Automatic design of optical systems based on correctable reinforced search genetic algorithm

doi:10.11772/j.issn.1001-9081.2023081156

Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (9): 2838-2847.DOI: 10.11772/j.issn.1001-9081.2023081156

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Automatic design of optical systems based on correctable reinforced search genetic algorithm

Dong LIU¹^,², Chenhang LI¹^,³, Changmao WU³, Faxin RU¹, Yuanyuan XIA³()

^1.College of Computer and Information Engineering，Henan Normal University，Xinxiang Henan 453007，China
^2.Henan Provincial Key Laboratory of Artificial Intelligence and Personalized Learning in Education，Xinxiang Henan 453007，China
^3.Science & Technology on Integrated Information System Laboratory，Institute of Software，Chinese Academy of Sciences，Beijing 100190，China

Received:2023-08-28 Revised:2023-11-08 Accepted:2024-01-31 Online:2024-09-14 Published:2024-09-10
Contact: Yuanyuan XIA
About author:LIU Dong， born in 1976， Ph. D.， professor. His research interests include education big data mining， social network analysis.
LI Chenhang， born in 1997， M. S. candidate. His research interests include optical system design and optimization.
WU Changmao， born in 1974， Ph. D.， associate research fellow. His research interests include numerical optimization， parallel software and parallel algorithm.
RU Faxin， born in 1996， M. S. His research interests include optical system design and optimization.
Supported by:
National Key Research and Development Program of China(2021YFB3601401);National Natural Science Foundation of China(62072160)

基于可校正强化搜索遗传算法的光学系统自动设计

刘栋¹^,², 李晨航¹^,³, 吴长茂³, 茹法鑫¹, 夏媛媛³()

^1.河南师范大学计算机与信息工程学院，河南新乡 453007
^2.教育人工智能与个性化学习河南省重点实验室，河南新乡 453007
^3.中国科学院软件研究所天基综合信息系统重点实验室，北京 100190

通讯作者: 夏媛媛
作者简介:刘栋（1976—），男，河南新乡人，教授，博士，CCF会员，主要研究方向：教育大数据挖掘、社会网络分析
李晨航（1997—），男，河南三门峡人，硕士研究生，主要研究方向：光学系统设计与优化
吴长茂（1974—），男，北京人，副研究员，博士，主要研究方向：数值优化、并行软件与并行算法
茹法鑫（1996—），男，河南新乡人，硕士，主要研究方向：光学系统设计与优化；
基金资助:
国家重点研发计划项目(2021YFB3601401);国家自然科学基金资助项目(62072160)

Abstract

Abstract:

Both the Damped Least Squares （DLS） and Genetic Algorithm （GA） are applicable to automatic design of optical systems. Although DLS has a high search efficiency， it is susceptible to falling into local optima traps. Conversely， GA has strong global search capability in the parameter space of optical structures but weak local search capability. To address these challenges， a Correctable Reinforced Search GA （CRSGA） was proposed. Firstly， DLS was introduced after the GA crossover operation to enhance local search capability. Additionally， a correction strategy was introduced to rollback individuals with deteriorated fitness values before the next iteration， thereby achieving corrective evolutionary results. The improvement of two aspects to genetic algorithm enhanced strengths and compensated for weaknesses. Three typical optical system design experiments， including Double Gaussian （DG）， Reversed Telephoto （RT）， and Finite Conjugate Distance Imaging （FCDI）， were conducted to validate the effectiveness of CRSGA. CRSGA outperforms both DLS and GA， and its optimization outcomes are about 8.92%， 12.19%， and 9.39% respectively better than those of commercial optical design software Zemax DLS. In particularly， the optimization outcomes achieve a significant improvement， reaching 99.98%， 94.33%， and 88.45% respectively compared to the Zemax HAMMER algorithm. In conclusion， it is shown that the proposed algorithm is effective for optical system optimization and can be used for automatic optical system design.

Key words: optical system design, optical optimization, damped least square method, global optimization, improved genetic algorithm

摘要：

阻尼最小二乘法（DLS）与遗传算法（GA）均适用于光学系统自动设计，前者搜索效率高但极易陷入局部极值陷阱，后者光学结构参数空间全局搜索能力强但局部搜索能力弱。针对上述问题，提出一种可校正强化搜索GA（CRSGA）。该算法在GA基础上进行了两方面的改进：首先，在GA交叉算子后，引入DLS增强局部搜索能力；其次，引入校正策略，即在下轮迭代前按比例回滚进化后评价函数值变差的个体以校正进化结果。选取双高斯（DG）、反远摄（RT）和有限共轭距成像（FCDI）这3种典型光学系统设计实验以验证CRSGA的有效性，CRSGA优化效果优于DLS、GA，且依次优于商业光学设计软件Zemax阻尼最小二乘法约8.92%、12.19%和9.39%，特别是优化结果分别达到Zemax HAMMER算法的99.98%、94.33%和88.45%。实验结果表明，所提算法对光学系统优化效果良好，可用于光学系统自动设计工作。

关键词: 光学系统设计, 光学优化, 阻尼最小二乘法, 全局优化, 改进遗传算法

CLC Number:

TP39

Dong LIU, Chenhang LI, Changmao WU, Faxin RU, Yuanyuan XIA. Automatic design of optical systems based on correctable reinforced search genetic algorithm[J]. Journal of Computer Applications, 2024, 44(9): 2838-2847.

刘栋, 李晨航, 吴长茂, 茹法鑫, 夏媛媛. 基于可校正强化搜索遗传算法的光学系统自动设计[J]. 《计算机应用》唯一官方网站, 2024, 44(9): 2838-2847.

Figures/Tables 21

Fig. 1 2D structure of optical system

Fig. 2 Flow of CRSGA

Tab. 1 CRSGA parameter description

参数	范围	含义
$N$	$N ∈ N *$	种群中个体数
$n$	$n ∈ N *$	个体中结构参数量
$J$	$J ∈ [1, N]$	个体编号
$i$	$i ∈ [1, n]$	结构参数编号
$X J$	$X J ∈ {X 1, X 2, …, X N}$	第J个个体也指一组结构参数
$x i$	$x i ∈ {x 1, x 2, ⋯, x n}$	第i个结构参数
$X n e w J$	$X n e w J ∈ X n e w 1, X n e w 2, …, X n e w N$	第J个体的子代
$X b e s t J$	$X b e s t J ∈ X b e s t 1, X b e s t 2, …, X b e s t N$	存储第J个个体历史最优的一组结构参数
$M F i n i t J$	$M F i n i t J ∈ [0, ∞)$	第J个个体的初始评价函数值
$M F n e w J$	$M F n e w J ∈ [0, ∞)$	第J个个体的子代评价函数值
$M F b e s t J$	$M F b e s t J ∈ [0, ∞)$	第J个个体的最优评价函数值

Tab. 1 CRSGA parameter description

参数	范围	含义
$N$	$N ∈ N *$	种群中个体数
$n$	$n ∈ N *$	个体中结构参数量
$J$	$J ∈ [1, N]$	个体编号
$i$	$i ∈ [1, n]$	结构参数编号
$X J$	$X J ∈ {X 1, X 2, …, X N}$	第J个个体也指一组结构参数
$x i$	$x i ∈ {x 1, x 2, ⋯, x n}$	第i个结构参数
$X n e w J$	$X n e w J ∈ X n e w 1, X n e w 2, …, X n e w N$	第J个体的子代
$X b e s t J$	$X b e s t J ∈ X b e s t 1, X b e s t 2, …, X b e s t N$	存储第J个个体历史最优的一组结构参数
$M F i n i t J$	$M F i n i t J ∈ [0, ∞)$	第J个个体的初始评价函数值
$M F n e w J$	$M F n e w J ∈ [0, ∞)$	第J个个体的子代评价函数值
$M F b e s t J$	$M F b e s t J ∈ [0, ∞)$	第J个个体的最优评价函数值

Fig. 3 Principle of crossover operation

Fig. 4 Detailed flow of cross operation

Fig. 5 Principle of mutation operation

Fig. 6 Detailed flow of mutation operation

Fig. 7 Principle of correction strategy

Fig. 8 Optimization results for DG system： 2D diagrams

Fig. 9 Optimization results for DG system： standard spot diagrams

Fig. 10 Optimization results for DG system： FFT MTF diagrams

Fig. 11 Optimization results for RT system： 2D diagrams

Fig. 12 Optimization results for RT system： standard spot diagrams

Fig. 13 Optimization results for RT system： FFT MTF diagrams

Fig. 14 Optimization results for FCDI system： 2D diagrams

Fig. 15 Optimization results for FCDI system： standard spot diagrams

Fig. 16 Optimization results for FCDI systems： FFT MTF diagrams

Fig. 17 Comparison of decline of evaluation functions of different optimization algorithms

Fig. 18 Fluctuations of optimization results of different algorithms

Fig. 19 Comparison of optimization results of different system models corresponding to optimization methods

Tab. 2 Evaluation function values for different system models corresponding to optimization methods

光学系统	DLS	GA	Zemax DLS	Zemax HAMMER	CRSGA
DG光学系统	0.003 567 943	0.004 249 817	0.003 306 057	0.003 010 415	0.003 011 093
RT光学系统	0.020 462 115	0.021 789 366	0.008 098 845	0.006 708 602	0.007 111 276
FCDI光学系统	0.328 974 516	0.256 871 452	0.055 824 961	0.044 741 395	0.050 582 101

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Automatic design of optical systems based on correctable reinforced search genetic algorithm

基于可校正强化搜索遗传算法的光学系统自动设计

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