||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.
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