约束优化

How to deal with the restrictions of deep excavation is a very difficult problem. This paper analyzes the restrictions of pile-support structure detailedly, uses a castigatory function to deal with the restrictions, and adds the castigation to the function. Now the problem has changed to solve a minimal problem, and GA can be used to the optimal design successfully.

束条件的处理是遗传算法应用到深基坑支护结构优化的难题和重点，本文详细分析了桩撑支护结构的约束条件，采用了罚函数法对约束条件进行处理并反映到适应度函数上，使其变为无约束的极小值问题，从而使遗传算法得以顺利实施。

The primary work of this paper includes: 1 The general process and the fundamental theory of genetic algorithm is introduced systematically, which is also be applied to an example; 2 The penalty function method and the constraint tournament method are introduced in the paper, which are used to process the constraint limit. Via analyzing the basic principle of NSGA-II ,which is elaborated in the paper, the fast non- dominated sorting method, congestion distance and its comparison operator, the elite strategy and the main process of NSGA-II is researched particularly. 3 Via modeling the fire distribution problem, the model is computed by the algorithm of NSGA-II, which is combined with both the penalty function method and the restraint league tournament method The optimization of two goals are also realized in the paper. The results derived from the VC++6.0 indicate that, two algorithms both have the high convergence, simultaneously the Pareto optimal solution also maintain the variety of distribution.

本文所作的主要工作如下：系统地介绍了遗传算法的一般流程和基本理论，并应用于一个函数优化的实例；研究了用于处理约束限制的罚函数法和约束联赛法，论述了NSGA-II的基本原理，并对其提出的快速非支配排序法、拥挤度及其比较算子、精英策略及NSGA-II的主要流程作了详细的研究；建立了火力分配问题的模型，并将NSGA-II算法分别与罚函数法和约束联赛法相结合对该模型进行了计算，实现了对两个目标的最优化；用VC++6.0编程计算后所得的结果表明，两种算法均具有很好的收敛性，同时Pareto最优解也保持了好的多样性分布。

The model is set up in view of the optimum design of midship section of container ships with crankle strength and frequency constraints according to CCS rules and thin-walled beam theory .

结合CCS规范和薄壁杆件理论，建立了考虑弯扭强度和频率约束的集装箱船中剖面优化设计的模型，考虑到中剖面优化设计中的设计变量为连续和离散的混合变量，利用isight中集成的自适应模拟退火算法，建立了巴拿马型集装箱船中剖面优化设计系统，并对3100TEU集装箱船中剖面进行了优化设计，取得了合理的结果。

Since any equality constraint is equivalent to two inequality constraints, the algorithm LTR can be used for solving nonsmooth optimization problems with equality and inequality constraints.

同时，由于等式约束等价于两个不等式约束，故算法LTR也适合于求解带一般线性约束的非光滑优化问题。

The whole state space is divided into invariant subspace, safe subspace, dangerous subspace and dead subspace according to the constraints and the safe margin of the system, and the state reference trajectory is chosen with respect to the subspace in which the state prediction lies in, in this way GPC is applied under the prerequisite for the viability of the system.

研究了系统在线性不等式约束条件下的预测控制问题，将广义预测控制算法化为对控制量的一步优化，根据约束条件和输出预测在线修改控制量的加权系数，提出了一种变加权系数的改进算法，使系统始终满足给定的约束条件。

Secondly, all kinds of incremental transmission losses algorithms are derived completely. And the merit and demerit of these algorithms are compared in detail through the analysis of the calculate example.

传统的经典静态优化方法，由于没有考虑各时段之间的动态约束，因而难以计及负荷的未来变化对当前优化调度的要求，在面对动态变化的负荷时，优化过程带有明显的局限性，但其算法简单、计算速度快的优点仍对动态优化调度具有很强的吸引力。

The control parameters are optimized by using the method of Constrained Steepest Descent with State Equations.

采用状态方程有约束最速下降法对控制系统控制参数进行优化，建立了直流电机位置控制系统性能优化的数学模型，结合具体的位置控制系统推导CSDSE优化方法，并给出优化程序的编制步骤。

The modified particle swarm optimization is utilized to solve the proposed reactive power optimization model; and combining with non–stationary multi-stage assignment penalty function, the reactive power optimization problem is transferred into a problem to solve extreme-value without constraints, thus the calculation accuracy and global convergence ability of MPSO are effectively improved, and power grid company can achieve maximal economic benefit by means of the proposed algorithm.

应用改进粒子群优化算法求解该无功优化模型，并结合动态调整罚函数法将无功优化问题转化成无约束求极值问题，从而有效地提高了改进粒子群优化算法的全局收敛能力和计算精度，使电网公司取得了最大经济效益。

The strong and weak points as well as the scope of application of the modeling method based on the target function for the optimization WOB model are summarized.

以综合钻井成本最低为准则，建立了钻井成本目标函数，讨论了影响钻井成本的因素，给出了钻压优化模型的约束条件，在以上基础上建立了钻压优化模型，并给出了钻压优化模型在线实时求解过程中有关参数的确定方法，最后总结了基于目标函数钻压优化模型建模方法优缺点和适用范围。

Based on the analytical results, this paper put forward its investigative preconditions: organizational members participate in cooperation with the condition of optimizing their personal objectives; optimization of organizational objectives must be based on its members'objective optimization; members'cooperative dedications under the condition of their own objective optimization are resource restrictions of their organizational objective optimization.

根据分析结论提出了本文的研究前提：成员以个人目标优化为条件参与组织合作，组织目标优化受到成员目标优化的制约，即组织成员在个人目标优化条件下的合作投入是组织目标优化的资源约束。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。