约束优化

PSO is a population-based optimization algorithm, which mimics the social behavior of animals in a flock. It makes use of individual and group memory to update each particle position allowing global and local search optimization. The objective function considered was the total weight of the structure subjected to stresses, displacements and forces constraints. The effects of the parameters were investigated as well and such combination of tuning parameters promote a better global search behavior avoiding premature convergence while rapidly converging to the optimal solution. Results showed the effectiveness of the proposed method by comparing with ANSYS Design Optimization Tool (zero-order method). The PSO with the tuning parameters makes it an ideal method for offshore wind turbines foundations optimization tasks.(2) A reliability analysis method for pile foundation bearing axial loads based PSOThe performance function of pile foundation's axially bearing capacity sometimes is nonlinear and complex, on the basis of geometric meaning of structural reliability index, an optimum model with PSO for structural reliability analysis under arbitrary random variables was established, The PSO algorithm is very efficient to solve global optimization problemsIts use in structural reliability field presents not only the advantage of its facility of implementation, but also the possibility to obtain the design point and the failure probability with a good accuracy. In addition, PSO is a zero order algorithm, for no derivative is necessary for its implementation.

本文的研究针对桩式海上风机基础结构的特点，在国内外有关研究成果的基础上对海上风机基础结构优化设计理论和可靠度方法一些相关问题进行了较为深入的研究，具体做了以下几个方面的工作：(1)基于粒子群优化的桩式海上风机基础确定性优化设计方法桩式海上风机基础的优化设计是一个复杂的、非线性约束的优化问题，针对传统的基于梯度信息的优化方法在处理非线性问题中易陷入局部最优解的问题，本文将一种耦合惩罚函数的PSO算法引入到海上风机基础结构概念设计中，PSO算法是从群体动物聚集觅食这一活动中受到启发而发展的，该算法利用个体和群体的信息共享不断改进自身的位置从而进行局部和全局最优搜索，本文中以桩和三脚架连接段直径及壁厚为设计变量，以基础总重量作为优化的目标函数，在给定的约束条件下建立了三脚架基础优化数学模型，另外本文还研究了PSO参数变化对结果的影响，协调的参数组合可以避免陷入早熟收敛而能够快速的获得全局的最优解，通过与ANSYS优化模块的计算结果比较验证了该方法的有效性，本方法为海上风机基础的确定性设计提供了一条有效的途径。

Not considering the restriction of the depot s transporting ability in the existing achievement of emergency dispatch, consequently, this chapter establishes a sole-resource optimized dispatch model aimed at "the shortest dispatch time" which includes the constraint of transporting ability under time restriction firstly. Moreover, the chapter deduces the algorithm of the model by mathematical induction step by step. Secondl y, it simplifies the former model and gives a simpler sole-objective model and corresponding algorithm including the constraint of transporting ability. At last, on the basis of the improved model, this chapter discusses a two-phase programming model and a multi-objective programming model which are aimed at "the shortest dispatch time" and "the fewest number of mobilized depots" including the constraint of transporting ability under time restriction.

由于现有应急调运的研究成果中没有考虑到各物资供应点受运输能力的约束，因此本章首先建立限制期内以"应急调运时间最短"为目标且含有运输能力约束的单物资调运优化模型：并利用逐步递推法推导出具体的求解算法；然后，进一步地将此模型及算法进行简化，建立更加简单的含有运输能力约束的单目标优化模型：并且讨论其算法；最后，在改进的优化模型的基础上，讨论限制期内含有运输能力约束且以"调运时间最短"、"出动的供应点数目最少"为目标的双层规划及多目标规划的优化模型及解法。

The calculation of an example indicates that the combined optimal model is better than the single one in terms of simul.

大坝安全的组合优化监控模型实际上为一带约束的优化问题，将DNA遗传算法应用于大坝安全监控领域中，用罚函数法将有约束的优化问题转换为无约束的优化问题，建立了大坝安全监控的组合优化模型。

The thesis advances a new optimality design method which can consider stress and proper frequency restriction condition synthetically, through basing on stress optimality criteria methods, owing to optimality criteria don't relate to multi-constraint and apply incomprehensively.

本文针对优化准则法不能考虑多种优化约束条件、通用性差的缺点，基于应力优化准则法和固有频率优化准则法，提出了一种可以综合考虑设计模型的应力约束条件和固有频率约束条件的优化设计方法。

There exits several MDO algorithms. But they are in our opinion either nonefficient or complicated. So we devised an algorithm called Subspace Approximation Optimization . In the SAO algorithm, the whole system is decomposed into one system-level optimization and several disciplinary optimizations so that a large and complicated problem can be divided into several easy-solving sub-problems. The coupling relationships and the coordination among disciplines are presented by equality constraints and these equality constraints are assigned to relevant disciplines. The optimums of design variables in system level optimization are transferred to discipline level optimization. The optimums of design variables in discipline level correspond to the point that is the nearest to the optimums of design variables in system level. If the optimums of design variables in system level are out of feasible region of discipline 1eve1, linear constraints can be built in the system level optimization using the design variable optimums obtained by the discipline level optimization. The system level optimization would improve the design of the whole system with these linear constraints.

目前，国内外已经发展出了多种飞机多学科设计优化算法，本文的重点是针对协同优化算法的不足，提出了子空间近似优化算法(Subspace ApproximatingOptimization，SAO)，SAO算法中，整个系统的优化问题被分解成一个系统级优化和若干学科级优化，而各个学科之间的耦合与权衡关系则被当作等式约束，这些等式约束将被分配到各个学科级优化中去，系统级优化的任务是寻找整个系统的最优解，而学科级优化的目标函数是以系统级优化分配下来的设计点为圆心的超球半径的平方，因此，如果系统级优化分配下来的设计点在学科级优化可行域内，则学科级优化目标函数为0，反之，则学科级优化的最优点是系统级优化当前设计点距离可行域最近的点。

And the GNCP is reformulated as unconstrained optimization problem.

然后建立了GNCP问题的无约束优化问题的转化形式。

Aggregate function which approximates the maximum function, is introduced, and data clustering problem is reformulated as the unconstrained optimization.

借助于近似极大值函数的凝聚函数，将传统数据聚类问题转化为无约束优化问题求解。

Firstly, a new quasi convex-concave extension definition is introduced to study general constrained optimization problem, which is much approximate function's shape than the interval extension.

首先，对一般约束优化问题，引入一新的概念，即拟凸-凹扩张，它比区间扩张能更好地逼近函数的形状。

Nonlinear rescaling methods,based on a class of nonlinear Lagrangians,are important in constrained optimization.

非线性重新尺度化方法是求解约束优化问题的一类重要的算法。

In Chapter 4, a new algorithm for the solution of nonlinear complementarity problems is developed.

第四章对求解互补问题的可微的无约束优化法作了研究。

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。