【作者】 邱玉霞；

【导师】 谢克明；

【作者基本信息】 太原理工大学 ， 电路与系统， 2007， 博士

【摘要】 计算智能方法往往具有自学习、自组织、自适应的特征和简单、通用、鲁棒性强、适于并行处理的优点。在并行搜索、联想记忆、模式识别、知识自动获取等方面得到了广泛的应用。进化计算与粗糙集理论是计算智能的两个热点研究方向，是目前信息科学、自动化科学、计算机科学的交叉和前沿研究领域。思维进化算法是模拟人类思维进化过程的一种新型进化计算方法。本文分别以进化计算和粗糙集为研究目标，研究内容分为四大部分，一是进化计算的数列模型及其在收敛性分析中的应用；二是基于种群信息熵的思维进化算法自适应搜索策略研究；三是基于位编码可分辨矩阵的决策规则获取算法的研究；四是基于思维进化算法和粗糙集的图像处理方法的研究。具体内容包括：1．从进化机制出发，研究了进化算法的种群进化的特点并定义了种群适值函数，进而建立了进化的数列模型，并分析了在该模型下几种典型进化算法的收敛特性；2．研究了思维进化算法的进化机理，引入信息论中信息熵的概念，提出了基于种群进化熵的思维进化算法并在进化计算的统一框架下，证明了该算法在数列意义下是收敛的，数值优化实验表明该算法具有良好的性能；3．研究了粗糙集理论的可分辨矩阵，提出了基于位编码可分辨矩阵规则获取策略，并将其成功应用于水泥窑炉运行操作的决策规则获取；4．提出了基于粗糙集理论和思维进化算法的图像分析新方法，将基于种群进化熵的思维进化算法应用于数字图像分割的最佳阈值寻优；应用粗糙集理论中决策表建立形状分类机制，并应用基于位编码可分辨矩阵的规则获取算法，提取决策规则；将上述方法综合应用于染色体畸变分析系统的设计中。本文的创新性成果包括：(1)建立了进化计算方法的数列模型。把复杂的随机过程映射成为种群适值序列，从该序列的性质来分析种群的进化过程，从而便于用数学方法分析种群的进化过程，为进化计算理论研究提供了一种新方法；(2)应用数列模型分析了几种典型进化算法的收敛性。给出了基于种群适值链的进化算法的收敛条件，使用区间套等定理证明了进化计算方法的全收敛性；(3)提出了基于种群进化熵的思维进化算法。将信息论中信息熵的思想引入思维进化算法的进化操作设计，改进了思维进化算法的趋同操作，算法可根据种群进化信息估计种群进化熵，实现搜索区域自适应调整，提高了搜索效率；(4)提出了基于位编码可分辨矩阵的规则获取策略。首先分析了可分辨矩阵求取属性值约简的可能性及合理性，进而提出了基于位编码可分辨矩阵规则获取算法。该算法以位编码可分辨矩阵为基础，实现属性和属性值约简，并将其应用于水泥窑炉运行操作的决策规则约简；(5)将基于种群进化熵的思维进化算法和粗糙集理论分别应用于图像处理的图像分割和形状分类中。设计了基于思维进化算法与粗糙集理论的染色体畸变分析系统。更多还原

【Abstract】 Computing Intelligence (CI) methods not only have the property of self-study, self-organizing, self-adaptive, but also is excellent for simple, current, strong robust and available for parallel process. Hereby, CI has been widely applied in parallel search, associateon memory, pattern recognition, knowledge automatic acquiring etc. Evolutionary Computing (EC) and Rough Sets Theory (RST) are the two hot directions for CI research and vest in the cross-frontier research area of the information science, the automation science and the computer science. Mind Evolutionary Algorithm (MEA) is a new kind of EC algorithm simulating the evolutionary course of human mind. This paper is based on the study of EC and RST and composed of four parts. First, study on numeral sequence model of EC and its application in convergency analysis. Second, study on Mind Evolutionary Algorithm Based on Population Entropy (PEMEA). Third, study on the decision rules reduct strategy in RST based on bit coded discemibility matrix. Fourth, study on digital image processing method based on PEMEA and RST.Specifically, including the following sections:1. Propose a numeral sequence model for evolutionary computation. A mapping between the evolutionary process of population and a numeral sequence consisted with population fitness function value is built. Thus the sequence reflects the status of the population in evolution. Then, the convergency of several typical evolutionary algorithms analyzed with the model.2. Study the evolutionary mechanism and then introduce the concept of entropy into the design of MEA. A new MEA based on population evolutionary entropy is presented and its convergency is proved under the uniform frame of EC. Then numeral optimal experiment is done to analyze the algorithmic performance.3. Present a decision-rule extraction algorithm based on bit-coded discernibility matrix in RST. At last, it is successfully used to extract the decision rules for course operation of cement kiln. 4. Present new methods of image processing using PEMEA and RST. PEMEA is employed to optimize the segmentation threshold and then the image is segmented with the optimal threshold. A form classification system is built with decision table in RST and the decision-rule extraction algorithm based on bit-coded discernibility matrix is used to reduct the decision rules. At last, an analysis system for chromosome aberrance is designed based on the two methods.The innovations of this paper are as follows:(1) Propose a numeral sequence model for EC. The complex random process of population evolution is mapped to a numeral sequence. Thus some properties are figured out by analyzing the sequence. That provides a new method for the theory research on EC.(2) Employ the numeral sequence model of EC to analyze the convergency of several typical evolutionary algorithms. The convergence condition with population fitness chain is presented. Some theorems in functions analysis such as interval sheath theorem are used in the proof of their convergency.(3) Present a new mind evolution algorithm based on population evolution entropy (PEMEA). The thinking of information entropy in information theory is introduced in the design of evolutionary operation for MEA. With the improved ’similartax’ operator, the algorithm estimates the population evolutionary entropy and then automatically adjusts the control parameters accordingly. The self-adaptive search strategy improves the algorithmic efficiency.(4) Present an extraction strategy based on bit-coded discernibility matrix. Firstly, the rationality of decision rules reduction with discemibility matrix is analyzed. Then a new decision-rule extraction algorithm is presented. The algorithm is based on bit-coded discemibility matrix, performing the reduction of both attributes and attributes’ value. At last, it is successfully used to extract the decision rules for course operation of cement kiln.(5) Respectively apply PEMEA and RST to image segmentation and image analysis. Design an analysis system for chromosome aberrance based on PEMEA and RST.更多还原