约束优化

It is difficult for a variety of traditionary methods based grads information to solve the constrained optimization problem with non-differential coefficient,multi-modal,nonconve and non-linear functions.

在现实生活中许多实际问题都可以转化为约束优化问题，并且实际问题通常都很复杂，其函数形态各具特色，传统基于梯度信息的各种求解策略对于具有不可微、多峰及非凸的非线性函数约束优化问题很难凑效。

Parametric evaluation function can condense the complicated multi-objective and multi-constrait problem into a single-objective unconstrained problem, then solved with conjugate gradient method.The parametric evaluation function method decreases the optimization difficulty,and makes the solution away from the boundary of feasible region during the optimization process,which makes all the objectives optimized simultaneously.

参数评价函数把复杂的多目标多约束优化问题转化为单目标无约束问题，然后用共轭梯度法进行求解，不但降低了求解难度，而且使得在优化过程中其解远离可行域的边界，保证了对多目标中所有目标同时进行优化。

An optimal design for a flexible assembly system can be regarded as a constrained optimization problem.

工程设计过程可看作是一约束确定与满足过程，柔性装配系统的优化设计也是一约束优化问题。

This algorithm constructs a set of linear equations. As a result, the relation of the reconstructed design variables and the original design variables is derived, the variable number of optimum design is decreased from m + n + 2 to 4, and the equality constraint optimization problem is converted into reduced- dimension no equality constraint optimization problem.

该算法通过构造一组线性方程，得到了由重构设计变量到原设计变量的映射关系，使优化设计的变量由原来的m + n + 2个减少到4个，并将有等式约束优化问题转换成降维的无等式约束优化问题。

With the primary goal function, the optimization problem is changed to a nonrestraint one.

在无约束优化过程中，通过逐步增大罚因子，使无约束优化问题的解逼近原约束优化问题的解，用随机搜索优化方法得到了拱坝的优化体型。

The PID parameter tuning of non-linear control system is set as the engineering background. The aim is the optimal design of PID parameter. On the basis of the design and research of the advanced PID parameter tuning, the mathematical model-transfer functionis developed through correlation analysis on statistical method.And with the optimization algorithm under constraint condition, the non-linear, Isqnonlin is set as object function. Then with connection of the non-linear constrain optimization algorithm and simulink technique, a set of adjust parameters which fit the performance index of the control system are found. And optimization design process and steps are provided.

本文以非线性控制系统PID参数整定为工程背景，以PID参数的优化设计为目标，在分析和研究国内外PID参数先进整定方法的基础上，运用相关分析实验统计方法建立对象的数学模型——传递函数，把PID参数设计问题转化为一种非线性优化设计问题，借助于约束条件下的优化算法，以非线性最小平方指标为目标函数，将非线性约束优化算法同Simulink仿真技术相结合，找出符合控制系统品质指标的一组调节参数。

A proper k total colouring of a graph G is a colouring to its vertices and edges using k colours such that no two adjacent or incident elements of G may be assigned the same colour.

利用梯度投影与罚函数相结合的技巧，将带不等式和等式约束的优化问题化成一个无约束问题，提出了初始点可任意的求解不等式、等式约束优化问题的摄动梯度投影算法；参数δk取不同的数还可以得到一类梯度投影算法，从而得出了在搜索方向和步长不精确条件下的梯度投影法，保证了在实际应用中更容易实现；在较弱条件下，证明了该算法的全局收敛性。

With the improvements to the initial population and disposal of objective function, we choose DE as the searching method in EAFSC to investigate it performance in classic unrestraint optimization, Minimax Optimization and nonlinear equations.

其次结合对初始种群和目标函数的处理，以DE为例分别探讨EAFSC在典型的无约束优化、Minimax优化和约束优化问题、非线性方程及方程组求根中的应用。

Various efficient, convergent and robust algorithms have been developed for such a SCOP. However, a more general constrained optimization problem with not only logic AND but also OR relationships exists in many practical applications.

但是，在实际应用中有很多更一般的约束优化问题，其等式或不等式约束之间不仅包含逻辑&与&关系，而且还包含逻辑&或&关系，现有的针对标准约束优化问题的各种算法不再适用。

Quasi-convex relaxation algorithm, which aims to solve ordinary constraint global optimization problems, is produced by a combination of branch-and-bound method with quasi-convex lower bound and quasi-concave upper bound functions developed from quasi convex-concave extension. This algorithm extends the interval algorithm with box constraint to general constraint global optimization problem.

利用拟凸-凹扩张中构造出的函数的拟凸下界函数和拟凹上界函数，与分枝定界方法相结合，建立了求一般约束全局优化问题的拟凸松弛算法，这一算法是将盒子约束的区间算法推广到一般约束优化问题中。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。