Genetic Algorithms for Optimization Problems with Their Applications

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姓名

林淑惠(Shu-Hui Lin) 查詢紙本館藏

畢業系所

數學系

論文名稱

(Genetic Algorithms for Optimization Problems with Their Applications)

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摘要(中)

近年來，人工智慧的議題逐漸受到重視，越來越多人以此求解最佳化的問題。而基因演算法為人工智慧的分支之一，它是以達爾文進化論為理念發展出來的：仿照天擇，利用族群的整體資訊，將適應力高的基因遺傳給下一代，並經由突變避免遺漏掉更好的基因。換成最佳化的問題來討論，遺傳優良基因可視為快速收斂至最佳解，而突變則是避免掉入局部最佳解。也因此，基因演算法對於找出全域最佳解的效率相當高，值得探討研究。

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。

摘要(英)

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.

關鍵字(中)

★ 基因演算法
★ 打靶法
★ 非線性最小平方
★ 軌道最佳化

關鍵字(英)

★ Genetic Algorithms
★ Shooting method
★ Nonlinear Least Squares
★ Trajectory Optimization
★ Full-space quasi Lagrange-Newton-Krylov algorithm

論文目次

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 A framework of optimization problems . . . . . . . . . . . . . . . . . . . . 3

2.1 Genetic algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Parameters study of genetic algorithms . . . . . . . . . . . . . . . . . . . . 8

3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Unconstrained optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.1 Nonlinear least squares . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.2 Using shooting method to boundary value problem . . . . . . . . . 18

3.2 Constrained optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Full-space quasi Lagrange-Newton-Krylov algorithm . . . . . . . . 26

3.2.2 Trajectory optimization . . . . . . . . . . . . . . . . . . . . . . . . 28

4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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指導教授

黃楓南(Feng-Nan Hwang)

審核日期

2018-7-25

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