以基因演算法設計繞射光學元件之突變機制研究

Study of Mutation System of Genetic Algorithm for Optimization Design of Diffractive Optical Elements

林錦明(Chih-Ming Lin)

指導教授 ： 徐巍峰

國立臺北科技大學/電資學院/光電工程系研究所/碩士(2007年)

摘要

本篇論文主要以基因演算法進行繞射光學元件設計，並針對基因演算法之突變機制深入探討。回顧前人相關研究論文，學者提出許多不同的突變機制以提升演算法優化效率，卻鮮少對於突變機制的本質與相關影響因素深入研究。我們將由此著手，針對交配圖形、目標圖形、族群大小、以及繞射元件大小等因素，以不同的系統參數進行模擬，釐清各種因素對於突變機制以及優化效能的影響。
經由研究與分析的結果，初始族群大小以及繞射元件大小皆會對演算法優化效能造成影響。交配機制方面，我們選擇以固定交配圖形的方式進行突變機制分析。在初始族群方面，最佳突變率會因族群個體數的增加而有降低的趨勢；在元件大小方面，元件總像素值越少，相對解空間也隨之越小，其優化速度也越快。由模擬結果發現64 64像素繞射元件之最佳突變率落在0.03~0.05%之間，相當於每個元件4096像素中平均約1~2像素會進行突變。48 48像素繞射元件之最佳突變率落在0.03~0.06%之間，相當於每個元件2304像素中平均約1像素會進行突變。32 32像素繞射元件之最佳突變率落在0.04~0.08%之間，相當於每個元件1024像素中平均不到1像素會進行突變。

關鍵字

基因演算法 ； 繞射光學元件 ； 突變機制

並列摘要

In this thesis, we study the mutation system of the genetic algorithm (GA) for optimization design of the binary phase diffractive optical elements (DOEs). The GA scheme adopted here was the simple genetic algorithm. We discussed the relationship between parameters of mutation system and convergent properties by the simulation results of binary DOEs that were designed using GA. We discussed the effects of the number of population, and the size of elements on the performance of optimization design. The number of population determined the population density of solution space. As the number of population increased, the mutation rate to obtain the highest efficiency of optimization design reduced. The size of elements governed the size of solution space. As the size of elements reduced, the final convergence value of the fitness function increased. Among the cases at simulated, the optimal mutation rate to achieve the best performance of the binary DOEs was obtained in 0.03% ~ 0.08%, depended on parameters discussed above. These rates correspond to 0.41 ~ 2.05 pixels per DOE, and give an important reference for the use of GA to design the DOEs.

並列關鍵字

diffractive optical elements ； genetic algorithm ； mutation system

參考文獻

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