优化问题

This prject provides the linear and nonlinear optimization problems and several combinatorial problems with several new powerful tools.

本研究为线性及非线性优化问题和多种组合优化问题提供了多种新的有力求解工具。

In order to solve the problem of local extremum encountered in the process of optimizing the complex multimodal functions, an interval decomposed optimization method is presented based on genetic algorithm.

为解决遗传算法面对复杂多模态函数优化问题时易陷入局部极值的问题，提出一种区间分解优化思想。

In order to solve the problem of local extremum encountered in the process ot optimizing the complex multimodal functions, an interval decomposed optimization method is presented based on genetic algorithm.

为解决遗传算法面对复杂多模态函数优化问题时易陷入局部极值的问题，提出一种区间分解优化思想。

Since the model is a large scale and NP-hard combinational optimization problem in the real navigation environment, a hybrid simulated annealing algorithm is employed to search the suboptimal solution composed of a lockage timetable and a ship scheduling, The search starts by trimming the existing lockage timetable based on heuristic rules; the result is then used to compute the ship scheduling by the depth-first-search algorithm. The obtained solution is finally updated by the Metropolis rule.

本文首先提出了该问题的混合整数非线性规划模型，在实际通航调度环境中，该模型属于强NP-hard复杂度的大规模组合优化问题，因此设计了一种混合模拟退火算法来搜索次优化调度方案，该算法将解分解为闸次时间表和船舶调度计划两部分，在搜索过程中用启发式规则对闸次时间表进行调整，然后用深度优先搜索算法根据闸次时间表求解船舶调度计划，最后根据Metropolis规则对当前解进行更新。

Ant Colony Algorithm is a new developed bionic optimization algorithm, which simulate the ants'finding food process. Because of its simple mechanism, plus-feedback parallelization, strong lustiness and excellent distributed compu- tational mechanism, it has shown its excellent capability and huge developing potential in solving many complicated optimization problems, and it has been successfully applied to production problem such as scheduling problems and routing problems. But it also has some disadvantages, it need longer searching time than others and tend to precocity and stagnation.

蚁群算法是一种最新发展的模拟昆虫王国中蚂蚁觅食行为的仿生优化算法，该算法采用了正反馈并行自催化机制，具有较强的鲁棒性、优良的分布式计算机制、易于与其它方法结合等优点，在解决许多复杂优化问题方面已经展现出其优异的性能和巨大的发展潜力，并已成功地应用于诸如生产调度、布线等生产问题。

And it is proved to be more efficient than Newton method from the theorectical of view.

另一方面，将Newton-PCG算法应用于求解单和函数优化问题，利用单和函数优化问题的特殊性，进一步开发Newton-PCG技术建立了更有效的特殊算法。

At first this thesis researches the multi-layer tactic of the recurrent optimization of the nonlinear predictive control which converts the optimization with nonlinear dynamic restriction into the optimization with linear dynamic restriction and the repetitive coordination.

在这里引入了大系统理论中的分级递阶思想，将一个一揽子求解的带有动态非线性约束的优化问题转化为由线性约束的优化和迭代协调两个层次组成的分级递阶问题。

Conceptually, we present the principle of optimality for defuzzification and the optimal defuzzification mapping; methodologically, we convert the problem of finding the optimal defuzzification mapping into the one of finding the optimal parameters, suggesting a specific method for its realization—POD method; operationally, we advance that the learning of the parameters for defuzzification can be realized by the learning process using extended Kalman filter.

在概念上，提出了解模糊的优化原理和最优解模糊映射；在方法上，将求最优解模糊映射问题转化为一个参数优化问题，并提出了一个具体实现方法——POD方法；在实际操作上，我们提出可用基于增广Kalman滤波的参数学习算法来完成解模糊过程参数的学习。

At last ,the piecewise linear interpolation function is applied to deal with complicated constraints conditions for solving the objective function .The simulation results on the three gorges cascaded hydropower system long term optimal dispatch under the flood and dry power price and comparison with other algorithms show that it is greatly efficient to solve engineering optimal problems with complicated constraints.

针对模型中复杂的约束条件，采用分段线性插值函数实现了对目标函数的求解，并通过对丰枯电价下三峡梯级水电系统长期优化调度问题的计算及与其它算法的对比，验证了该算法可运用在解决具有复杂约束条件的工程优化问题中。

Based on the special decomposition of Hankel matrix, we can transform the problem of approximating a given matrix with a positive semidefinite real Hankel matrix of lower rank to a smooth unconstrained optimization problem.

对矩阵的低秩Hankel半正定矩阵逼近，采用特殊的分解形式，可将其转化为一个无约束的优化问题进行求解，本文应用拟牛顿方法求解无约束优化问题。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。