The detailed research work done in this thesis is listed below . 1 . the aco algorithm is a heuristic search method with a solution construction graph that explicitly describes the whole solution space of optimization problems . therefore , the definition of the construction graph directly influences computation cost and search efficiency 具体的研究内容有以下几点： ( 1 )蚁群优化算法由于是一种基于显式表达解空间的启发式搜索方法，解构造图显式地描述了优化问题的整个解空间，所以解构造图的定义方法会直接影响到算法的计算量和搜索性能。
But , there are two difficulties in the method . one is the existing of numerously discrete variables , high dimensionality and great solution spaces , which may lead to the explosion of combination . the other is that the relationship between optimization object and the design variables is often very complex , and can hardly be expressed by plaint equation 然而，协同优化设计面临着以下两个难点：离散型设计变量多、维数高、解空间十分庞大，优化设计面临着组合爆炸问题；优化目标与设计变量间的关系非常复杂，往往难以建立起显式的函数关系。
According to the rules and considerations which are based and taken into account in the practical work , this paper proposes a new model for distribution maintenance scheduling which intends to find the most economical maintenance schedule without violating any restrictions and also the paper makes a deep research of ga , sa and ts . by constructing two effective instructive rules which derive from the feature of distribution maintenance schedule and introducing ts into mutation operation of ga in the earlier generations , the proposed method improves the convergence of optimization and shortens the calculation time . the proposed model and method are applied to a practical system , and numerical results verify ' the correctness and validity of them 本文结合实际电力调度计划工作中检修计划的制定原则和所要考虑的各种因素，抽象出适合配电网检修计划优化的数学模型：对遗传算法、模拟退火算法以及禁忌搜索算法等多种算法进行了研究和分析比较，针对遗传算法的不足提出了通过对实际问题的分析抽象出一定规则指导算法在解空间进行搜索和两阶段变异算子两项改进措施，并应用于配电网检修计划优化，编制了相应的应用软件；应用该软件对我国南方某地区供电局某月的检修计划进行优化的结果表明，本文所提出的模型和改进的优化方法是正确和有效的。
The non - linear inversion methods are developed to overcome the difficulties met when the linear inversion methods are used in the geophysical inversion problems . this paper presents the simulated annealing is hopeful for the inversion problem of resistivity map reconstruction . due to the slow speed caused by the global searching , so for , the method is limited in the processing the 1 - d model 为了克服像传统线性反演方法中解易陷入局部极小的不足，本文采用了模拟退火这种非线性方法实现了高密度电法一维反演，初步取得到较好反演结果，但由于它随机搜索全局解空间，计算量非常大，因此目前主要应用于一维地电结构的反演。
Supported by national 863 project , this dissertation mainly focus on some key problems , including association rule mining with item constraints , association rule mining with fuzzy quantitative constraints , optimized association rule mining , web usage mining and quantitative association rule mining using statistical method . some new definitions , theorems and algorithms are presented and tested , and some problems in both theory and practical applications are solved successfully 本文在国家863项目的资助下，主要对含有项目约束的关联规则挖掘、模糊数值约束的关联规则挖掘、优化关联规则的解空间、 web使用挖掘及数值型关联规则挖掘的统计方法进行了深入的研究和探讨，提出了一系列的定义、定理及新算法，解决了若干理论和实际方面的问题。
The pheromone - based parameterized probabilistic model for the aco algorithm is presented as the solution construction graph that the combinatorial optimization problem can be mapped on . based on the solution construction graph , the unified framework of the aco algorithm is presented . an iterative update procedure of the solutions distribution in the problem ' s probabilistic model is proposed , that will converge to the optimal solutions with probability one , then the minimum cross - entropy pheromone update rule is proposed to approximate the iterative update procedure by minimizing the cross - entropy distance and monte - carlo sampling 基于解空间参数化概率分布模型，首先提出了一个以概率1收敛于最优解的解空间概率分布的迭代更新过程，然后提出了通过最小化不同分布间的交互熵距离以及蒙特卡洛采样来逼近此迭代过程的最小交互熵信息素更新规则，接着分别给出了弧模式以及结点模式信息素分布模型下的最小交互熵等式。
Analyzed the similarity between scheme solving problem and traveling salesman problem ( tsp ) , the scheme solving problem for conceptual design is transformed into an optimal path problem in combinatorial optimization , where the dynamic programming based solution space model and the longest path based optimization model are developed 摘要通过分析概念设计方案求解问题与旅行商问题的相似性，将方案求解问题转化为组合优化的最优路径问题，建立了基于动态规划的解空间模型和基于最长路径的优化模型。
A smoothing technique is combined with optimum approximation and finite element piece - wise interpolation in the method , it can simultaneously process measured vector components , imp ro ve smoothing capability of solution , space composed of original discrete points and increase the accuracy of the solution , especialy its derivatives 该方法结合最佳逼近、有限元分片插值与光顺技巧，对测量向量各独立分量进行处理，改善了原离散点构成的解空间的光滑性，提高了解尤其是导数场的精度，在测量区域内再现了光顺向量函数及连续的导数。
The solution space and the algorithm to solve eeg inverse problem were mainly investigated . the following achievements have been obtained : 1 ) based on the segmented brain data from mri , the images contour points were obtained and then the brain was divided into many small cubes . these cubic grids formed the inverse problem solution space 本论文的主要工作和结果如下： 1 )对从mri图像中提取出来脑部轮廓进行分析处理，结合对脑部三角形剖分方法，对脑部进行六面体网格剖分，构造出基于电流分布模型求解脑电逆问题所需要的解空间。
In 1860 , schrodinger first put forward the concept " schrodinger equations " in quantum mechanics and since then , the study on schrodinger equations has never stopped , for the mathematical description of many physical phenomena belongs to the field of schrodinger equations , such as nonlinear optic , plasma physics , fluid mechanics etc . as for the form of schrodinger equations , linear schrodinger equations was gradually replaced by nonlinear schrodinger equations ; as for the methods of solving schrodinger equations , the modulus estimate of energy , the principle of contraction mapping , fourier transformation and harmonic analysis are used ; as for the space of the solutions , many people have worked on the problem in bounded domain , euclidean space of dimension n , periodic bounded conditions and mixed regions and they also combined it with the generalization from low dimension to high dimension ) dinger方程，如非线性光学、等离子物理、流体力学[ 21 ]等；在方程形式上，从线性schr ( ? ) dinger方程到非线性schr ( ? ) dinger方程；在处理方法上，用能量模估计、压缩映象原理和fourier变换调和分析等；在方程解空间上，研究有界区域、 n维欧氏空间、周期性有界区域和混合区域等，并且结合从低维向高维推广。
