非线性优化

PSO is a population-based optimization algorithm, which mimics the social behavior of animals in a flock. It makes use of individual and group memory to update each particle position allowing global and local search optimization. The objective function considered was the total weight of the structure subjected to stresses, displacements and forces constraints. The effects of the parameters were investigated as well and such combination of tuning parameters promote a better global search behavior avoiding premature convergence while rapidly converging to the optimal solution. Results showed the effectiveness of the proposed method by comparing with ANSYS Design Optimization Tool (zero-order method). The PSO with the tuning parameters makes it an ideal method for offshore wind turbines foundations optimization tasks.(2) A reliability analysis method for pile foundation bearing axial loads based PSOThe performance function of pile foundation's axially bearing capacity sometimes is nonlinear and complex, on the basis of geometric meaning of structural reliability index, an optimum model with PSO for structural reliability analysis under arbitrary random variables was established, The PSO algorithm is very efficient to solve global optimization problemsIts use in structural reliability field presents not only the advantage of its facility of implementation, but also the possibility to obtain the design point and the failure probability with a good accuracy. In addition, PSO is a zero order algorithm, for no derivative is necessary for its implementation.

本文的研究针对桩式海上风机基础结构的特点，在国内外有关研究成果的基础上对海上风机基础结构优化设计理论和可靠度方法一些相关问题进行了较为深入的研究，具体做了以下几个方面的工作：(1)基于粒子群优化的桩式海上风机基础确定性优化设计方法桩式海上风机基础的优化设计是一个复杂的、非线性约束的优化问题，针对传统的基于梯度信息的优化方法在处理非线性问题中易陷入局部最优解的问题，本文将一种耦合惩罚函数的PSO算法引入到海上风机基础结构概念设计中，PSO算法是从群体动物聚集觅食这一活动中受到启发而发展的，该算法利用个体和群体的信息共享不断改进自身的位置从而进行局部和全局最优搜索，本文中以桩和三脚架连接段直径及壁厚为设计变量，以基础总重量作为优化的目标函数，在给定的约束条件下建立了三脚架基础优化数学模型，另外本文还研究了PSO参数变化对结果的影响，协调的参数组合可以避免陷入早熟收敛而能够快速的获得全局的最优解，通过与ANSYS优化模块的计算结果比较验证了该方法的有效性，本方法为海上风机基础的确定性设计提供了一条有效的途径。

Optimal algorithm of combined nonlinear Hopfield network appears powerful validity in solving nonlinear planning, which includes nonlinear objective function, linear constrains and high-demension of decision-making variants, for its ability of nonlinear parallel computation. It is prominent among optimal algorithms because of its function of simply implement with electrocircuit hardware. Genetic algorithm is expressly suitable for optimal calculation regarding the planning of massive, highly nonlinear, inconsecutively differentiable and multiobjective function as well as objective function without analytical expression. However, it inclines to prematurity, as well as its limitation in ability of partial optimal search. Introducing the optimal algorithm of niche genetic simulated annealing to standard Genetic algorithm, can therefore improve the full-scale or partial search ability of Genetic algorithm effectively. It has a far-flung perspective in the field of systemic planning of water pollution control.

组合式非线性Hopfield网络优化算法所具有的非线性大规模并行计算能力在求解具有非线性目标函数、线性约束条件及高维决策变量的非线性规划问题方面显示出了强大的生命力，它易于电路硬件实现的功能更是在优化算法中独树一帜；遗传算法采用概率搜索技术，不受目标函数与约束条件的限制，特别适合大规模、高度非线性的不连续可微的多峰目标函数及无解析表达式的目标函数的规划问题的优化计算，但其存在容易早熟、局部寻优能力较差等缺点，本文在标准遗传算法中引入小生境技术及模拟退火算法有效地改善遗传算法的全局和局部搜索性能，提高了全局最优解的寻优质量，小生境遗传退火模拟优化算法在水污染控制系统规划中的应用前景极为广阔。

Finally, according to the various properties of the optimization algorithms, the optimization algorithms have been applied to predicting the silicon content of hot metal and to optimizing the operation parameters of the blast furnace to meet the need of the higher hot metal output and the lower coke rate. Major research work in this paper includes:(1) Based on the study of the statistic property of the Logistic chaos map, the author has proposed the nested intervals chaos search method which improves the ergodicity of the chaos search by searching the area once more where the probability distribution is small.

高炉炼铁生产是一个复杂的非线性过程，高炉生产操作参数的优化涉及优化模型的建立、多目标优化、约束条件的检验等多个问题，对于这么一个复杂的优化问题，传统、单一的优化方法已存在局限性，因此本文研究了两种新型的具有不同特点的优化方法：基于混沌理论的优化方法和基于人工免疫理论的优化方法，并设计了几种混合优化方法。

A problem of cable force optimization of cable-stayed bridge is equated as a nonlinear implicit optimization model. In the mathematical model, the object function is minimizing summation of bending strain energy and axial strain energy, and the constrain conditions are nonlinear and related to reasonable finished dead state. The optimization model is solved by projection gradient method, fully considering all kinds geometric nonlinearity.

把超千米级斜拉桥的索力优化问题归结为非线性隐式优化的数学模型，以系统最小弯压应变能为目标，根据合理成桥状态指定各种非线性约束条件，利用投影梯度法进行优化问题的求解，求解过程中充分考虑了各种几何非线性的影响。

The optimal combination of the preserved quality parameters for the freeze-drying technology of pteridium aquilinum was obtained through optimized theory in nonlinear method.

并利用非线性优化理论确定了搁板加热温度为42.5℃、干燥室压力为55Pa、物料厚度为16.3mm时，蕨菜的Vc质量比可达2.387mg/g。

To locate the critical failure surface of slope, and achieve the surface geometric parameters is a real challenge to engineers, especially in some complex slope geo-conditions, for the sake of its tanglesome multifactor and nonlinearity.

许多复杂的边坡稳定性分析中，边坡潜在危险滑动面的搜索是个重要而又非常复杂的非线性优化问题。

Furthermore, these results have passed largely unknown and unreferenced in the nonlinear optimization literature.

而且，这些结果都没在非线性优化文献中得到重视和引用。

The result of calculation example shows that AGA is practical and effective.AGA may be wieldy applied to handling comples nonlinear optimal problems in enginering.

实例计算的结果说明了，该方法是可行的和有效的，在处理各种工程复杂非线性优化问题中具有广泛的应用价值。

By using the quadratic regression orthogonal experimental method with three factors and five levels, the relationships between the microwave power applied, the sample thickness, the pressure in drying chamber and the rehydration ratios, chlorophyll and vitamin C retention ratios of dried Chinese gooseberry slices, as well as the energy consumption of drying process, were analyzed, and the regression mathematical models for experimental indices and factors were established. At last, the optimal combination of the parameters for the microwave-vacuum drying technology of Chinese gooseberry slices was obtained through nonlinear optimization method with many targets.

通过3因素5水平的二次回归正交试验，分析了微波功率、物料厚度、干燥室压力与猕猴桃切片干制品复水率、叶绿素含量、维生素C含量及单位耗电量的关系，建立了各指标与试验因素间的回归数学模型，并利用多目标非线性优化方法，确定了猕猴桃切片微波真空干燥最优工艺参数。

2Based on the nonlinear theory, we found the reservoir seismic nonlinearprediction and evaluation method technology, it is constituted by three nonlinearmethods and the technologys of the fracture prediction, the seismic inversion and thereservoir synthesis prediction evaluation: The seismic nonlinear prediction ofreservoir fracture is one new method which is composed with the phase spacereconstruction, the nonlinear parameters pick-up technology and the syntheticprediction evaluation method. The reservoir seismic high resolution nonlinearinversion is a new seismic inversion way which the BP algorithm is embeded in theauto-adapted genetic algorithms interior to have the predominances of neural networktechnology and genetic algorithms, it adopts the new embedded GA-BP mixalgorithms and the nonlinear mapping technology, and realizes the inversionautomatically, obtains the high resolution seismic inversion profile. The reservoirseismic nonlinear synthesis prediction and evaluation is a new method which iscombined organically of genetic algorithms and adaptive neural fuzzy inferencesystem, it will optimize the new seismic attribute space which are processed to take the input, uses the new adaptive mix algorithm which GDand LSE(least-square estimation) mix algorithms of ANFIS network insert to the GAinterior and taboo search algorithms is added to the intercrossed operation place,the simulation of the evaluation parameters is used quantitative evaluation guide lineto the reservoir quality and oil-gas distribution.

2基于非线性理论，创建了储层地震非线性预测与评价方法技术，它是由裂缝预测、地震反演和储层综合预测与评价等三大非线性方法与技术组成：储层裂缝地震非线性预测是由相空间重建、非线性参数提取与预测技术及综合评价方法组成的一种新型裂缝预测方法；储层地震高分辨率非线性反演是将BP算法嵌入自适应遗传算法内部所构成的集遗传算法和神经网络技术优势于一体的新的地震反演方法，它采用嵌入式新的混合算法及非线性映射技术，自动实现反演，获得高分辨率地震反演剖面；储层地震非线性综合预测与评价是由遗传算法与自适应神经网络—模糊推理系统有机地相结合而产生的储层预测与评价的新方法，它将优化处理所形成的新地震属性参数空间作为输入，采用将ANFIS网络中的混合算法嵌入到GA算法内部与禁忌搜索算法加在交叉操作处产生新的自适应混合算法，将综合评价参数作为储层品质和含油气性的定量评价指标。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。