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研究生:侯采君
研究生(外文):Tsai-Chun Hou
論文名稱:以基因演算法設計繞射光學元件之交配機制研究
論文名稱(外文):The Study of Crossover Mechanism of Genetic Algorithm for Diffractive Optical Elements
指導教授:徐巍峰
口試委員:李佳翰林晃巖
口試日期:2007-07-23
學位類別:碩士
校院名稱:國立臺北科技大學
系所名稱:光電工程系所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:68
中文關鍵詞:繞射光學元件基因演算法族群回填動態變換式交配圖形交配像素
外文關鍵詞:diffractive optical elements (DOEs)genetic algorithm(GA)population- reloadpopulation-purificationmovement crossover figure
相關次數:
  • 被引用被引用:3
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基因演算法中,一般認為交配機制比突變機制更為重要,然而目前以基因演算法設計繞射光學元件所得結果卻非如此,模擬結果發現僅以交配機制的演化結果遠低於突變機制,因此我們在基因演算法中完全除去突變機制,純粹以交配機制來進行演化,本論文即深入的探討此一結果,希望能藉由設計新的實驗方法來釐清交配機制(包括交配圖形和交配頻率)在基因演算法中的意義和重要性。主要妨礙本研究的問題為族群純化問題,所以本論文目是為清楚了解族群純化的問題,並找出適當的交配運算方式,。
本研究中,我們發現在固定使用同個交配圖形下加入一種子個體,族群在20世代左右就會完全純化,若能在族群未完全純化時就改變交配圖形,可以促進族群的演化,但經過相當的世代後(約1000世代),族群的純化也會達相當高的程度而減緩演化的進行,因此,我們採取族群回填方式更新族群個體,以便觀察交配運算對演化的影響。我們共設計了五種交配圖形系列以進行動態式交配運算,在經過十萬世代後,發現圓盤及方形系列有較佳的演化結果,因為圓盤與方形交配圖形能隨著圖形的變換而改變交配像素的多寡,為影響評估函數好壞的主要原因。
In the genetic algorithm, it is generally acknowledged the crossover mechanism is even more important than the mutation mechanism. However, the crossover mechanism did not increase the performance of phase-only diffractive optical elements(DOEs) as expected in our early study. In order to identify the effect of the crossover mechanism.
we removed the mutation mechanism and only used only the crossover mechanism to simulate the evolution to design the DOEs. The simulation results of evolution for the crossover mechanism were poor compared with the mutation mechanism, which was different from this algorithm applying to other problems. We believe the main reason of the poor result by only using the crossover mechanism is the population-purity. Therefore, in this thesis, we analyzed the population-purification situation and different crossover mechanism for designing the diffractive optical elements in using the genetic algorithm.
In this research, by using a regular crossover pattern and by adding a seed individual of best performance in the population, we found the populations were completely purified (individuals of the population all become the same) in about 20 generations. By dynamically changing the crossover patterns, the population was purified in hundreds to thousands generations. Therefore, we used a method of the population reload every 1000 generations in order to analyze the effect of different crossover patterns. In the population-reload method, the crossover pattern was changed every 10 generations, the initial population replaced the purified population every 1000 generations, and a total 100,000 generations of the GA revolution. Then, 5 different designs of crossover pattern of random parameters were designed to compare the performance of the binary-phase DOEs. No significant improvement of performance was observed in the simulation results when the number of exchanged pixels was about a half of the total pixels. However, the performance of the DOEs was significantly increased when the number of exchanged pixels decreased, or even increased. Consequently, according to the simulation results obtained in this study, we believe that the spatial location of the exchanged pixels of the crossover mechanism influenced the DOE performance more significantly than the number and pattern of the exchanged pixels.
摘 要 i
ABSTRACT ii
誌 謝 iv
目錄 v
表目錄 viii
圖目錄 ix
第一章 導論 1
1.1 繞射光學元件概述 1
1.2 基因演算法概述 2
1.3 研究動機 3
1.4 論文架構 4
第二章 繞射理論 5
2.1 Fresnel繞射與Fraunhofer繞射 5
2.2 繞射光學元件編碼 8
2.2.1繞射光學元件設計 8
2.2.2電腦模擬繞射光學元件 10
2.3 評估函數與適應函數 12
2.3.1繞射效率 12
2.3.2均方根誤差 13
2.3.3最小訊雜比 13
2.3.4適應函數 13
第三章 基因演算法 14
3.1何謂基因演算法 14
3.2基因演算法介紹 14
3.2.1基因演算法源起 14
3.2.2基因演算法演化流程 16
3.2.3基因編碼方式 18
3.2.4初始族群 19
3.2.5適應函數 19
3.2.6選擇〈複製〉運算子 19
3.2.7交配運算子 21
3.2.8 突變運算子 23
3.2.9 反轉運算子 24
3.2.10終止演化條件 24
3.3基因演算法的特性 25
第四章 以基因演算法設計繞射光學元件之交配機制模擬架構 27
4.1 繞射光學元件模擬架構 27
4.2 運算參數設計 29
4.3 基因演算法流程 30
4.3.1 初始族群 31
4.3.2 評估函數與適應函數 31
4.3.3 選擇/複製個體 32
4.3.4 交配機制 32
4.3.5 族群取代 32
4.3.6 族群回填機制 33
4.4 交配圖形設計 33
第五章 以基因演算法設計繞射光學元件之交配機制模擬結果 36
5.1 族群純化 36
5.1.1 加入一種子個體分析〈總世代數:100000〉 36
5.1.2交配圖形變換頻率探討〈總世代數:1000〉 38
5.1.3 固定式與動態變換式交配圖形比較〈總世代數:1000〉 41
5.2 族群回填探討 43
5.2.1 回填世代數比較〈總世代數:100000〉 43
5.3 交配圖形探討 45
5.3.1交配圖形系列之比較 45
5.3.2交配圖形交配像素比率之研究 47
第六章 結論 54
參考文獻 55
附錄A:Dilemmas of Using the Genetic Algorithms in the Design of Diffractive Optical Elements 57
附錄B:以基因演算法設計繞射光學元件之“交配機制”影響評估 60
附錄C:以基因演算法設計繞射光學元件之最佳“突變機率”探討 64
符號彙編 68
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