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研究生:林育宏
研究生(外文):Yu-Hong Lin 林育宏
論文名稱:機率分配導引式仿水流演算法:應用於類神經網路之參數訓練
論文名稱(外文):Probability Distribution-Guided Water Flow-like Algorithm for Continuous Optimization: Application to Feed-forward Neural Network Training
指導教授:楊烽正楊烽正引用關係
口試委員:黃奎隆胡黃德羅士哲
口試日期:2015-04-24
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:工業工程學研究所
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:159
中文關鍵詞:仿水流演算法前饋式類神經網路連續型優化問題
外文關鍵詞:Water Flow-like AlgorithmFeed-forward Neural NetworkContinuous Optimization Problem
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  • 被引用被引用:0
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本研究展示以母水流流域及子水流代理人架構的新式仿水流演算法 (Probability Distributioin-Guided Water Flow-like Algorithm,PWFA)。PWFA的主要特色是利用連續型機率分配仿傚水流分流、匯流、及降水,使水流代理人的解朝優演化。效能驗證的求解對象是單一目標的連續型優化問題及前饋式類神經網路的權重參數優化問題,共有29個標竿優化函數及五個UCI資料集。實例測試時,比較本法與倒傳遞演算法、共軛梯度法、兩種仿水流演算法、三種遺傳演算法、及四種粒子群演算法的求解效能。數值結果顯示PWFA求解僅具單一全域最佳解的單峰型及多峰型優化函數的效能優於其他優化演算法;而求解具多個全域最佳解的多峰型函數時,PWFA與三種粒子群演算法在不同函數下各有優勢。此外,前饋式類神經網路參數優化問題的實測結果顯示,PWFA與粒子群演算法的優化效能皆屬最佳者。

Water flow-like algorithm (WFA) is inspired by the nature of water flow during circulating in the physical space. Initailly, WFA was developed to be a heuristic algorithm for combinatorial optimization. Thanks to WFA’s underlying ideal, this work propose a novel version of WFA for continuous optimization, called probability distribution-guided water flow-like algorithm (PWFA). In PWFA, basins are conceptualized as subspaces in the solution space, which help subflows to stochastically move toward the lowest position (the global optimum). To imitate the behavior of water flow heuristically, the flows perform spltting and moving, merging and precipitation operation to traverse in the space. Moreover, for evaluating PWFA’s performance, a large set of benchmark test functions and other basic optimization techiques from the literature are adopted for numerical test. In addition, the application to the training of feed-forward neural network (FNN) for pattern classification is also present as a test case for this algorithm. For the reason, a system prototype for solving continuous optimization problem and FNN parameter optimization is implemented by this work. The results show, first, that PWFA has a better performance than other optimization methods on uni-modal functions and multi-modal functions with single one optimum, and second, that this algorithm represents a competitive performance to other basic methods as solving multi-modal functions with many optimums. Additionally, the results of the application show PWFA is comparable to several optimization techniques included as well.

口試委員會審定書 i
誌謝 ii
摘要 iv
Abstract v
表目錄 ix
圖目錄 xii
第一章 緒論 1
  1.1 研究背景 1
  1.2 研究目的 2
  1.3 研究方法 3
  1.4 章節概述 5
第二章 文獻探討 6
  2.1 仿水流演算法 6
  2.2 粒子群演算法 8
  2.3 遺傳演算法 10
第三章 機率分配導引式仿水流演算法 12
  3.1 機率分配導引式仿水流的演化概念 12
    3.1.1 分流移步 12
    3.1.2 匯流 17
    3.1.3 降水 18
  3.2 演算程序使用的資料結構 21
  3.3 機率分配導引式仿水流演算法的演算程序 22
    3.3.1 整體演算流程 22
    3.3.2 初始化 23
    3.3.3 分流移步作業 27
    3.3.4 匯流作業 29
    3.3.5 降水作業 35
  3.4 小結 38
第四章 連續型優化問題求解 40
  4.1 連續型優化問題 40
  4.2 連續型優化問題的數學模型 40
  4.3 連續型優化問題的標竿範例及求解法 42
    4.3.1 29個標竿優化函數的介紹 42
    4.3.2 七個優化求解法及參數設定 46
  4.4 連續型優化問題的效能評量指標 48
  4.5 連續型優化問題的求解系統 50
  4.6 範例測試及求解效能比較 57
    4.6.1 範例測試的實驗設定 57
    4.6.2 七個優化求解法求解29個標竿優化函數的效能比較 57
  4.7 小結 72
第五章 前饋式類神經網路參數優化問題求解 74
  5.1 前饋式類神經網路參數優化問題 74
  5.2 前饋式類神經網路參數優化問題的數學模型 75
  5.3 前饋式類神經網路參數優化問題的標竿範例及求解法 83
    5.3.1 五個標竿分類問題的介紹 83
    5.3.2 11個求解法及參數設定 84
  5.4 前饋式類神經網路參數優化問題的效能評量指標 87
  5.5 前饋式類神經網路參數優化問題的求解系統 90
  5.6 範例測試及求解效能比較 97
    5.6.1 範例測試的實驗設定 97
    5.6.2 11個優化求解法求解五個標竿分類問題的效能比較 98
  5.7 小結 114
第六章 結論 116
  6.1 總結 116
  6.2 未來研究建議 117
參考文獻 119
附錄A 121
附錄B 150
附錄C 158


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