约束优化

Based on a great many literature, this paper analyzes and summarizes the genetic algorithm for the design of structural optimization. The basic conceptions and primary characteristics are introduced in this paper. This paper discuss some primary factor when genetic algorithm applied on optimal design, for example the mathematical model、the constrained problem、the initial population and the controls parameter of genetic algorithm Aimed at the characteristic of structural optimization and finite-element analysis, this paper accomplishes the optimal program based on the simple genetic algorithm.

在广泛阅读文献和调研的基础上，本文对遗传算法及其在结构优化设计应用中的相关内容进行了分析和综合，对结构优化设计的基本概念、主要特点进行了介绍，对遗传算法应用于结构优化设计时的数学建模、约束条件处理、初始种群的产生及其遗传算法控制参数的选择几个关键因素作了概要的分析与研究。

Based on a great many literature, this paper analyzes and summarizes the genetic algorithm for the design of structural optimization. The basic conceptions and primary characteristics are introduced in this paper. This paper discuss some primary factor when genetic algorithm applied on optimal design, for example the mathematical model、the constrained problem、the initial population and the controls parameter of genetic algorithmAimed at the characteristic of structural optimization and finite-element analysis, this paper accomplishes the optimal program based on the simple genetic algorithm.

在广泛阅读文献和调研的基础上，本文对遗传算法及其在结构优化设计应用中的相关内容进行了分析和综合，对结构优化设计的基本概念、主要特点进行了介绍，对遗传算法应用于结构优化设计时的数学建模、约束条件处理、初始种群的产生及其遗传算法控制参数的选择几个关键因素作了概要的分析与研究。

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。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

刘莹 ，刘三阳，盛宝怀运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理。引入向量优化弱Benson真有效元的概念，对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足Lagrange乘子型的必要及充分条件，并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件。

The effective heat-transfer temperature difference of every effect of multi-effect evaporation subsystem and the preheat temperature rise Δt_(p,j of every level of multi-level preheat subsystem of the design model were distributed by equal heating area, equal heat-transfer temperature difference, and free proration methods.

设计型模型对多效蒸发子系统各效有效传热温差Δt_i的分配和多级预热子系统各级预热温升Δt_的分配分别采用等面积法、等温差法、自由配比法等进行分配并采用矩阵法结合迭代法进行设计模拟计算，其中自由配比法巧妙地将具有复杂约束条件的决策变量Δt_i和Δt_转化为取值0～1的中间决策变量τ_i、τ_，为Δt_i和Δt_的自由搜索进而为优化设计提供了一个简便的方法；在常规设计模拟计算的基础上，建立了复杂多效蒸发系统优化设计模型，该模型以系统年总费用最小为优化目标，以生蒸汽温度T_0、冷凝器中二次蒸汽温度T_K、蒸发温差配比系数τ_i和预热温升配比系数τ_为决策变量，采用遗传算法结合矩阵法求解。

The uniformity degree and rank of the population are given to measure the distribution and quality of the solutions in the population based on the characteristic. Using the uniform degree of the population as objective function and the rank as the constrained condition, the bi-objective optimization problem is transformed into a single objective constrained optimization problem. The computational equations of the charge and force exerted on the particles are presented.

针对这一特点，定义了种群的均匀度和序值，来度量种群中解的分布和质量，将双目标优化问题转化为以均匀度为目标函数，序值为约束条件的单目标优化问题；设计了双目标优化问题粒子的电荷和受力的计算公式，提出了一种新的类电磁算法求解问题。

As to the topology structure of the network with constraints, a new tree encoding for Genetic Algorithms was developed to represent a tree solution containing the information of degree and connectivity on for its corresongding genetic operators, which could be used to solve the minimum spanning tree problem with degree constraint, capacity constraint, and leaf constraint.

本项目主要研究了带约束网络拓扑结构的设计与优化；供应链网络拓扑结构的设计与优化；移动信息网络位置管理的策略与优化。

An optimization model of electricity and heat efficiency about intermediate frequency coreless induction furnace in the nonmagnetic process is established by using some restriction parameters such as power supply frequency and the diameter of steel stab,and its optimization design is done based on particle swarm optimization algorithms.

以电源频率和坯料直径为约束参数，建立了无芯中频感应电炉无磁性期电热效率优化模型，采用粒子群优化算法对其进行了优化。

In chapter 7, quality loss cost is first used in the model of simultaneous design of tolerance, and economically attainable accuracy of position is first considered as constraint condition. It is first proven that the function of simultaneous design of tolerance is non-convex program; discrete and continuos Simulated Annealing are introduced; the optimum software to solve this model is given.

第七章首次将质量损失成本用于公差并行设计的优化数学模型中，并首次考虑位置精度的经济加工精度范围作为约束条件；论证了公差并行设计优化模型的非凸规划问题；着重介绍了离散型和连续型的模拟退火算法SA；研制了公差并行设计的优化软件。

Taking Rong hu bridge project as the background, the paper Studies on the optimization of dead load cable tension, construct system of controlling, effect of non-linear factor, limit bearing capacity of structure and spatial stress of concrete-filled steel tubular tower and the combination of girder, which are based on the hybrid cable-stayed bridge.Asking for the maximal deformation of tower and girder to be minimized and cable permissible stress as constraint conditions, the paper tries to solve the ideal dead load cable tension by combining finite element calculation and optimize analysis.

本文以蓉湖大桥工程为背景，就混合梁斜拉桥的成桥恒载索力优化、施工监控体系、过程非线性因素影响、结构极限承载力、索塔和主梁结合部的空间应力分析等问题开展研究：关于索力的优化，是以斜拉桥索塔和梁的最大变位最小为目标，以拉索容许应力为约束条件，采用有限元计算与优化分析相结合的方法来确定斜拉桥的成桥合理恒载索力。

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。