臺灣博碩士論文加值系統

在投資組合問題中，除了要考慮收益外，同時須考慮風險因素，所以投資組合問題是屬於一種多目標的問題。當可供選擇的股票標的數量愈多時，問題的複雜度就更高，其所需要的求解時間也相對的更多。因此，本研究希望藉由有效的啟發式演算法在合理的求解時間下，求得效益較佳的投資組合。近年來有學者分別提出以基因演算法、粒子群演算法來求解投資組合最佳化問題，而這類演算法都是在空間中反覆隨機搜尋，缺乏自我檢查的機制。本文提出的細菌覓食演算法，當解在某個搜尋方向無法再改善時，能夠隨機轉向繼續搜尋以求得最佳解。本文經由實驗證明，細菌覓食演算法確實能在合理的求解時間下，找到相當靠近題庫標準解的效率前緣曲線，而且在各種不同的風險條件下都能提供投資組合解，使投資者有更多的選擇機會。

Portfolio optimization (PO) is a mixed quadratic and integer programming problem, and an effective solution approach is essential for most investors in order to raise expected returns and reduce investment risks. To solve this problem, various heuristic algorithms, such as genetic algorithms and particle swarm optimization, have been proposed in the past. This paper aims to examine the potential of bacterial foraging optimization algorithms (BFO) for solving the portfolio optimization problem. Bacterial foraging optimization algorithm is a new swarm intelligence technique and has successfully applied to some real world problems. Through three operations, chemotaxis, reproduction, and elimination and dispersal, the proposed BFO algorithm can effectively solve a PO problem with cardinality and bounding constraints. The performance of BFO approach was evaluated by performing computational tests on five benchmark data sets, and the computational results were compared to those obtained with existing heuristic algorithms. Experimental results demonstrate that the proposed algorithm is very competitive in portfolio optimization.

摘要 II
圖目錄 VII
表目錄 IX
第1章　簡介 1
1.1 研究背景與動機 1
1.2 研究範圍與限制 2
1.3 研究方法與流程 2
1.4 論文架構 3
第2章　文獻探討 4
2.1 投資組合問題簡介 4
2.2 求解投資組合問題之研究 5
2.3 基因演算法(GENETIC ALGORITHM，GA) 8
2.4 模擬退火法(SIMULATED ANNEALING，SA) 9
2.5 禁忌搜尋法(TABU SEARCH，TS) 10
2.6 粒子群演算法(PARTICLE SWARM OPTIMIZATION，PSO) 12
2.7 各演算法求解投資組合問題之比較 13
第3章　細菌覓食演算法方法論 15
3.1 細菌覓食演算法 15
3.2 應用BFO於投資組合最佳化 16
3.3 數學模式 17
3.4 解的表達 19
3.5 演算流程 20
3.6 不可行解處理 23
第4章　範例說明 28
4.1 細菌初始狀態 28
4.2 細菌翻轉 29
4.3 細菌游泳 31
4.4 細菌複製 33
4.5 細菌淘汰 33
第5章　實驗結果及比較 36
5.1 實驗方法 36
5.2 參數調整及設定 37
5.2.1 細菌每步移動長度的調整 38
5.2.2 細菌數及趨化次數的調整 40
5.3 衡量指標 42
5.4 實驗結果 45
5.4.1 第一階段實驗結果 46
5.4.2 第二階段實驗結果 54
5.5 投資比例修補方法之比較 63
第6章　結論 66
參考文獻 69
附錄A 題庫前處理 71
附錄B非限制式及限制式之效率前緣曲線 73
附錄C最佳解及非支配解的更新 74
附錄D 實作CHANG等學者(2000)的交配方式之實驗結果 78

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