The method of wing shape optimization of space shutlle has been developed with penalty function approach in which the objective function is the mass of the wing and the constraints are the hypersonic re - entry flight cross range , lift / drag ratio , and subsonic flight lift / drag ratio , the margin of the longitudial static stability and the magnitude of the horizontal landing speed etc 摘要介绍了在满足高超音速再入横向机动航程，高超音速再入飞行时的升阻比，亚音速进场飞行时的升阻比，纵向静稳定性裕度和水平着陆速度等飞行性能设计要求下，用罚函数法寻求使航天飞机机翼质量为最小的外形优化方法并给出了算例。
The parameter control methods are very similar to penalty function methods , both of them are to solve constrained optimization problems by solving a series of sub - unconstrained optimization problems . but parameter control methods are different from penalty function methods . firstly , the penalty coefficient of penalty function methods are preassigned , while the parameters of parameter control methodsare generated automatically according to some rule prescribed 参数控制算法虽然与罚函数法非常类似，都是通过求解一系列无约束极小化问题来逼近约束优化问题的最优解，但罚函数法中的罚因子是预先设定的，而参数控制算法中的参数是自动产生的。
This paper summarized the characteristic and localizations of the special contact elements that can simulate the joints in rockmass . except for those , three kinds of numerical methods for dynamic contact analysis were introduced . then , the augment lagrangian method that combined lagrangian multiplier and penalty function was applied to the dynamic contact analysis with friction 本文阐述了模拟岩体裂隙节理的特殊接触面单元，分析其特点和局限性；介绍了三种处理动力接触问题的数值算法，利用lagrange乘子法和罚函数法联合的增广lagrange乘子法建立起裂隙节理的动力摩擦接触条件和本构方程以及有限元基本方程，并运用此数值方法分析一具有贯通节理面的动力摩擦接触问题，得出一些基本规律。
First , the nonlinear ls problem without constraint is converted to that subjected to inequality constraints by putting constraints on the do as of the received signals and toas of the first arrived signal with geometrically based single - bounce ( gbsb ) statistical channel model and cost - 207 model . then , a penalty function is used in the estimation of ms position 首先，用基于几何结构的单次反射圆模型和cost - 207模型，对期望定位用户的各条多径信号的波达方向和最先到达多径信号的时间进行约束，将传统的解无约束的非线性最小二乘定位问题或近似线性最小二乘定位问题转化为解不等式约束的非线性最小二乘定位问题；然后，用内点罚函数法估计移动台的位置。
In the fourth chapter , several methods for handling constrains by genetic algorithms for nonlinear programming problems are introduced . these methods were grouped into four categories : methods based on preserving feasibility of solutions , methods based on penalty functions , methods which make a clear distinction between feasible and infeasible solutions and other hybrid methods 在第四章中介绍了处理约束的四类方法：算子修正法，罚函数法，可行域搜索法，以及混合遗传算法，并对这些方法做了详细的分析，指出了他们优劣之处。
Optimal design with three variables is then done to the elbow - bar mechanism of the mp1040b moulding machine by utilizing the method of punishing function for constraint problems and variational scale for unconstraint problems . the optimal target function is the maxium of gradient in one work travel for the moulding plank of the elbow - bar mechanism . the result shows that the maximal gradient of moulding plank in one motion period declines by 25 . 7 after optimization , and the angular acceleration of the bottom moulding plank decreases greatly 动力学分析中，各构件的质量和转动惯量是通过pro / engineer软件，先建立各个构件几何模型而求得；然后，利用解决约束问题的罚函数法和处理无约束问题的变尺度法对mp1040b型模切机肘杆机构进行三个设计变量的优化设计，优化目标函数为肘杆机构的下模切板在一个工作行程中达到的最大倾斜程度；通过优化设计，模切机肘杆机构的下模切板在一个工作行程中的最大倾斜程度降低了25 . 7 ，其角加速度明显减小，提高了模切机动力学性能。
5 , under the dynamic reliability constraint of isolation or seismic decrease equipment , taking the mean largest displacement of the main structure as the objective function , an optimal method of the base - isolation structure and the " adding story and seismic decrease " structure ( the tmd seismic decrease structure ) is brought forward by using the penalty function method to solve the optimal isolation and seismic parameters 5 、提出了以结构最大位移响应的期望值为目标函数，以控制装置反应的动力可靠度为约束条件，运用罚函数法优化求解基础隔震与“加层减震” ( tmd减震)结构中隔震装置和减震装置参数的优选方法。
The main achievements in this paper are summarized as follows . firstly , with the purpose of solving the low precision problem in the processing procedure of constraint condition , the augmented lagrange multiplier method is applied instead of the penalty function method . the practice indicates that the augmented lagrange multiplier method has a good effect on the enhancement of the precision 本文的主要工作是:首先针对罚函数法处理约束所带来的约束条件满足精度不高的问题,尝试采用增广拉格朗日乘子法处理约束,并且实践证明,用该方法可以获得很好的效果,得到了能够更好满足约束指标的最优解。
Abstract : optimum design of individual foundation considering the effect of strength and deformation is discussed in this paper . the optimal mathematical model of determining the bottom surface demention of individual foundation under eccentric load is derived . the optimal solution is decided by method of optimization and the method we select is penalty fonction and complex method . the program of optimum algorithm is comiled and design and drawing of individual foundation is completed . the final results of engineering samples suggest that the cost of material and engineering amount can reduce approximatly 5 % - 6 % . a fair - sized economic efficiency can be received by using optimum method to design foundation 文摘:笔者讨论了独立基础在考虑强度和变形条件下的优化设计.导出了确定独立基础底面尺寸的优化数学模型，导出了偏心荷载作用下基础的高度和底面配筋的计算公式，求解优化解采用最优化方法的复合形法和罚函数法.通过基础实例和工程实例的计算表明优化设计可以节省材料和工程量5 16 .所以将本文优化方法用于基础设计，会产生较大的经济效益
Based on the genetic algorithm ' s global searching capability with probability regulation and euclid ' s space distance metric to settle multi - objective , the algorithm that integrates multi - objective ' s decision - making into the modified genetic algorithm to solute the optimal model with discrete variables and multi - objective is proposed . during the algorithm ' s design , the euclid ' s space distance metric is proposed to transform the multi - objective problem into single objective problem . and some modified measure to fitness function and crossover probability and mutation probability are used to improve the performance of the algorithm and avoid premature convergence 算法设计过程中，利用欧几里德空间距离准则和罚函数法，将含有约束条件的多目标规划问题转化为无约束的单目标优化问题；针对简单遗传算法出现的早熟，构造随进化代数动态调整适应度的适应度函数和随个体适应度自适应调整的交叉、变异概率；提出比例选择与精英保留策略相结合的选择、两点交叉和简单变异的改进遗传算法。
