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研究生: 黃國玉
Kuo-yu Huang
論文名稱: 混沌啟發式演算法之動態導引與類聚分群模式
Dynamic Guiding and Clustering Approach in Chaos Heuristic Algorithms
指導教授: 鄭明淵
Min-Yuan Cheng
口試委員: 王維志
Wei-Chih Wang
曾惠斌
Hui-Ping Tserng
張行道
Shing-Tao Chang
余文德
Wen-Der Yu
陳鴻銘
Hung-Ming Chen
學位類別: 博士
Doctor
系所名稱: 工程學院 - 營建工程系
Department of Civil and Construction Engineering
論文出版年: 2011
畢業學年度: 99
語文別: 中文
論文頁數: 83
中文關鍵詞: 混沌映射粒子群最佳化演算法基因演算法K-means演算法
外文關鍵詞: Chaos Mapping, Particle Swarm Optimization, Genetic Algorithms, K-means Algorithms
相關次數: 點閱:299下載:7
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  • 本研究所提出以基因演算法為基礎的架構,係依混沌映射及類聚分群的模式,並承續基因演算法的特性所構成。混沌映射的遍歷、不重複的特性,可以有效的提昇尋獲最佳解的效率;而援引類聚分群演算法的群聚特性,可以增進系統的收斂效果。在結合上述混沌、類聚分群、基因演算法等各演算邏輯的新演算法中,將展現出優異的演化效果。

    研究中所提出將粒子群最佳化演算法,結合混沌映射和動態導引機制後,即擁有遍歷、不重複和動態、難以預測的屬性;進一步將混沌映射轉化為搜尋機制後,並配合對全域最佳解動態導引的設計,可以促使系統同時具有快速搜尋,和從區域最佳解脫離的潛在優勢,因而有助於演算法尋獲最佳解的效率。

    證諸實際驗證的結果,並與其他傳統的啟發式演算法比較,顯示本研究根據基因演算法、及粒子群最佳化演算法,所提出的「混沌類聚分群基因演算法」及「混沌動態導引粒子群最佳化演算法」,可以顯著的提高尋獲最佳解的效能;而在求解最佳化問題時,本研究所提出的演算法更具有相對的優勢。


    The proposed approach brings up a manner of cognition that inherits the paradigm in Genetic Algorithms (GA) to implement a chaotic mapping and enhanced by K-means clustering approach. Chaotic mapping, enjoyed ergodicity, irregularity and the stochastic properties in heuristic optimization approach, contributes to global search evidently. In the meantime, K-means clustering approach with grouping property in the proposed algorithm could more easily lead to convergence.

    Dynamic guiding approach coupled with Particle Swarm Optimization (PSO) often implied fluctuation movement during evolution. Chaos properties employed in PSO were to search for optimal solution. The proposed algorithm incorporated dynamic guiding approach and chaos attributions into PSO would inevitably bring to a desirable optimal solution.

    As proven in multi-dimensional design space and compared with other conventional heuristic based algorithms, the proposed approaches could improve the search performance significantly, and show the superiority in solving optimization problems over other algorithms reported in this study.

    目 錄 第一章 緒論 1.1 前言 ---------------------------------------------1 1.2 研究動機與研究目的 -------------------------------2 1.3 研究範圍 -----------------------------------------2 1.4 研究限制 -----------------------------------------3 1.5 研究方法與步驟 -----------------------------------3 1.6 論文架構 -----------------------------------------5 第二章 文獻探討 2.1 基因演算法 ---------------------------------------7 2.1.1 基因演算法程序 -------------------------------7 2.1.1.1 染色體編碼 -------------------------------7 2.1.1.2 染色體初始化 -----------------------------8 2.1.1.3 選擇程序 ---------------------------------8 2.1.1.4 交配程序 --------------------------------10 2.1.1.5 突變程序 --------------------------------11 2.1.2 基因演算法流程 ------------------------------12 2.1.3 基因演算法與傳統演算法之差異性 --------------13 2.2 粒子群最佳化演算法 ------------------------------14 2.2.1 PSO演化過程 ---------------------------------14 2.2.2 慣性權重 ------------------------------------17 2.2.3 慣性權重變更---------------------------------17 2.2.4 粒子最大速度限制 ----------------------------18 2.2.5 收縮因子 ------------------------------------19 2.2.6 典型PSO演算法 -------------------------------20 2.2.7 PSO特性 -------------------------------------21 2.2.8 PSO演算法流程--------------------------------21 2.3 混沌演算法 --------------------------------------22 2.4 K-means演算法 -----------------------------------25 第三章 混沌類聚分群基因演算法 3.1 K-means、Chaos與GA演算法融合 -------------------28 3.2 基因演算法 --------------------------------------28 3.2.1 初始及選擇操作程序 --------------------------28 3.2.2 交配操作程序 --------------------------------30 3.2.3 突變操作程序 --------------------------------31 3.3 混沌基因演算法 ----------------------------------32 3.4 類聚分群基因演算法 ------------------------------35 3.5 混沌類聚分群基因演算法 --------------------------38 3.6 限制因素 ----------------------------------------41 第四章 混沌動態導引粒子群最佳化演算法 4.1 粒子群最佳化演算法 ------------------------------42 4.2 動態導引與粒子群最佳化演算法 --------------------43 4.3 混沌搜尋、導引與粒子群最佳化演算法 --------------46 4.4 混沌動態導引粒子群最佳化演算法 ------------------49 4.5 限制因素 ----------------------------------------51 第五章 混沌類聚分群基因演算法實證 5.1 實證案例說明 ------------------------------------52 5.2 組合型態驗證 ------------------------------------53 5.2.1 實證結果分析 --------------------------------54 5.2.2 實證過程分析 --------------------------------56 5.2.3 實證綜合分析 --------------------------------58 第六章 混沌動態導引粒子群最佳化演算法實證 6.1 驗證說明 ----------------------------------------59 6.2 驗證函數 ----------------------------------------59 6.2.1 Griewank函數 --------------------------------59 6.2.2 Rosenbrock函數 ------------------------------60 6.2.3 Rastrigin 函數 --------------------------------61 6.2.4 Ackley 函數 ---------------------------------63 6.2.5 函數型態 ------------------------------------64 6.3 實證環境 ----------------------------------------64 6.4 實證結果分析-------------------------------------65 6.4.1 動態導引粒子群最佳化演算法實證 --------------65 6.4.2 混沌粒子群最佳化演算法實證 ------------------65 6.4.3 混沌動態導引粒子群最佳化演算法實證 ----------67 6.5 實證過程分析 ------------------------------------70 6.5.1 Rastrigin函數演化過程實證 ---------------------70 6.5.2 Ackley函數演化過程實證 ----------------------71 6.5.3 Rosenbrock函數演化過程實證 -------------------72 6.5.4 Griewank函數演化過程實證 --------------------73 6.6 實證綜合分析 ------------------------------------73 第七章 結論與建議 7.1 混沌類聚分群基因演算法 --------------------------75 7.1.1 結論 ----------------------------------------75 7.1.2 未來研究的建議 ------------------------------76 7.2 混沌動態導引粒子群最佳化演算法 ------------------76 7.2.1 結論 ----------------------------------------76 7.2.2 未來研究的建議 ------------------------------77 參考文獻 英文部份 --------------------------------------------79 中文部份 --------------------------------------------83 圖 目 錄 圖 1-1 研究方法與步驟 ------------------------------------4 圖 2-1 二進制編碼圖 --------------------------------------8 圖 2-2 俄羅斯輪盤式選擇 ----------------------------------9 圖 2-3 染色體單點交配示意圖 -----------------------------10 圖 2-4 染色體雙點交配示意圖 -----------------------------11 圖 2-5 染色體字罩交配示意圖 -----------------------------11 圖 2-6 染色體編碼突變示意圖 -----------------------------12 圖 2-7 基因順序反轉突變示意圖 ---------------------------12 圖 2-8 基因演算法流程圖 ---------------------------------13 圖 2-9 粒子移動方向示意圖 -------------------------------16 圖 2-10 不同粒子最大速度下慣性權重與失敗次數關聯圖-------19 圖 2-11 粒子群最佳化演算法流程圖 ------------------------22 圖 2-12 混沌演算邏輯之羅吉斯映射圖 ----------------------23 圖 2-13 混沌演算邏輯之羅吉斯映射分佈頻率圖 --------------24 圖 2-14 混沌散佈圖 --------------------------------------25 圖 2-15 K-means分群演算法示意圖 -------------------------26 圖 3-1 混沌基因演算法觀念性架構圖 -----------------------33 圖 3-2 混沌演算法啟用機率圖------------------------------35 圖 3-3 類聚分群基因演算法觀念性架構圖 -------------------36 圖 3-4 Schaffer’s f6示意圖 ---------------------------------37 圖 3-5 類聚分群基因演算法染色體及各群中心點收斂軌跡示意圖 --37 圖 3-6 類聚分群基因演算法中心點軌跡圖 -------------------38 圖 3-7 混沌類聚分群基因演算法觀念性架構圖 ---------------39 圖 3-8 混沌類聚分群基因演算法中心點軌跡圖 ---------------41 圖 4-1 動態導引粒子群最佳化演算法觀念性架構圖 -----------44 圖 4-2 混沌粒子群最佳化演算法觀念性架構圖 ---------------47 圖 4-3 混沌粒子群最佳化演算法搜尋全域最佳解軌跡示意圖 ---48 圖 4-4 整體最佳解鄰近混沌搜尋示意流程圖 -----------------49 圖 4-5 混沌動態導引粒子群最佳化演算法觀念性架構圖 -------50 圖 5-1 歷年職業傷害千人率趨勢圖 -------------------------52 圖 5-2 營建工地分佈示意圖 -------------------------------54 圖 5-3 各演算法收斂曲線圖 -------------------------------57 圖 6-1 Griewangk函數3D示意圖-----------------------------59 圖 6-2 Griewangk函數3D近距離示意圖 --------------------60 圖 6-3 Rosenbrock函數3D示意圖----------------------------61 圖 6-4 Rastrigin函數3D示意圖-----------------------------62 圖 6-5 Rastrigin函數3D近距離示意圖-----------------------62 圖 6-6 Ackley函數3D示意圖--------------------------------63 圖 6-7 Ackley函數3D近距離示意圖--------------------------63 圖 6-8 Rastrigin 函數平均收斂曲線圖----------------------70 圖 6-9 Ackley 函數平均收斂曲線圖-------------------------71 圖 6-10 Rosenbrock 函數平均收斂曲線圖--------------------72 圖 6-11 Griewank 函數平均收斂曲線圖----------------------73 表 目 錄 表 3-1 初始染色體模擬結構 ------------------------------29 表 3-2 排序後初始染色體 --------------------------------29 表 3-3 順序排列之初始染色體 ----------------------------29 表 3-4 工地距離矩陣表 ----------------------------------29 表 3-5 初始化後染色體及適應值 --------------------------30 表 3-6 單點法染色體交配表 ------------------------------30 表 3-7 單點法染色體交配表(子世代基因修正) --------------31 表 3-8 單點法染色體交配表(父世代基因修正) --------------31 表 3-9 工地距離矩陣表(突變操作) ------------------------32 表 3-10 工地巡查順序距離表 ------------------------------32 表 3-11 混沌散佈點基因編碼 ------------------------------34 表 5-1 各工地途程距離矩陣 ------------------------------53 表 5-2 各模式績效比較表 --------------------------------55 表 6-1 各驗證函數型態-----------------------------------64 表 6-2 DPSO與PSO結果比較表------------------------------65 表 6-3 CPSO結果比較表-----------------------------------66 表 6-4 Rosenbrock函數最佳化結果比較表-------------------68 表 6-5 Rastrigin函數最佳化結果比較表--------------------68 表 6-6 Griewank函數最佳化結果比較表---------------------69 表 6-7 Ackley函數最佳化結果比較表-----------------------69

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