摘要
本研究旨在比較窮舉法、基因演算法及Excel 規劃求解演化式算法在求解二級圓柱螺旋齒輪減速機中心距最小化優化問題之差異。文中首先以窮舉法求解優化問題以找到全局最佳解，之後以自行建立之基因演算法MATLAB程式求解優化問題，最後以Excel規劃求解演化式算法求解優化問題。為了探討演化式算法參數對最佳解求解能力之影響，本研究應用田口式直交表L9(34)規劃實驗，並以變異數分析法識別對求解能力影響顯著之算法參數。變異數分析結果顯示，不含改進的最長時限為顯著參數，母體大小與突變率則非顯著參數。不含改進的最長時限增加，可以顯著提昇最佳解之求解能力。
關鍵字：窮舉法、基因演算法、演化式算法、齒輪、減速機。
ABSTRACT
This paper has applied enumerative method, genetic algorithm, and evolutionary algorithm in Excel Solver to solve the center distance minimization optimization problem of a two-stage cylindrical helical gear reducer. First of all, an enumerative method is applied to solve the optimization problem to search the global optimal solution. Then, a genetic algorithm program created in MATLAB by the authors is applied to solve the optimization problem. Next, the evolutionary algorithm in Excel Solver is applied to solve the optimization problem. In order to understand the effect of parameters of the evolutionary algorithm on the ability of solving the global optimal solution, the Taguchi orthogonal array L9(34) is applied to plan a set of experiments and the analysis of variance (ANOVA) method is applied to identify significant parameters of the evolutionary algorithm. The results of ANOVA show that the maximum allowable time for the solution without improvement is a significant parameter while the size of population and the mutation rate are not significant parameters. Increasing the maximum allowable time for the solution without improvement can advance significantly the ability of finding the optimal solution.
Keywords: Enumeration Method; Genetic Algorithm; Evolutionary Algorithm; Gear; Reducer.
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