逃逸函数算法及其在光学设计中的应用

用阻尼最小二乘法进行光学系统的优化 ,得到的结果往往是评价函数在结构变量空间的一个局部极小值。日本东京工艺大学的一色教授提出了能够跳出此局部极小值继续寻找其它结果的逃逸函数全局优化算法 ,该算法的运行由多个不加或加入逃逸函数的阻尼最小二乘法局部优化组成。描述了逃逸函数的基本原理 ,给出了北京理工大学研制的GOLD软件在加入了这种算法后对光学系统进行全局优化的设计实例。实验证明了逃逸函数算法是提高光学设计效率和质量的一种有效工具。     

在定域法中实现光学全局优化

把不等式法用于光学优化设计中,同时使用了“逃逸函数”技术,从而实现了光学系统设计的全局优化在使用逃逸函数时,两个因子H和W的确定是能否“逃逸”优化“陷阱”的关键用这种技术借助于C++开发的程序成功地设计了一些典型的光学系统.     

光学系统设计中全局优化方法的实现

 把变尺度法用于光学优化设计中，同时使用了“逃逸函数”技术, 从而实现了光学系统设计的全局优化。在使用逃逸函数时，两个因子H和W的确定是能否“逃逸”优化“陷井”的关键。用这种技术借助于C语言开发的程序成功地设计了一典型的光学系统。     

混入逃逸函数的实数编码遗传算法优化光学系统

为了得到超多参量光学系统的最佳设计,将标准遗传算法的二进制编码改为实数编码以提高算法的鲁棒性和计算效率,并在评价函数中混入逃逸函数避免优化过程陷入局部极值.用改进后的遗传算法和CODE V对鱼眼镜头光学系统和折反射全景成像系统的设计案例进行光学参量优化,并应用Zemax对两种优化结果进行光线追迹成像模拟.计算结果表明,应用改进遗传算法比混入逃逸函数的遗传算法或CODE V软件优化所得到光学系统的成像质量有明显提高,在优化超多参量光学系统时具有较为理想的鲁棒性和计算效率.     

红外系统冷屏形状的优化设计

一次成像的简化式红外光学系统冷屏与出瞳不能匹配,致使系统受到杂散光干扰。在此情况下,对冷屏的开孔形状进行合理优化设计对杂散光的抑制十分必要。利用数学中的最优化计算来解决冷屏形状的优化问题,建立了优化变量和优化目标函数的数学模型,提出了全局优化和局部优化相结合的方法,分别用区间穷举法和阻尼最小二乘法完成,以得到较优的冷屏开孔形状。利用本方法,对一个现有的简化式热像光学系统设计了冷屏开孔形状,解决了该系统中由冷屏与出瞳不匹配造成的杂散光干扰的问题,从而验证了提出的冷屏优化设计方法的正确性与实用性。     

一种采用优势个体多方向强制搜索策略的换热网络优化方法

提出一种采用优势个体多方向强制搜索策略的进化算法, 通过考察种群中个体差异性指标, 用以评价当前种群全局搜索的健康度。当优化结果出现长期停滞, 即健康度指标变差时, 启动优势个体多方向强制搜索策略, 扩大优势个体在靠近局部最优解区域的搜索方向, 保证算法全过程的全局搜索能力。用15SP和20SP算例进行验证, 与文献中最优结果相比, 分别下降了1.09%、0.83%, 表明优势个体多方向强制搜索策略充分发挥了优势个体的进化潜力, 提高了算法的优化效能。     

基于Memetic算法的编码曝光最优码字序列搜索方法

提出了一种基于Memetic算法的编码曝光最优码字序列搜索方法。分析了编码曝光成像理论模型,建立了最优码字选取的适应度函数准则。引入Memetic算法框架并开展了最优编码序列搜索,利用遗传搜索算法进行了全局最优解搜索,并在此基础上利用模拟退火算法进行了局部最优解求解,通过适应度函数的阈值约束及种群和最优解的更新迭代,得到了最优码字搜索结果。研究结果表明,相比其他方法,所提算法兼顾了全局最优与局部最优的求解,得到的最优码字序列具有更优性能指标,算法执行效率高,复原图像的主客观评价质量更好。     

角度受限下稀疏投影数据的改进粒子群优化随机CT重建

当计算机断层成像(CT)中X射线的采样范围和数量受限时,得到的稀疏投影数据完备性很低,重建算法的搜索空间巨大。基于凸优化思路的迭代求解算法及其改进采用固定搜索路径,难以在有限时间内收敛至全局最优解;粒子群优化具有全局搜索能力,但计算成本和存储代价过高。为解决这类不完备投影数据的重建问题,提出基于粒子群优化的随机稀疏重建算法。首先,通过随机策略生成具有多样性的初始种群,以保证算法的搜索能力;其次,随机选择梯度下降或基于个体历史最优解和全局历史最优解的随机方向进行迭代,以兼顾算法效率和搜索方向的多样性;最后,基于适应度评价,有针对性地重新生成随机初始种群,强制跳离局部最优。针对角度受限下无噪声和含噪声的稀疏投影数据,分别进行重建实验。结果显示,与常见的凸优化迭代和粒子群优化算法相比,本文算法既能保证算法效率,又在重建质量和算法稳健性上具有明显优势。     

基于枝状超结构的蒸汽管网优化及禁忌搜索策略

本文通过对蒸汽管网枝状超结构的分析,利用惩罚函数的优化技术,建立了一种基于混合整数非线性模型的蒸汽管网优化方法;同时,鉴于整型变量数目庞大所造成的最优解搜索效率下降的问题,提出了一种"禁忌搜索"的方法,提高了最优化算法的效率.     

SVM参数优化方法分析与决策

针对支持向量机应用过程中的参数选择问题,从UCI数据库选择样本集,分别采用传统的网格法、智能优化算法中的粒子群法及遗传算法实现核函数参数寻优过程,将所得最佳参数应用到样本测试中。在深入分析优化过程中各参数关系、参数对支持向量机性能的影响以及传统与智能优化算法的优劣后,得出了核函数优化策略。即先使用智能优化算法初步确定最优解范围,再结合网格法进行高精度寻优。实验数据验证了参数优化策略的有效性,为扩大支持向量机泛化率、提高应用性做了铺垫。     

Global and local optimization for optical systems

Issues concerning the efficiency of the Global Explorer (GE) algorithm are studied. Global optimization with GE consists of many local optimization runs with or without the escape function using the damped-least-squares method. In order to improve the efficiency of the local optimization and the GE run, two search schemes are incorporated. The first one searches for the best damping factor which effectively determines the optimum direction of the solution vector in the multi-dimensional variable space, and the second search is conducted along that direction to find the optimum length of the solution vector. Experiments are also made to determine the optimum default values for the parameters of the escape function. The algorithm with the improvements is successfully implemented in the GOLD program developed by Beijing Institute of Technology. Design examples using the software are given, which show that the global optimization feature is practical and powerful.     

Improved Local Search with Momentum for Bayesian Networks Structure Learning

Bayesian Networks structure learning (BNSL) is a troublesome problem that aims to search for an optimal structure. An exact search tends to sacrifice a significant amount of time and memory to promote accuracy, while the local search can tackle complex networks with thousands of variables but commonly gets stuck in a local optimum. In this paper, two novel and practical operators and a derived operator are proposed to perturb structures and maintain the acyclicity. Then, we design a framework, incorporating an influential perturbation factor integrated by three proposed operators, to escape current local optimal and improve the dilemma that outcomes trap in local optimal. The experimental results illustrate that our algorithm can output competitive results compared with the state-of-the-art constraint-based method in most cases. Meanwhile, our algorithm reaches an equivalent or better solution found by the state-of-the-art exact search and hybrid methods.     

DESIGNING A DIFFRACTIVE OPTICAL ELEMENT FOR CONTROLLING THE BEAM PROFILE IN A THREE-DIMENSIONAL SPACE USING THE SIMULATED ANNEALING ALGORITHM

We have designed a spatially quantized diffractive optical element (DOE) for controlling the beam profile in a three-dimensional space with the help of the simulated annealing (SA) algorithm. In this paper, we investigate the annealing schedule and the neighbourhood which are the deterministic parameters of the process that warrant the quality of the SA algorithm. The algorithm is employed to solve the discrete stochastic optimization problem of the design of a DOE. The objective function which constrains the optimization is also studied. The computed results demonstrate that the procedure of the algorithm converges stably to an optimal solution close to the global optimum with an acceptable computing time. The results meet the design requirement well and are applicable.     

基于改进遗传算法的移动机器人路径规划

针对传统遗传算法存在的搜索效率低、易于陷入局部最优解的问题,提出了一种改进的遗传算法。采用简单的一维编码替代复杂的二维编码,节约了存储空间。在遗传算子的设计中,重新定义了交叉算子和变异算子,避免了陷入局部最优。最后将最短路径和免碰撞相结合作为适应度函数进行遗传优化。实验结果表明,改进的算法能够快速、有效的规划出最优路径。     

Two-stage adaptive PMD compensation in 40-Gb/s OTDM optical communication system

An experiment of two-stage adaptive compensation for polarization mode dispersion (PMD) in a 40-Gb/s optical time-division multiplexed communication system is reported. The PMD monitoring technique based on degree of polarization was adopted. The particle swarm optimization (PSO) algorithm was introduced in adaptive PMD compensation. The comparison was made to estimate the effectiveness between PSO algorithms with global neighborhood structure (GPSO) and with local neighborhood structure (LPSO).The LPSO algorithm is shown to be more effective to search global optimum for PMD compensation than GPSO algorithm. The two-stage PMD compensator is shown to be effective for both first- and second order PMD, and the compensator is shown to be bit rate independent. The optimum searching time is within one hundred milliseconds.     

Lens Design: Global Optimization with Escape Function

The technique of using the ‘escape function’ for global optimization in lens design is described. This includes how to identify two solutions as independent; the threshold value for this criterion can be chosen to determine how to explore local solutions—rough or fine. Choice of appropriate values for two parameters in the escape function is most important, since this will affect the efficiency of the automatic global optimization process. There are two problems, i.e. giving default values at the beginning of the design, and determining a default rule to change them when the escape is unsuccessful. The latter was solved by assuming a ‘saddle path’ as the best route to escape. An exact solution for the former was not found, but a hint for finding a second best solution is shown based on the statistical study of local minima.     

Lens Design: An Attempt to Use ‘Escape Function’ as a Tool in Global Optimization

In designing lenses with the damped least squares method, the solution obtained by optimization routine is a local minimum of the merit function. To get out of this and seek a different solution, we propose to use an ‘escape function’ as an additional operand of the lens system, to be controlled. Experiments were made on simple models of merit function and the advantage of this technique was ascertained. We also planted this algorithm into OSLO SIX (lens design software by Sinclair Optics) by means of CCL (C-compatible language) and applied it to actual lens design. Experiments convinced us that the method would be an effective tool for global optimization.     

Logistic型混合自适应分数阶达尔文粒子群优化算法

针对分数阶达尔文微粒群优化(FDPSO)算法收敛速度慢,收敛精度不高的问题,改进其算法中分数阶速度更新策略,同时引入Logistic型混合分数阶自适应动态调整策略,得到一种改进的自适应分数阶达尔文粒子群优化(LFDPSO)算法,通过理论分析,证明了该算法在给定条件下的收敛性,并由数值实验表明,Logistic型混合自适应分数阶达尔文粒子群(LFDPSO)算法在收敛精度和收敛速度上得到了有效改善与提高,粒子在局部最优时的逃逸能力、全局寻优及智能搜索能力显著增强。     

布里渊散射谱参数提取问题的混合优化算法研究与应用

提出了一种将Particle Swarm Optimization(PSO)算法和Levenberg-Marquardt(LM)算法按概率混合优化的新算法,将其用于Pseudo-Voigt型布里渊散射谱以提高其拟合度和频移提取精度。新算法以PSO算法为主框架,首先用PSO算法进行全局搜索,在优化一定次数后每次优化随机产生一个概率rand(0,1),若rand(0,1)小于或等于事先设定的概率P,则把PSO算法得到的最优解作为LM算法的初值进行局部深度搜索,将LM算法得到的最优解替换先前PSO算法的最优解,继续使用PSO算法进行全局搜索;若rand(0,1)大于P则仍然用PSO算法搜索,等待下一次优化产生随机概率rand(0,1)进行判断,交替使用两种算法直至获得理想的全局最优解。仿真分析和实验表明,新算法克服了单一算法的缺点,提高了布里渊散射谱的拟合度和频移提取的精度,充分证明了新算法的实用性和可行性。