塔布搜尋法(tabu search)是一種常用的啟發式搜尋法(heuristic search)，其主要精神在於利用塔布串列(tabu list)記錄最近幾個移動(move)，避免搜尋過程中，重複相同的路徑或形成迴圈(cycle)。塔布搜尋演算法步驟由一個啟始解(initial solution)開始，在每次的鄰近解搜尋中，移動到未被塔布限制住的最佳鄰近解(neighborhood)，直到滿足終止條件而停止移動。傳統塔布搜尋法存在著兩個缺點，其一為當搜尋結束時，塔布搜尋法提供的僅是一個搜尋過程中的最優解，但是並無法得知這個最優解的品質。其二為雖然塔布串列可以避免落入小迴圈中，但是無法保證搜尋工作不會重複搜尋已搜尋過的區域或是形成大迴圈。
一種能改善塔布搜尋速度的方法是利用多個處理器同時進行塔布搜尋，稱為平行塔布搜尋法。我們建議的平行塔布搜尋法利用多處理器進行平行塔布搜尋，以提昇增加搜尋速度並解決傳統塔布搜尋法的兩個缺點，並嘗試利用涵蓋比率估計搜尋過程中所找到的最優解為真正最佳解的機率。

最後，本論文設計一系列求解數字排序問題的實驗，利用統計上的檢定方法來比較傳統平行塔布搜尋與改善後的搜尋法之搜尋速度，並驗證涵蓋比率與最佳解間的關係。結果顯示本論文所提出的平行塔布搜尋法的搜尋效率確實優於傳統的塔布搜尋法。而涵蓋比率雖不能用來估計已知最優解的信賴程度，但是實驗顯示，找到最優解是真正最佳解的機率將大於利用涵蓋比率計算出的估計值。

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Tabu search is a widely used heuristic search method. One of the main components of tabu search is tabu list, which makes several latest moves forbidden in order to escape from a small loop. The algorithm starts from an initial solution, and moves the current solution to the best neighborhood which is not forbidden. These iterations will be repeated until the terminating condition is reached. There are two main drawbacks in the traditional tabu search. First, tabu search only provides an approximate solution. There is no way to know the quality of the obtained solutions. Second, although tabu list helps the search avoiding a small cycling problem, it cannot prevent a previously searched area to be searched again or forming a large cycle.
The computation efficiency of a tabu search can be improved by implementing a parallel tabu search, which uses multiple processors to search in parallel. In the study, we propose an enhanced parallel tabu search, which attempts to compute more efficiently and conquer the two drawbacks mentioned above. The ratio of finding the old local optimum solutions may suggest the confidence level of the best solution we find at the end of search. Also, the historical memory of local optimum solutions helps us to avoid searching old areas again.

To validate the efficiency of the new approach, we will use a series of number sequencing problems. In addition, we apply statistical method to test the suggested relationship between the ratio of old local optimum and the confidence level of the obtained solution. The result of experiments shows that it takes less time for the enhanced parallel tabu search to find global optimum solutions than conventional one. The ratio of finding the old local optimums does not precisely estimates the confidence level of the best solution. However, our results show that the probability of finding the global optimal solutions should be larger than the computed ratio.

1.1研究背景 1

1.2研究動機 1

1.3研究架構 3

第2章 文獻回顧 4

2.1塔布搜尋法 4

2.2平行塔布搜尋法 9

2.3塔布搜尋效率的改善方法 11

第3章 方法構建 13

3.1改進之平行塔布搜尋法 13

3.1.1子空間的定義 13

3.1.2隨機起始解 14

3.1.3長期記憶結構 15

3.1.4落入涵蓋區域的比率 16

3.2改進之平行處理演算法 19

3.3改進之平行塔布搜尋法的優點 23

第4章 實驗設計與分析 24

4.1問題描述 24

4.1.1多個處理器的模擬方法 24

4.1.2數字排序問題 25

4.2 求解數字排序問題的改進之平行塔布搜尋法的設定 26

4.3 離開舊區域最佳解後脫離方向的比較 27

4.4涵蓋比率的實驗設計 29

4.4.1落入涵蓋區域的比率的實驗 29

4.4.2驗證子空間是否為均勻的分佈 32

4.5比較搜尋速度的實驗結果與分析 35

第5章 結論與未來展望 38

參考文獻 39

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