本篇論文將介紹基因演算法的緣由、步驟程序及應用。其中，我們需要搭配打靶法、最小平方法來解決最佳化問題。特別是軌道最佳化，我們可以了解到如何藉此找出適當的初始值，並與兩篇論文的結果做比較：一篇是於西元2017年由王璿豪先生等人共同著作的期刊論文``A full-space quasi Lagrange-Newton-Krylov algorithm for trajectory optimization problems" (簡稱為WLHH) ，另外一篇論文於西元2018年由連政杰先生所著的``A parallel full-space Lagrange-Newton method for low-thrust orbit transfer trajectory optimization problems" (簡稱為CCL) 。而後我們欲證明初始值在可行解區域上或非可行解區域上的效益是否有差別，相關數據結果將會於最後呈現。;More recently, people put more and more emphasis on the artificial intelligence (AI) issue and solve optimization problems by it. However, genetic algorithms (GAs) is one branch of AI. It is based on the theory of evolution from Darwin: imitating the natural selection and using the total information of groups, the chromosomes with high adaptability are inherited to the new generation. In addition to this, the chromosomes may be mutated due to avoid missing the greater genes. In other words, inheritance is considered as converging to the optimal solution rapidly and mutation is preventing from falling into the local extrema. Consequently, the efficiency of finding the global extrema is excellent for GAs. It is worth to explore and research.
We will introduce the summary and the applications of GAs in this paper. Besides, we need to solve the optimization problem by shooting method and the least square method. Especially trajectory optimization, we can understand how to find the suitable initial guess, and compare the result with two papers: one is a journal paper ``A full-space quasi Lagrange-Newton-Krylov algorithm for trajectory optimization problems" written by Hsuan-Hao Wang et al. in 2017 (called WLHH), another is ``A parallel full-space Lagrange-Newton method for low-thrust orbit transfer trajectory optimization problems" written by Cheng-Chieh Lien in 2018 (called CCL) . If the initial guess is one of the feasible solutions, is the effect whether better or not? The numerical results will be presented at the end.