最优法

The formal solution of partial differential equations is given on characteristic line, the existence of the optimal control is proven by using Ekeland\'s variational principle, Gronwall Lemma and adjoint system, then the necessary condition of optimality is obtained by means of the conception of normal cone.

用特征线法表示出偏微分方程的形式解，利用Ekeland变分原理，Gronwall引理和共轭系统证明了最优控制的存在性，并借助于法锥概念得到了最优控制的必要性条件。

It is improved to solve the prematurely and stagnation problems of traditional Ant Colony Optimization in the paper. First, mean value method is used to update pheromone to avoid premature convergence which leads to non-globally optimal solution. Second, Pheromone is updated by Best Track to speed the rate of convergence which will help to avoid locally optimal solution.

本文针对基本蚁群算法比较容易陷入早熟和停滞，对现有蚁群算法的信息素更新规则进行了改进，一是采用平均值法更新信息素，避免算法过早收敛于非全局最优解；二是采用最佳路径法更新信息素，可加快收敛速度，并使算法跳出局部最优解。

Simulation of Loop domain near active site was carried out with the PROLOOP programm. The initial model was energy-minimized by the 500 steps of steepest descents method and 500 steps of conjugate gradients . The Vanderwal contacts were eliminated, and the energy of the static electric interation and hydrogen binding were adjusted

优化工作用PROLOOP程序，将活性中心附近LOOP前后的有关残基构象进行最佳拟合，并采用GROMOS软件包中的能量优化程序，作500步最陡速降法及500步共扼梯度法进行优化，彻底消除范德华半径重叠，并进行原子间静电和氢键作用的优化调整，最终得到UK-B链最优结构。

E forecasting precision with the method of moving average can be improved by the optimal moving step length n.

为选用移动平均法中最优移动步长n，利用计算机的计算功能，设计了一种较为精确地确定移动平均法中最优移动步长n的方法。

The optimal models and algorithms for making up pairs and non-pairs locomotive turn-around diagram are given out. Specially, a more efficient way to consider both the optimum and the equilibrium of this problem is also presented as follows: at first formulate the network flow model of this problem and solve it by the method of the minimal cost flow and then use the labeling method to readjust the solution.

对成对和不成对机车周转图编制问题进行了探讨，给出了其最优配置的数学模型和算法；在此基础上，提出了把均衡性与最优化综合考虑的不成对机车周转图的改进算法——首先建立网络流模型用最小费用流算法求得问题的初始最优解，然后用标记法对该解进行调整，使其在最优的基础上达到均衡。

Based on the method of multi-objective fuzzy optimization and the overhead traveling crane design, a mathematical model of fuzzy optimization for main box beam section is established. A fuzzy goal anthology is constructed. The fuzziness of multi-objective function and constraints is defined. The transformation of the fuzzy constraints set to normal constraints set in real number domain is realized by applying optimal level cut set method. The optimal solution and optimal constraint value of sub-objective function in the feasible field are found using the genetic algorithms.

应用多目标模糊优化方法，以工程设计中桥式起重机箱形主梁设计为实例，建立了桥式起重机箱形主梁多目标模糊优化设计的数学模型，构造了模糊目标集，确定了多目标函数的模糊性和约束的模糊性，并应用最优水平截集法实现了模糊约束到实数论域上的集合转换，从而用遗传算法寻求到子目标函数在可行域空间的最优解和约束最优值。

The optimality of the derived recursive algorithm is described based on the duality between the theory of optimal estimation and optimal process.

通过最优估计与最优控制理论的对偶性，说明了递推算法的最优估计解的存在和唯一性。

A new optimal power flow model with reliability constraint is proposed to obtain an economic and secure operation schedule of the power system, where the reliability index constraint is constructed based on z transform theory to take the uncertainties of electric power system into account, and the objective aims at minimizing the total cost of the system to satisfy the expected loss of load probability.

提出一种考虑可靠性指标的最优潮流模型。该模型能考虑系统中的随机因素，通过z变换法构造电力系统的可靠性指标约束，将该约束添加到经典最优潮流模型中共同求解，从而使电为系统的调度或控制能在满足一定的失负荷概率指标的前提下实现最优运行。

The result pointed out that the vertical distribution of foliage for each species was different,however,generally speaking,the foliage in upper crown (0.3CL) for broad-leaved species in natural secondary forest took a small percentage,about 10%;in middle or middle lower of the crown(0.4CL to 0.8CL) the branches here took the majority percentage of whole foliage,almost 60%to 75%;but in lower crown(0.8CL),there was about 10%of whole foliage.(5)The interspecies competition of trees in secondary forest was expressed by Hegyi competitioin index,and the active competitor was calculated by the competition zone radius and the tree position,DBH,and distance in the zone,it was not all competitors in tranditional calculation.The study introduced crown area overlap index to describe the crown competition between subject tree and its competitors,furthermore,the crown area was classified into 5 levels with a method of equal crown projection area,therefor,the resulting crown area overlap index showed more realities of existing stand conditons.(6)Based on the theoretics of multiply divide,the spatial strcture optimizing model of secondary forest stand selective thinning was developed by diversity mingling,aggregation index,competition index and crown area overlap index,also designed 10 constraint conditions which were related to forestry meanings,the objective function was solved by the implicit enumeration method with LINGO 9.0,using 0-1 integer programming.

并且得出，每个树种在树冠内相对高度上的叶量的垂直分布是不同的，天然次生林阔叶树种的叶量在树冠的上部(0.3CL以下)所占比例很小，约占10%左右；在树冠的中部以及中下部(0.4CL～0.8CL)，叶量所占比例最大，几乎集中了整个树冠60%～75%的叶量；而在树冠的下部(0.8CL以下)，几乎占很少的叶量，大约10%左右。5、采用Hegyi竞争指数来表现次生林内林木的竞争关系，并且根据竞争圈的大小和林木在竞争圈内的分布位置、大小与距离来计算有效的竞争木，并不是传统意义上的全部竞争木；本研究提出用树冠叠加指数来表示林木与周围树木的树冠竞争情况，并采用等树冠投影面积法把树冠分为5级，这样计算的树冠叠加指数更加与现实林分相符。6、本研究基于乘除法的思想，用多样性混交度、聚集指数、竞争指数和树冠叠加指数构建了天然次生林择伐空间优化模型，设计了10个与林学意义相一致的约束条件，并采用0-1整数规划的思路，在LINGO9.0软件中使用了隐枚举法对目标函数求得最优解。7、以M702标准地为应用实例，具体计算出了每株采伐木，经过择伐后，目标函数值按模型设计的要求发生了极大的改变，增加了5倍多，说明了最后这个解的优良性，满足了设计的要求。

This thesis applies factor analysis in ship type optimization and uses this method to comprehensively grade the alternative ship types of second Carriage iron ore shipment from Majishan to Bao steel and finally gets the optimal ship type for this line.

本论文主要内容包括：第二章主要分析了国际铁矿石运输现状；第三章介绍我国进口铁矿石的情况，分析了我们铁矿石运输存在的不足并预测了发展趋势；第四章介绍了传统的船型论证方法、步骤；第五章计算了从马迹山到宝钢原料码头的船型方案的主要指标，并用传统的方法做了船型方案的选优；第六章介绍了因子分析法在船型论证中的应用，并用因子分析法对船型选优做了综合评定，得出适合马迹山到宝钢的二程矿石运输的最优船型。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。