非线性优化

The main theorem of this paper is to, firstly, on the grounds of experience preliminarily estimate the parameter of the pavement nonlinear model, simulate the process with computer procedure, and check the result with the data collected in sit, then set the aim function and the superiority back-calculation method, if the function is not satisfied, it is to the method adjust the parameter and make the model impend the actuality, If the function is satisfied, it is to end the process, and record the stress, deformation, displacement and the parameter as the actual condition.

本文分析的主要原理：首先根据经验，初估路面结构层应力应变非线性参数，利用计算机程序模拟承载板试验测回弹弯沉的过程，通过现场实测的弯沉数据来检核该模拟过程的真实性，设定目标函数，选定适当的优化反算方法，当目标函数不满足时，即利用该优化反算方法调整本构模型参数，使得模型能够逐步向真实解逼近，当目标函数得到满足时，则认为此时反算得到的路面结构层的应力、应变、位移场为真实的应力、应变、位移场，所推算得到的非线性应力应变模型为真实的路面结构层应力应变模型。

To inequality constraint s, a check procedure and a penalty function procedure are proposed, and equality constraints are dealt with by a procedure of solving equations in which tear equations may be converged by an iterating way or a penalty function way.

在无约束非线性规划问题全局优化的模拟退火算法基础上，进行有约束问题求解的进一步探讨，对不等式约束条件提出了检验法和罚函数法的处理方法，对等式约束条件开发了罚函数法和解方程法的求解步骤，并进行了分析比较，从而形成了完整的求取非线性规划问题全局优化的模拟退火算法。

In view of the problem of parametric optimization in a nonlinear control system,this paper presents a new simulating method of optimization to be combined with the theory of a nonlinear control system,optimization theory and genetic algorithm.

摘 要］本文针对非线性控制系统参数优化问题，结合非线性控制系统理论、最优化理论及遗传算法，提出了一种新的仿真优化方法。

Sampling points were obtained by using optimal Latin hypercube design of experimental method,meantime,in order to improve computing efficiency,application of stepwise regression response surface approximate method in the MDO system of the vehicle crashworthiness and free mode of Body-In-White,the approximate model was optimized by using sequential quadratic programming method.

采用最优拉丁方试验设计方法进行样本数据设计，同时，为了提高计算效率，采用了一种新型的响应面构建方法——逐步回归响应面方法构建了整车耐撞性与白车身自由模态多学科系统的近似模型，利用序列二次规划优化方法对此近似模型进行优化，避免了整车碰撞传统优化设计方法计算量大，在碰撞非线性系统优化中常常易导致收敛缓慢甚至不收敛的缺点，在满足了CMVDR294安全法规的同时，使得白车身的扭转模态值得到提高，汽车重量得到较大程度的减轻。

On global optimal algorithms, a heuristic 0-1 Integer Liner Programming algorithm is achieved, which combines heuristic enumeration method and revised simplex method. Simulation experiments show that the degree and optimization efficiency in our algorithm is obviously improved compared with the MATLAB 7 bintprog function that is a 0-1 integer programming algorithm. Moreover our algorithm isn\'t relevant to the scale changes of Web services composition and candidate service sets, thus it is applicable for the scenes that the scales of Web services composition changed dynamically. But for Web services composition with service alliance, the algorithm is unable because the non-linear global optimal model of the fitness function and QoS constraints can\'t be expressed in linear mode.

在全局优化算法研究上，基于启发式0-1整线性规划算法结合了修正单纯形法和启发式枚举法，仿真实验表明该算法与MATLAB 7的0-1整数规划方法比较，在优化程度及优化效率上得到了显著改进，并且对服务组合和候选服务集合的规模变化没有明显的相关性，因而该算法可用于服务组合规模动态变化的场景，但该算法不能应用于存在服务联盟的非线性全局优化模型。

By use of first-order linear expansion of Taylor series, the linearization process of both nonlinear constraints and objective function of long-term optimal scheduling model are performed and an optimal scheduling model based on seccessive linear programming is built; an approach to solve Optimal scheduling of cascade hydropower station problem by seccessive linear programming is put forward, the scale-down factor of iteration step length is used to ensure that the algorithm can converge to the optimal solution of optimization problem quickly and accurately.

通过采用泰勒级数一阶描述形式，对优化调度目标函数和约束条件中的非线性约束进行线性化处理，建立了基于连续线性规划算法的优化调度数学模型，提出了用连续线性规划技术求解梯级水电站优化调度问题的算法，并采用迭代步长的动态比例缩减因子保证算法能快速准确地收敛到优化问题的最优解。

On this basis, according to historical data, apply ANN and differential simulation method to get the quantitatively correlative relations between each production and its own influence factors, and introduce the new methods of prediction for dynamic indexes with gas-field development (The combinatorial prediction method based on fuzzy comprehensive evaluation, the method of ANN to select optimally combinatorial prediction models and the ANN prediction method based on genetic algorithm).(2) Base on mathematical programming, combine with quantitative economics and techno-economics, introduce economical indexes to establish production"s distribution optimal model, production"s constitution optimal model and measured production"s constitution optimal model, including multi-objective models and five-years models. Upon this, the optimal project for all gas field and each gas-collected factory can be got. Also, introduce the time value of capitals to improve on these models.(3) Base on the optimal solution theory and algorithm theory for the nonlinear programming problem, introduce the SUMT algorithm and genetic algorithm to study how to solve the models, and on the basis of normal genetic algorithm, make use of auto-adaptively modulating method to improve on normal genetic algorithm; Base on algorithm"s convergence theory and calculation"s complexity theory to analyze seriatim SUMT algorithm"s convergence and genetic algorithms convergence, and compare performance with each other.

在此基础上，利用神经网络方法和微分模拟方法根据历史数据得到各分项产量与其影响因素之间的定量关联关系，并引入气田开发动态指标新的预测方法(基于模糊综合评判的组合预测方法、神经网络优选组合预测模型预测方法以及基于遗传优化的神经网络预测方法)；(2)以数学规划为基础，结合数量经济学和技术经济学，引入经济指标建立产量分配优化模型、产量构成优化模型、措施产量构成优化模型、气田开发多目标规划模型以及五年规划模型，进而获得全气田及各采气厂的最优方案，并引入资金时间价值对五年规划模型进行改进；(3)以非线性规划问题的最优解及算法理论为基础，引入SUMT算法以及遗传算法对模型的求解进行研究，并在原有的遗传算法基础上，引入自适应调整方法对遗传算法进行改进；以算法的收敛性理论和计算复杂性理论为基础，逐一分析SUMT算法以及遗传算法的收敛性，并比较三种算法的优劣性。

But the researches on vibration characteristics of motor-driven elastic linkage systems have shown that the dynamic responses of linkage systems are nonlinear and multi-modality. They may bring some nonlinear vibration, such as superharmonic resonances, subharmonic resonances, multiple resonances, and combination resonances, under some circumstances.

然而，弹性连杆机构的非线性振动特性研究表明，机构的动态响应特性十分复杂，并且在一定条件下会产生超谐共振、亚谐共振、多重共振、组合共振等非线性振动行为，这些共振就会对以机构动态性能为目标的优化设计产生重要影响，而使优化设计工作常常只能得到一个局部最优值，甚至只是一个比初始设计略微好些的设计点。

It includes two aspects in content: one is the best choice for plane disposal of pipeline, and its methods follows as decision-making plot, simple trapeziform and optimizing trunkform etc; the other one is optimizing pipe parameter when the plane disposal of pipeline has been fixed, and the methods of which are linear programming, unlinear programming, dynamic optimizing, direct optimizing, hereditary arithmetic and so on.

污水管网优化设计包括两个方面的内容：一是管线平面布置的优化选择；其方法有：决策图法，简约梯度法，优化树法等。二是在管线平面布置已定情况下进行管道参数的优化；其方法有：线性规划法，非线性规划法，动态优化法，遗传算法，直接优化法等。

One is a large scale nonlinear programming model with equalities, the other is a more complicated NP hard and nonlinear compound 0-1 programming model. It is difficult for the existed algorithms to fulfill the demands of efficiency and size for the above problems. Two corresponding genetic algorithms are presented, in which several suitable genetic operations are constructed to make the optimization search process in the range of feasible solutions.

一个为大规模的带等式约束的非线性规划模型，另一个为更为复杂的带NP难解问题的混合非线性0-1规划，已有算法都难以满足上述两种问题的求解规模及效率的需要，我们给出了相应的遗传算法，确定了适当的遗传操作，使得问题的寻优过程始终都在可行解范围内进行，不仅提高了优化速度，而且有效地提高了优化效果。

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。