以和諧搜尋演算法為基礎之混合式全域搜尋演算法求解含凹形節線成本最小成本轉運問題之研究

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劉向邦(Xiang-Bang Liu) 查詢紙本館藏

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土木工程學系

論文名稱

以和諧搜尋演算法為基礎之混合式全域搜尋演算法求解含凹形節線成本最小成本轉運問題之研究
(Hybrid Global Search Algorithm Based on Harmony Search for Concave Cost Minimum Cost Network Flow Problems)

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摘要(中)

傳統在最小成本轉運問題定式下，常以線性方式來定義運送成本，藉以簡化問題的複雜度。在實務上，貨物運送的單位成本常隨數量的增加而遞減，其成本函數曲線為凹形。以往有不少含凹形成本節線之研究，但侷限於不同之特殊網路且方法屬傳統區域搜尋法或傳統啟發解法，近期雖有學者開始以新近鄰近搜尋法求解簡化的運輸問題，以達到較大範圍的搜尋方式，期能找到較優於傳統啟發解法之解，卻忽略運輸網路常見的轉運問題。因此近期有學者發展類遺傳演算法、類螞蟻族群演算法及粒子群演算法以求解含凹形節線成本最小成本網路流動問題。另外，新近的和諧搜尋演算法目前在各領域的問題求解上效果頗佳，甚至有發現較遺傳演算法為佳，但尚未發現有應用於含凹形節線成本最小成本網路流動問題，緣此，本研究針對含凹形節線成本之最小成本網路流動問題，以和諧搜尋演算法之搜尋概念為基礎，並結合粒子群演算法、螞蟻族群演算法、門檻值接受法與凹形成本網路啟發解法之特點，以節線及路徑為基礎發展一混合式全域搜尋法，期能有效的求解含凹形節線成本之最小成本網路流動問題。
在求解方法上，本研究以和諧搜尋演算法為基礎，利用和諧搜尋演算法中以和弦記憶空間為母體之選擇機制之全域搜尋法與調音機制之區域搜尋法重新組成新可行解，並加入PSO速度更新策略、ACS費洛蒙更新策略、TA與凹形成本網路啟發解法之演算特色，針對凹形成本網路流動問題之特性，發展一套適合凹形節線成本轉運問題之類和諧搜尋演算法。最後，為測試本研究演算法在不同規模及參數的網路問題之求解績效，本研究設計一隨機網路產生器，產生大量隨機網路，在個人電腦上以C++語言撰寫所有相關的電腦程式，並測試新近發展之遺傳演算法、門檻值接受法、大洪水法、類螞蟻族群演算法及粒子群演算法，以評估本研究演算法之求解績效，進而提供實務界求解此類實際的網路運送問題之參考。測試結果顯示，本研究演算法求解品質良好。

摘要(英)

Traditionally, the minimum cost transshipment problems were simplified as linear cost problems in order to reduce problem complexity. In practice, the unit cost for transporting freight usually decreases as the amount of freight increases. Hence, in actual operations the transportation cost function can usually be formulated as a concave cost function. Great efforts have been devoted to the development of solution algorithms. However, they were confined to specical transportation networks. Besides, their methods were focused on local search algorithms or traditional heuristics. Recently, researchers began to use advanced neighborhood search algorithms to solve concave cost bi-partite transportation network problems to enlarge search area and find near-optimal solutions. This type of research, however, neglected flow transfers in transportation networks. Recently, there has been research adopting the genetic algorithm (GA), the ant colony system algorithm (ACS) and the particle swarm optimization algorithm (PSO) for solving concave cost network problems, and obtaining better solutions than some neighborhood search algorithms do. The harmony search (HS), a global search algorithm, has led to good results in many applications. In some applications, HS was even more effective than GA. Since there has not yet been any research applying HS to minimum concave cost network flow problems, we employ HS, coupled with the techniques of PSO, ACS and TA, to develop one global search algorithms for efficiently solving minimum concave cost network flow problems.
In the solution method, we take the harmony search as the foundation, use a global search which is harmony memory consideration and a local search which is Pitch Adjusting to compose the new feasible solution, we also join the velocity update rules in PSO, the pheromone update rules in ACS, TA and the concave cost initial solution algorithm, we develop a analogous harmony search which is fitting the minimum cost transshipment problems with concave costs. Finally, to evaluate our algorithms we designed a network generator to create a sufficient number of problem instances. The C++ computer language was used to code all the necessary programs and the test was performed on personal computers. To evaluate our algorithm, we also tested the recently designed TA, GDA, GA, ACS and PSO that solve minimum concave cost network flow problems. The results show that the developed algorithms performed well in the tests.

關鍵字(中)

★ 和諧搜尋演算法
★ 凹形節線成本
★ 區域搜尋
★ 全域搜尋
★ 最小成本網路流動問題

關鍵字(英)

★ concave arc cost
★ global search
★ local search
★ minimum cost network flow problem
★ hamony search

論文目次

摘要............................................................................................................................... I
ABSTRACT.................................................................................................................. II
誌謝…………………………………………………………………………………..III
目錄…………………………………………………………………………………..IV
圖目錄………………………………………………………………………………..VI
表目錄……………………………………………………………………………… VII
第一章緒論...............................................................................................................1
1.1 研究背景與動機.............................................................................................1
1.2 研究目的與範圍.............................................................................................2
1.3 研究方法與流程.............................................................................................3
第二章文獻回顧.......................................................................................................4
2.1 凹形成本網路流動問題.................................................................................4
2.2 鄰近搜尋法.....................................................................................................5
2.3 和諧搜尋演算法.............................................................................................9
2.4 全域式演算法...............................................................................................11
2.5 文獻評析.......................................................................................................16
第三章問題描述與求解演算法設計.....................................................................17
3.1 問題定式及特性...........................................................................................17
3.2 求解演算法設計...........................................................................................19
3.2.1 演算法之步驟....................................................................................19
3.2.2 初始解產生策略................................................................................19
3.2.3 可行解產生策略................................................................................20
3.2.4 PSO 速度更新公式............................................................................23
3.2.5 PSO 加入節線策略............................................................................24
3.2.6 供需節點對選擇策略........................................................................24
3.2.7 虛擬節線成本產生策略....................................................................25
3.2.8 狀態轉移策略....................................................................................25
3.2.9 費洛蒙更新策略................................................................................26
3.2.10 變數調整策略..................................................................................27
3.2.11 門檻值觀念......................................................................................27
3.2.12 鄰近搜尋法之改善策略..................................................................27
3.2.13 演算法終止機制..............................................................................28
3.2.14 小結..................................................................................................28
第四章實證分析.....................................................................................................32
4.1 網路產生器設計...........................................................................................32
4.1.1 隨機網路產生法................................................................................32
4.1.2 供給(需求)節點與供給(需求)量的隨機產生法..............................33
4.2 AHS 求解策略測試.......................................................................................34
4.2.1 初始解相關參數................................................................................36
4.2.2 和諧搜尋演算法相關參數................................................................42
4.2.3 PSO 相關參數....................................................................................50
4.2.4 ACS 相關參數....................................................................................58
4.2.5 TA 相關參數.......................................................................................63
4.2.6 鄰近搜尋法搜尋範圍........................................................................67
4.2.7 最佳參數組合....................................................................................68
4.2.8 初始解與最終解之相關性................................................................70
4.2.9 AHS 收斂趨勢....................................................................................71
4.2.10 小結..................................................................................................74
4.3 AHS 與APSO、AACS、GA 與各區域搜尋法之求解績效比較..............75
第五章結論與建議………………………………………………………...……...80
5.1 結論...............................................................................................................80
5.2 貢獻...............................................................................................................81
5.3 建議...............................................................................................................82
參考文獻.....................................................................................................................83
附錄一 AHS 各方案參數值......................................................................................89
附錄二 AHS 各方案測試詳細結果..........................................................................93
附錄三 GA、AACS、APSO 與各區域搜尋法輸入參數值.................................. 111
附錄四各型網路目前最佳解................................................................................. 113

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指導教授

顏上堯(Shang-Yao Yan)

審核日期

2008-7-23

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