目标函数

Up to now, the performance index is almost described as an algebraic function of manipulating variables, it implies the response of performance index to the manipulating variables is instantaneous or the system is in steady state, and the effects of disturbances on the objective function are not taken into consideration.

在以往的工作中，大都把过程的调优变量与目标函数之间的关系用代数方程描述，这意味着目标函数对调优变量的响应是瞬时的，或假定过程处于静态，而且一般也不考虑过程中其它干扰对目标函数的影响，即在算法结构中，调优变量与目标函数构成唯一的因果关系。

In chapter two, under the assumption that the set of decision variables is convex and the objective functions are concave, it is shown that the set of noninferior solutions in valued space of the objective functions turns out to be a strictly decreasing, concave and no chinky block of surface, and it can be constructed recursively.

在第2章凸性假设下非劣解集的构造及其几何性质中，在假设决策变量集为凸集，目标函数向量是凹的情况下，证明了目标函数向量值空间中的非劣解集是一严格单调递减，无缝隙且凹的曲面块，并给出了m维目标函数向量值空间中非劣解集的一种递归构造方式。

The relationship between the topology and convegence of networks is approached and the reason causing overtraining and overfitting is analysed. Then the redundant weights and nodes in the network are defined by using improved activity function and a new algorithm called the BPNSO for determining the network structure for any application is proposed, which use dual optimization objective function combining the mean squre error of the network output with network complexity penalty function.

文章对网络拓扑结构与网络收敛性和稳定性的关系进行了探讨，分析了网络出现Overtraining或Overfitting的原因和解决的目标，提出了神经网络结构优化的策略，改进了活化函数，定义了冗余权值和冗余节点的概念，为辨识和删除冗余权值和冗余节点，提出采用优化目标函数中增加网络复杂度罚函数的双重优化目标函数，并对罚因子提出了基于学习误差和权值的自适应动态调整公式，论文定义了这种BP网络结构优化方法为BPNSO，并给出了完整的计算流程。

This problem involved many objective functions which had contradictions mutually and could not reconciled. According to different engineering requirements, the weighted and harmonic coefficient of each objective function was decided, and then it was changed to a single-objective optimization function. Engineering requirements on the system and related restrictions were given with the form of binding functions.

考虑问题所牵涉到的多个互相矛盾不可公度的目标函数，根据不同的工程要求，结合实践经验和计算经验确定各个目标函数的加权协调系数，然后将其表示为一个单目标优化函数；工程条件对系统的要求和相关限制，以约束函数的形式给出。

They are as following: to establish the selection method of the slaving designed quality functions according to the interrelationship among designed quality functions; to construct the measurement functions of the optimality robustness with the hypersurface characteristics around the current iterative point of designed quality functions.

具体地，根据设计性能函数之间相互关系给出了处于支配地位设计性能函数的选择方法；利用设计性能目标函数在当前迭代点附近的超曲面特征，构造设计性能目标函数的最优性健壮度量函数；按照系统有序化设计模型的最优解应同时具有可行性健壮与最优性健壮的要求，通过计算设计性能目标函数与约束函数对设计变量的波动与非设计参数的波动的一阶敏度来确定系统有序化设计模型中的健壮参数；并以此为基础建立了进一步考虑非设计参数波动对设计变量波动有影响的后健壮分析方法。

Optimal algorithm of combined nonlinear Hopfield network appears powerful validity in solving nonlinear planning, which includes nonlinear objective function, linear constrains and high-demension of decision-making variants, for its ability of nonlinear parallel computation. It is prominent among optimal algorithms because of its function of simply implement with electrocircuit hardware. Genetic algorithm is expressly suitable for optimal calculation regarding the planning of massive, highly nonlinear, inconsecutively differentiable and multiobjective function as well as objective function without analytical expression. However, it inclines to prematurity, as well as its limitation in ability of partial optimal search. Introducing the optimal algorithm of niche genetic simulated annealing to standard Genetic algorithm, can therefore improve the full-scale or partial search ability of Genetic algorithm effectively. It has a far-flung perspective in the field of systemic planning of water pollution control.

组合式非线性Hopfield网络优化算法所具有的非线性大规模并行计算能力在求解具有非线性目标函数、线性约束条件及高维决策变量的非线性规划问题方面显示出了强大的生命力，它易于电路硬件实现的功能更是在优化算法中独树一帜；遗传算法采用概率搜索技术，不受目标函数与约束条件的限制，特别适合大规模、高度非线性的不连续可微的多峰目标函数及无解析表达式的目标函数的规划问题的优化计算，但其存在容易早熟、局部寻优能力较差等缺点，本文在标准遗传算法中引入小生境技术及模拟退火算法有效地改善遗传算法的全局和局部搜索性能，提高了全局最优解的寻优质量，小生境遗传退火模拟优化算法在水污染控制系统规划中的应用前景极为广阔。

The problem of multi-objective usually meet many conflict each other and can not use the objective of the same standard unit, then to employ membership function of fuzzy theory,at first each objective function to change fuzzy set and express with membership function, membership function include the maximum constraint, minimum constraint, the decrease function of monotonic property, to become optimal of the multi-objective function, but still to scanty of weighting value with regard to adjustment of objective function, thus this thesis proposes the method of combine orthogonal arrays and particle swarm optimization to solve the problem of multi-objective optimal power flow, each objective function separately add weighting value, to setting each weighting value of objective function in order to the result of anticipating.

多目标最佳化的问题通常会面临到许多互相冲突且不能用同ㄧ标准单位的目标，於是利用模糊理论中的归属函数，首先将各目标函数转换成模糊集合并以归属函数表示，归属函数包含了最大限制值、最小限制值、单调的递减函数所组成，将各目标函数利用归属函数表示，形成单一目标函数的最佳化，但是仍缺乏权重值对於目标函数的调整，於是本篇论文提出ㄧ种权重值设定与粒子群优演算法的方法去解决多目标最佳电力潮流的问题，将各目标函上分别加上权重值设定各目标函数的权重值，得到预期的效果。

Firstly, this paper definited pseudometric d for n -foldproduct of σ-algebra A of subsets of a given set X , and definited indicator function ; secondly, gave the concept of differentiable of set function at S° and concept of partial derivative at S° with respect to the ith argument Si through indicator function, and defound the weak efficient solution of and optimality necessary condition; Finally, obtained three weak duality results and strong duality results under generalized convexity conditions.

首先，对已知集X的子集的σ-代数A的n-折积A^n，定义了伪度量d，给出了相应的特征函数〈h，Is〉；其次，通过特征函数给出了集函数在S 可微的定义及集函数在S 关于第i个变量Si的偏导数定义；给出了多目标规划问题的弱有效解概念及的最优性必要条件；最后，分别在目标函数和约束函数的3种较弱凸性条件下，研究n-集函数多目标规划问题的对偶问题，获得了3个弱对偶结果和强对偶结果。

To eliminate the limit, a hybrid objective function weighted by antitangent function is constructed, which behaves like an objective function of norm for small data points and like an objective function of norm for large data points, restraining the influence of false data points on inversion procedure.

为了解决这一问题，利用反正切函数作为加权因子构造了反正切混合目标函数，并利用模型试验进行了验证。简要阐述了最优化目标函数的构造方法；给出了利用反正切函数构造混合目标函数的基本原理，并对目标函数的微分特征和概率特征进行了分析；利用模型论述了反正切混合目标函数中控制参数μ和σ的意义，μ控制反正切函数变化的速度，σ控制数据误差项被处理或加权的方式。

E. thickness of the copper wire wall, length of the single conductor wire, height of the solenoid, the exciting current and the current density, the working temperature of the conductor, time of exciting and demagnetizing, the cooling water pressure and flux density, etc..

所建立的数学模型包含3个目标函数（即能耗极小化目标函数、铜耗极小化目标函数和纯铁用量极小化目标函数）、7个设计变量（即铜管规格参数a、b、t，线圈匝数N〓、N〓，铁铠磁通密度B〓和冷却水压p）和8类14个约束条件（即铜管壁厚、单饼导线长度、螺线管高度、激磁电流与电流密度、导体工作温度、激退磁时间，冷却水压和铁铠磁通密度等约束条件）。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。