簡易檢索 / 詳目顯示

研究生: 徐誠佑
Cheng-Yu Hsu
論文名稱: 螞蟻演算法求解零壹多限制式背包問題
An ant colony optimization algorithm for the zero-one Multidimensional Knapsack Problem
指導教授: 陳茂生
Maw-Sheng Chern
口試委員:
學位類別: 碩士
Master
系所名稱: 工學院 - 工業工程與工程管理學系
Department of Industrial Engineering and Engineering Management
論文出版年: 2003
畢業學年度: 91
語文別: 中文
論文頁數: 80
中文關鍵詞: 背包問題螞蟻演算法
外文關鍵詞: Knapsack Problem, ACO algorithm, Ant System
相關次數: 點閱:3下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 在本文中,將討論如何設計一個螞蟻演算法(Ant Colony Optimization Algorithm, ACO Algorithm)用來解決零壹多限制式背包問題(zero-one Multidimensional Knapsack Problem, zero-one MKP)。零壹多限制式背包問題一般定義如下:如何在符合 條限制條件下,從 項物品內選出數項物品,以期達到效益極大化。
    設計螞蟻演算法主要可分為下列三個部份討論:1. 計算啟發法權值的方法(heuristic value),2. 螞蟻搜尋解的方法(solution construction)、3. 更新費洛蒙的方法(pheromone update)。在第一章將介紹過去曾被提出過各種不同設計的螞蟻演算法。在第二章將提出針對零壹多限制式背包問題的特性,可能有那些合適的螞蟻演算法可應用在該問題上。第三章將介紹兩種參數設定方法。在第四章則是對第二章所提出的設計以範例問題做試驗。由實驗之結果得知,本文所提出之螞蟻演算法比起過去的設計所需的運算時間較短,但解的品質相同。


    In this thesis, we design an Ant Colony Optimization Algorithm (ACO Algorithm) for the zero-one Multidimensional Knapsack Problem. The zero-one Multidimensional Knapsack Problem is the problem of choosing some of n items such that the corresponding profit sum is maximized without violating m constraints.
    ACO algorithm can be discussed with three aspects: heuristic value, solution construction, and pheromone update. In chapter 1, we introduce some different ACO algorithms that have been discussed. In chapter 2, we propose 5 kinds of ACO algorithm for the zero-one Multidimensional Knapsack Problem. In chapter 3, we try to set parameters using two different methods. In chapter 4, we discuss the computational results between the algorithms we proposed in chapter 2. Compared with the past algorithm, the ACO algorithm we designed can solve the zero-one Multidimensional Knapsack Problem with less computing time, and the solution qualities are the same.

    目錄 中文摘要……………………………………………………...……………………...Ⅰ 英文摘要……………………………………………………...……………………...Ⅱ 誌謝……………………………………………………...…………………………...Ⅲ 目錄……………………………………………………...…………………………...Ⅳ 表目錄……………………………………………………...………………………...Ⅶ 圖目錄……………………………………………………...………………………...Ⅷ 符號表……………………………………………………………………………..…Ⅸ 第一章 緒論 1 1.1 研究動機與背景 1 1.2 問題描述 1 1.3 研究目的 2 1.4 研究內容與步驟 3 1.5 零壹多限制式背包問題之相關文獻 4 1.6 螞蟻演算法之相關文獻 5 1.6.1 螞蟻系統 (Ant System, AS) 10 1.6.2 蟻族系統 (Ant Colony System, ACS) 11 1.6.3 隨機樹狀搜尋 (Approximate Nondeterministic Tree-Search, ANTS) 12 1.6.4 極大-極小螞蟻系統 (MAX-MIN Ant System, MMAS) 13 1.6.5 評等為基礎的螞蟻系統 (Rank-Based Version of Ant System, ASrank) 14 1.6.6 快速螞蟻系統 (Fast Ant System, FANT) 15 第二章 零壹多限制式背包問題之螞蟻演算法 17 2.1 費洛蒙表達方式 (PHEROMONE REPRESENTATION) 18 2.2 啟發法權值 (HEURISTIC VALUE) 18 2.2.1 Leguizamon and Michalewicz [15] 所使用的 (動態的 ) 18 2.2.2 利用Toyoda [27] 的啟發式解法計算 (動態的 ) 20 2.2.3 利用Loulou and Michaelides [17] 的啟發式解法計算 (動態的 ) 22 2.2.4 利用surrogate constraints [13] [20]計算 (靜態的 ) 23 2.3 螞蟻搜尋解的方法 (SOLUTION CONSTRUCTION) 25 2.3.1 配合動態的 搜尋方法 25 2.3.2 配合靜態的 搜尋方法 26 2.4 更新費洛蒙的方法 (PHEROMONE UPDATE) 26 2.5 區域搜尋的方法 (LOCAL SEARCH) 27 第三章 參數設定 29 3.1 的設定 29 3.2 的設定 31 3.3 及 的設定 33 3.3.1靜態的 及 設定 33 3.3.2動態的 及 設定 45 第四章 實例驗證 47 4.1 求解品質的比較 47 4.2 運算時間的比較 51 第五章 結論與後續研究方向 55 5.1 結論 55 5.2 後續研究方向 55 參考文獻 ………………………………………………………………………….56 附錄…………………………………………………………………………………..59 附錄A AS_MKP00 MATLAB程式碼……………………………………………59 附錄B AS_MKP01 MATLAB程式碼……………………………………………63 附錄C AS_MKP02 MATLAB程式碼……………………………………………66 附錄D AS_MKP03 MATLAB程式碼……………………………………………69 附錄E AS_MKP04 MATLAB程式碼……………………………………………72 附錄F AS_MKP05 MATLAB程式碼……………………………………………75

    參 考 文 獻
    [1] Beasley, J., “OR-Library: Distributing Test Problems by Electronic Mail,” http://www.ms.ic.ac.uk/info.html.
    [2] Bullnheimer, B., Hartl, R.F., and Strauss, C., “A new rank-based version of the ant system: a computational study,” Technical Report POM-03/97, Institute of Management science, University of Vienna. Accepted for publication in the Central European journal for Operations Research and Economics, (1997).
    [3] Bullnheimer, B., Hartl, R.F., and Strauss, C., “An improved Ant System algorithm for the Vehicle Routing Problem,” Annals of Operations Research, Vol.89, pp.319-328, (1999).
    [4] Dammeyer, F., and Voss, S., “Dynamic tabu list management using the reverse elimination method,” Annals of Operations Research, Vol.41, pp.31-46, (1993).
    [5] Dorigo, M., Maniezzo, V., and Colorni, A., “Positive feedback as a search stratey,” Technical Report 91-016, Dipartimento di Elettronica, Politecnico di Milano, IT, (1991).
    [6] Dorigo, M., “Optimization, Learning and Natural Algorithms,” (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, IT, (1992).
    [7] Dorigo, M., Maniezzo, V., and Colorni, A., “The ant system: Optimizatoin by a colony of cooperating agents,” IEEE Transactions on Systems, Man, and Cybernetics - Part B, Vol.26-1, pp.29-41, (1996).
    [8] Dorigo, M., and Gambardella, L.M., “Ant colony system: A cooperative learning approach to the traveling salesman problem,” IEEE Transactions on Evoluationary Computation, Vol.1-1, pp.53-66, (1997).
    [9] Dorigo M., and Gambardella, L.M., “Ant colonies for the traveling salesman problem,” BioSystems, Vol.43, pp.73-81, (1997).
    [10] Dorigo, M., Caro, G.D., Gambardella, L.M., “Ant Algorithms for discrete Optimization,” Artificial Life, Vol.5, No.3, pp.137-172, (1999).
    [11] Drexel, A. “A Simulated Annealing Approach to the Multiconstraint Zero-One Knapsack Problem,” Computing, Vol.40, pp.1-8, (1988).
    [12] Gambardella, L.M., Taillard, E.D., and Dorigo, M., “Ant colonies for the QAP,” Technical Report IDSIA-4-97, IDSIA, Lugano, Switzerland, 1997. Accepted for publication in the Journal of the Operational Research society (JORS), (1997).
    [13] Garfinkel, R.S., and Nemhauser, G.L., “Integer Programming,” John Wiley & Sons, New York, (1972).
    [14] Khuri, S., Baeck, T., and Heitkoetter, J., “The Zero/One Multiple Knapsack Problem and Genetic Algorithms,” to appear in the 1994 ACM Symposium on Applied Computing, SAC'94, Phoenix, Arizona, (1994).
    [15] Leguizamon, G., and Michalewicz, Z., “A New Version of Ant System for Subset Problems”, Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress on, Vol.2, pp.1459-1464, (1999).
    [16] Lin, Y.H., “A Bibliographical Survey on Some Well-Known Non-Standard Knapsack Problems,” Information Systems and Operations Research, Vol.36, No.4, pp.274-317, (1998).
    [17] Loulou, R., and Michaelides, E., “New Greedy-like Heuristics for Multidimensional Knapsack Problem,” Operations Research, Vol.27-6, pp.1101-1114, (1979).
    [18] Maniezzo, V., “Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem,” Technical Report CSR 98-1, C.L. in Scienze dell’Informazione, Universita di Bologna, Sede di Cesena, Italy, (1998).
    [19] Martello, S., and Toth, P., “Knapsack Problems, Algorithms and Computer Implementations,” John Wiley & Sons, New York, (1990).
    [20] Pirkul, H., “A heuristic solution procedure for the multiconstraint zero-one knapsack problem,” Naval Research Logistics Quarterly, Vol.34-2, pp.161-172, (1987).
    [21] Raidl, G. R., “Weight-codings in a genetic algorithm for the multi-constraint knapsack problem,” Proceedings of the 1999 IEEE Congress on Evolutionary Computation, Vol.1, pp.596-603, (1999).
    [22] Senju, S. and Toyoda, Y., “An Approach to Linear Programming with 0-1 Variables,” Management Science, Vol.15-4, pp.B196-B207, (1968).
    [23] Stutzle, T., “MAX-MIN Ant System for Quadratic Assignment Problems,” Technical Report AIDA-97-04, Intellectics Group, Department of Computer Science, Darmstadt University of Technology, Germany, July, (1997).
    [24] Stutzle, T., and Hoos, H.H., “The MAX-MIN Ant System and Local Search for the Traveling Salesman Problem,” In T. Baeck, Z. Michalewicz, and X. Yao, editors, Proceedings of the IEEE International Conference on Evolutionary Computation (ICEC’97), pp.309-314, (1997).
    [25] Stutzle, T., and Hoos, H.H., “Improvements on the Ant System: Introducing the MAX-MIN Ant System,” In R.F. Albrecht G.D. Smith, N.C. Steele, editor, Artificial Neural Networks and Genetic Algorithms, pp.245-249. springer Verlag, Wien New York, (1998).
    [26] Taillard, E.D., and Gambardella, L.M., “Adaptive Memories for the Quadratic Assignment Problem,” Technical Report IDSIA-87-97, IDSIA, Lugano, Switzerland, (1997).
    [27] Toyoda, Y., “A simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems,” Management Science, Vol.21, pp.1417-1427, (1975).

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)
    全文公開日期 本全文未授權公開 (國家圖書館:臺灣博碩士論文系統)
    QR CODE