约束优化

In this paper, we focused on the Thermal Power Generator unit commitment optimization. A mathematical model is presented and consuming minimization of generator is chosen for its objective function, with the power balance, generation capacity limits, maximum allowable start and stop times limits and time limits taken into consideration. The unit commitment optimization is constrained minimization problem.

本文主要对火电机组优化组合问题进行了研究，提出了机组优化组合的数学模型，该模型以发电总成本最小为目标函数，同时考虑了功率平衡约束、机组输出功率上、下限约束，机组最大允许启停次数和时间约束等约束条件。

Based on the ICMmethod,the discrete topological optimization problem about spot-weld's existence or not is transformed into the continuous optimization problem on[0,1].The optimization model is founded with maximizing the structural stiffness as objective and structural strength as constraints.The problem of multi-objectives and multi-constraints is transformed into the problem of single-objective and single-constraint with the K-S function.The displacement and stress are transformed into the explicit function of design variables with the Response Surface Methodology.The optimization model is solved with Sequential Quadratic Program.

基于ICM（Independent Continuous Mapping，即独立、连续、映射）方法，将焊点有无的离散拓扑优化问题转化为[0，1]区间上的连续优化问题；建立了以结构刚度最大为目标、结构强度为约束的连续拓扑优化模型；采用K-S函数将多目标和多约束问题转化为单目标和单约束问题；运用响应面方法将位移和应力转化为设计变量的显式函数，采用序列二次规划方法求解优化模型。

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。

To inequality constraint s, a check procedure and a penalty function procedure are proposed, and equality constraints are dealt with by a procedure of solving equations in which tear equations may be converged by an iterating way or a penalty function way.

在无约束非线性规划问题全局优化的模拟退火算法基础上，进行有约束问题求解的进一步探讨，对不等式约束条件提出了检验法和罚函数法的处理方法，对等式约束条件开发了罚函数法和解方程法的求解步骤，并进行了分析比较，从而形成了完整的求取非线性规划问题全局优化的模拟退火算法。

Because of the unstructured environments and the force impulse excitation of the following manipulators, the invertibility control input can not control the conducting manipulator exactly. In this paper, a new adaptive and sliding mode control scheme is developed assuming that all system parameters including the joint flexibility values are uncertain but within given bounds.

在以上方法的基础上，本文再对多杆柔性关节机械手在约束空间的轨迹优化规划问题进行了研究，首先利用坐标转换得出多杆柔性关节机械手的约束动力学模型，然后利用逆系统方法求出了系统在约束空间的次优化轨迹及力控制器。

The question of searching characteristic points or straight lines on moving rigid body is decomposed into two relatively independent sub-questions. The first one is to evaluate the characteristic of points and straight lines on moving rigid body, whose mathematics model is a kind of special non-differential max-mini optimal problem with inequality constraints. By the method of Saddle-point Programming and maximum entropy, the problem can be transformed as a differential optimal problem with single objective. The second oner is to search approximative character points or straight lines on moving rigid body within design space, whose mathematic model is nonlinear and non-differential problem with multiple constraints.

本文将在运动刚体上寻找特征点或直线的优化问题分解为两个相对独立的子问题，一是对运动刚体上点或直线的特征性评定，其实质是平面曲线的圆度或直线度的评定问题，优化模型是以最大误差为最小作为优化目标的约束不可微的优化问题，本文采用鞍点规划和极大熵方法，将其转化为单目标可微优化模型；二是在设计空间内，寻找运动刚体上特征性评定指标最小的近似特征点或直线，其优化模型是非线性、多约束的不可微优化问题，本文提出用遗传算法和BFGS局部搜索法相结合来求解。

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。

Considering the fact that the self constraints of the design variables can be formulated as the linear functions in the present process optimization, the nonlinear part of the constraints is dealt by introducing the concept of active constraint set. The linear part is dealt by the gradient projection method specially.

同时考虑到现在的优化求解问题中，设计变量自身的约束可以合理地表示成线性函数的形式，因此对于优化问题的非线性约束部分，通过引入活动约束集的概念进行处理；而对于线性边界约束，则采用梯度投影法作专门处理。

By use of first-order linear expansion of Taylor series, the linearization process of both nonlinear constraints and objective function of long-term optimal scheduling model are performed and an optimal scheduling model based on seccessive linear programming is built; an approach to solve Optimal scheduling of cascade hydropower station problem by seccessive linear programming is put forward, the scale-down factor of iteration step length is used to ensure that the algorithm can converge to the optimal solution of optimization problem quickly and accurately.

通过采用泰勒级数一阶描述形式，对优化调度目标函数和约束条件中的非线性约束进行线性化处理，建立了基于连续线性规划算法的优化调度数学模型，提出了用连续线性规划技术求解梯级水电站优化调度问题的算法，并采用迭代步长的动态比例缩减因子保证算法能快速准确地收敛到优化问题的最优解。

Because problem which has complementary constraints does not satisfyconstraints qualification, which is the assumption for nonlinear problem solvers, weuseεslackness technique to deal with this problem.

因为具有互补约束的优化问题一般不满足传统优化算法所要求的约束规范假设，所以本章采用了ε松弛的方法处理互补约束。

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。