, and find the constrained local minimum by applying DLM(Discrete Lagraingian Method). Afier a few iteration, the study shows that HS-DLM has great searching ability on the references’s cases and the force method has better efficiency of topology optimization design than displacement method.
