在機械加工的過程中，經常使用到曲線路徑的加工程序，而如何求得通過空間坐標之
最佳加工曲線路徑的表示方法，便是本論文的研究主體。
筆者，將利用具有多路徑搜尋求取最佳解功能的遺傳基因演算法則(Genetic
Algorithm)來演繹，以便與單路徑直接求解的NUOF Transform來相比較。
而傳統的基因演算法則是用來處理離散型的資料，且本論文的研究參數為實數型的資
料，故筆者引用實數型的基因演算法則來演繹。可以直接求取最佳解，同時也降低了連續
性資料與離散型資料因轉換而產生的誤差，再加上物種型式的概念建立，也減少了傳統基
因演算法則中因編碼與解碼所消耗的時間與電腦記憶體空間。
最後，在我們的實驗結果中，發現在不同的頻域中，不管演化世代數的多寡。其頻率
會逐漸收歛到該頻域的某一特定頻率，我們稱此頻率為最佳頻率。由於初始族群係根據邊
界條件隨機產生的，經過複製、交配與突變的結果，因交配世代的多寡而各有差異，故僅
列示最佳的結果以資參考。

The curves of tool path are the main concerns in the machining processes. How to get the optimal curve passing through those desired points will be the goal of this research.
In this study the Genetic Algorithm with the multi-pathed searching is used to find the optimal solution, and compared with the results from the single-pathed NUOF Transform.
Traditionally, the Genetic Algorithm is used for discrete datum. Because the parameters of the NUOF Series are real number, the algorithm for real-valued datum is used. It sounds reasonable to compute the coefficients of NUOF by a real-valued Genetic Algorithm. To do so, the error due to transformation from continuous to discrete datum can be avoided and vice versa. The computing time and memory space are lessened because of no need for coding and decoding. As the initial population are generated randomly, the answers obtained from processing reproduction, crossover and mutation are much different due to different number of generations. Finally, we found that the frequency in different frequency domains would converge in the vicinity of certain frequency. We can say this frequency is the optimal frequency in that frequency domain.