臺灣博碩士論文加值系統

本研究主要為應用萬用啟發式演算法(Metaheuristic)中的和弦演算法(Harmony Search；HS)來求解Chang等學者(2000)透過權重的設計，改良Markowitz(1952)的平均-變異數模型，所發展之同時考量報酬最大化與風險最小化的多目標投資組合問題。針對此問題之特性，本研究設計ㄧ混合式編碼之架構，且利用和弦演算法的和弦記憶空間、調音及隨機產生等三種機制產生新解，以達到平衡探索(Exploitation)與開發(Exploration)的作用，及有效率地產生高品質的解。根據各機制的調整，本研究共計提出十一種不同的和弦演算法架構，並利用OR-Library提供的五種全球性股市，介於1992年3月與1997年9月之間的實際數據進行測試，並與文獻中之模擬退火法(Simulated Annealing；SA)、禁忌搜尋法(Tabu Search；TS)與變動鄰域搜尋法(Variable Neighborhood Search；VNS)進行比較；和弦演算法於各例題中的表現皆優於文獻中的方法，為多目標投資組合最佳化問題提供一優異之求解方案。

This study proposes a harmony search algorithm for solving constrained portfolio optimization problems with the objective of investment return maximization and risk minimization according to Chang et al. (2000) which is based on the mean-variance model of Markowitz (1952). This study develops a hybrid encoding to deal with both continuous and combinatorial properties of the problem. The proposed algorithms employ harmony memory consideration, pitch adjustment and random search to achieve the balance between exploitation and exploration and generate high-quality new solutions effectively. The performance of the eleven proposed HS variations is tested using five global stock market indexes provided by the OR-Library from March 1992 to September 1997. The results of proposed HS algorithms are also compared with SA, TS and VNS algorithms in the literature. HS outperforms all the competing algorithms in all five test data sets, and proves to be a promising alterative in solving portfolio optimization problems.

摘 要 I
ABSTRACT II
致謝 III
第一章 緒論 1
1.1研究背景與動機 1
1.2研究目的 2
1.3研究範圍 3
1.4章節介紹 3
第二章 文獻探討 6
2.1投資組合問題 6
2.1.1投資組合理論 6
2.1.2投資組合相關研究 9
2.2多目標規劃問題 12
2.2.1多目標規劃問題定義 13
2.2.2多目標求解方法 15
2.2.3柏拉圖最佳解 16
2.2.4多目標求解衡量指標 20
2.3 和弦演算法 32
2.3.1和弦演算法介紹 32
2.3.2和弦演算法基本架構 33
2.3.3和弦演算法新解產生機制 34
2.3.4和弦演算法相關文獻 37
第三章 研究方法 43
3.1投資組合問題 43
3.1.1非受限投資組合最佳化問題 43
3.1.2受限投資組合最佳化問題 44
3.1.3多目標合併為單目標之比例分配 46
3.2多目標和弦演算法 46
3.2.1 HS-I 48
3.2.1.1 HS-I編碼 48
3.2.1.2權重分配機制 49
3.2.1.3初始和弦記憶空間之建立 51
3.2.1.4 HS-I產生新解 52
3.2.1.5 HS-I 非支配解集合更新 57
3.2.1.6 HS-I求解步驟 58
3.2.2 HS-II 61
3.2.3 HS-III 63
3.2.4 HS-IV 65
3.2.5 HS-V 68
3.2.6 HS-VI 71
3.2.7 HS- VII 73
3.2.8 HS-VIII 75
3.2.9 HS-IX 78
3.2.10 HS-X 81
3.2.11 HS-XI 83
3.2.12 HS 彙整 86
第四章 結果分析 89
4.1測試例題 89
4.2績效指標 90
4.3參數設定 91
4.4 HS與不同演算法之比較 93
4.4.1測試例題ㄧ（Hang Seng指標；股票數31） 93
4.4.2測試例題二（DAX指標；股票數85） 95
4.4.3測試例題三（FTSE指標；股票數89） 97
4.4.4測試例題四（S&P指標；股票數98） 99
4.4.5測試例題五（Nikkei指標；股票數225） 101
4.5非支配解集合分佈之探討 103
4.6測試例題比較之總結 106
第五章 結論與未來研究方向 108
5.1結論 108
5.2未來研究方向 110
參考文獻 111
附錄A 117
1.1 排序法介紹 117
1.2 氣泡排序法(BUBBLE SORT) 118
1.3 選擇排序法(SELECT SORT) 119
1.4 插入排序法(INSERTION SORT) 120
1.5 快速排序法(QUICK SORT) 120
1.6 堆積排序法(HEAP SORT) 122
2. 比較排序法優劣之實驗 125
2.1 排序法用於新解更新和弦記憶空間所需時間，以HS_I為測試方法 125
2.2 比較排序法優劣實驗之結論 125

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