优化问题

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。

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

Firstly, according to the difficulties in the optimization of chemical engineering and the intrinsic disadvantage of deterministic optimization algorithms, this work analyzed the importance and advantage of stochastic algorithms, and proposed some important aspects in research on them. Secondly, genetic algorithm was applied to two problems of data driven modeling, one of which was combination problem, the other was mixed integer nonlinear programming. Thirdly, systemic investigations were made on the basic structure, dynamic behavior and modifications of particle swarm optimization. Lastly, two kinds of proposed PSO algorithms were applied on calculation of phase equilibrium, which is nonconvex optimization.

本文首先根据化工优化中存在的困难和确定性优化算法内在的缺点，分析了随机优化算法的重要性，并提出研究随机优化算法应注意的问题；其次，将遗传算法应用于两个数据驱动建模问题，一为组合优化问题，一为混合整数优化问题；再次，从粒子群优化算法的基本结构、运动行为、改进方法做了系统的研究：最后，将提出的两种改进粒子群优化算法应用于相平衡计算问题，为非凸全局优化问题。

A novel hybrid algorithm, which combines predictor-corrector primal-dual interior point method and genetic algorithm, is presented for dynamic and static reactive optimization in this dissertation. The algorithm fully make use of the advantage of interior point method in solving successive optimization problem and the advantage of genetic algorithm in solving discrete optimization problem. The original problem is divided into three parts: total successive problem, discrete problem and successive problem.

结合内点法和遗传算法，本文提出了一种新颖的混合算法用于求解动、静态无功优化问题，算法充分利用了内点法易于求解连续优化问题和遗传算法易于求解离散优化问题的优势，将原优化问题分解为初步的连续优化问题、离散变量优化问题、连续变量优化问题这三个子问题分别求解。

Decision-making of ballast water adjustment of floating dock is studied as a two-step optimization problem. Two mathematical models are constructed for minimizing the ballast water adjustment quantity of every tank needed and the trim of the floating dock respectively.

将调节浮船坞浮态的调水计划决策问题归结为调节量优化和调水时间优化两步优化问题，分别提出了有约束问题的优化模型并详细介绍了应用惩罚函数法对优化问题进行求解的方法。

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 fine-grained genetic algorithm based algorithm which is for the parameters optimization problem of agent model is proposed. The fine-grained genetic algorithm is used to solve the parameters optimization problem of agent model. As to the parameters optimization problem of the agents colony model, the first step is to define the concept of "the parameters mode of the combat agents colony" to describe the parameters of the combat agent colony model. Then the genetic algorithm is used to solve the optimization problem with the parameters mode of the combat agent colony model as the genetic individual. Besides the algorithm, the algorithm dispatch tactic is also considered. And the two level sequence dispatch tactic and the two level nesting dispatch tactic are put forward for those complex parameters optimization problem. At last, the model parameters optimization under antagonism codition is studied. The means to solve this problem is to translate it into a kind of antagonism problem, then use the competitive co-evolutionary genetic algorithms to solve it.

其中：提出了一种基于细粒度模型的作战智能体模型参数优化求解算法，用细粒度模型遗传算法求解作战智能体模型参数优化问题；提出了"作战智能体群体参数模式"的概念，对作战智能体群体模型参数进行形式化描述，再以作战智能体群体参数模式为遗传个体，应用遗传算法求解作战智能体群体模型参数的优化问题；研究了上述优化问题求解算法的调度策略，提出了分层模型参数优化算法的双层顺序调度策略和双层嵌套调度策略，解决复杂的模型参数优化问题；将对抗条件下作战模型参数的优化问题转化为一种对抗性问题，应用竞争性共同进化遗传算法，进行求解。

The question of searching characteristic points or straight lines on moving rigid body is decomposed into two relatively independent sub-questions. The first one is to evaluate the characteristic of points and straight lines on moving rigid body, whose mathematics model is a kind of special non-differential max-mini optimal problem with inequality constraints. By the method of Saddle-point Programming and maximum entropy, the problem can be transformed as a differential optimal problem with single objective. The second oner is to search approximative character points or straight lines on moving rigid body within design space, whose mathematic model is nonlinear and non-differential problem with multiple constraints.

本文将在运动刚体上寻找特征点或直线的优化问题分解为两个相对独立的子问题，一是对运动刚体上点或直线的特征性评定，其实质是平面曲线的圆度或直线度的评定问题，优化模型是以最大误差为最小作为优化目标的约束不可微的优化问题，本文采用鞍点规划和极大熵方法，将其转化为单目标可微优化模型；二是在设计空间内，寻找运动刚体上特征性评定指标最小的近似特征点或直线，其优化模型是非线性、多约束的不可微优化问题，本文提出用遗传算法和BFGS局部搜索法相结合来求解。

The calculation of an example indicates that the combined optimal model is better than the single one in terms of simul.

大坝安全的组合优化监控模型实际上为一带约束的优化问题，将DNA遗传算法应用于大坝安全监控领域中，用罚函数法将有约束的优化问题转换为无约束的优化问题，建立了大坝安全监控的组合优化模型。

As the shape optimization design of structural element sections belong to structural optimization,which has its own traits such as discreteness, nondifferentiable and non-convexity,while the traditional optimal methods are not applicable.

结构截面形状优化设计属于工程结构优化问题，由于工程结构优化问题具有离散性、不可微性和非凸性等特点，而传统的优化算法对所优化的问题往往要求连续、可微、非凹等前提条件，所以已不再适合用于工程结构优化问题的求解。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。