本研究針對懸臂式擋土牆進行最佳化設計之研究，最佳化的數學模型共選取八個設計變數，包括牆身頂部寬度、牆身底部寬度、基礎版總寬度、基礎趾版寬度以及基礎版厚度五個獨立設計變數，而止滑榫寬度、厚度及位置為三個非獨立設計變數。除了依據現行的設計規範建立束制條件外，再以彈性力學之觀念推導計算牆頂的水平變位，並將其納入為束制條件之一。以工程造價為目標函數進行最低價可行解之搜尋，以實數編碼遺傳演算法（RGA）進行最佳解之搜尋，並以竭盡搜尋法（ESM）所得全域最佳解來檢驗遺傳演算法之搜尋性能。綜合以上的概念，以商用軟體Visual Basic 2005撰寫懸臂式擋土牆自動化設計程式，當最佳化分析完成後，會自動輸出開挖回填的土方量、混凝土與鋼筋的數量計算表，且繪製擋土牆之配筋圖。本研究的分析案例是採用道路工程標準圖（1991）建議之擋土牆設計尺寸，固定止滑榫的三個變數，僅由其餘五個獨立設計變數進行最佳化分析，分析結果顯示實數編碼遺傳演算法均有機會搜尋至全域最佳解，且其與最佳解之差距甚小，所需時間較竭盡搜尋法（ESM）大幅縮短。 This thesis presents the application of optimal algorithm to the minimum cost design of cantilever retaining wall. The design variables include five independent variables: width of stem at the top, width of stem at the bottom, total width of base, length of toe, and depth of base; three dependent variables: width of key, depth of key and position of key. The constrained conditions involve design codes of Taiwan and lateral displacement of retaining wall (1/200). The objective function is the combined costs of soil excavation, retaining wall, and soil backfill. The optimal algorithm is the real-coded genetic algorithm (RGA). Based on the above concept, the automatically optimal design program of cantilever retaining wall was developed by the commercial software of Visual Basic 2005. The design drawing of bar arrangement; the quantities of soil excavation, backfill and concrete, and the number of steels would automatically output after finishing the optimal analysis. Subsequently, the case study was conducted to verify the efficiency and validity of the algorithm by comparing the solutions with the global optimum solutions obtained from exhaustive search method (ESM). The dimensions of the testing example were suggested by the road engineering standard design drawing with a little rational assumption for some unknown conditions. Among the designed dimensions, the width of key, depth of key and position of key were fixed, and the rest variables were covered in optimal analysis. From the results, RGA can find the optimum solutions from ESM, and spend less time than ESM. The error between RGA and ESM solution are about 0.1%.
