基于多保留策略的复合型遗传算法及其收敛性分析

遗传算法(GA)作为一种新型的智能优化方法,以其结构简单、适应性强等特点在众多实际领域取得了成功的应用,但存在计算复杂度大、易于局部收敛等方面的不足。本文在分析现有遗传操作的不足和生物进化的基本特征基础上,从提高进化效率的角度出发,提出基于多保留策略的复合型遗传算法(简称MRS-CGA);进而利用Markov链理论和仿真技术,从不同的层面分析了算法的性能。讨论结果表明,算法从本质上推广了常规的GA,在计算效率和收敛性能上均明显地优于常规的GA。     

Fuzzy数序列的Fuzzy运算的收敛性

在Ｆｕｚｚｙ数的Ｆｕｚｚｙ运算及Ｆｕｚｚｙ数序列的收敛问题基础上，讨论了收敛序印象的Ｆｕｚｚｙ运算的性质，给出了几个Ｆｕｚｚｙ数序列的Ｆｕｚｚｙ运算的收敛定量。     

The order structure of fuzzy numbers based on the level characteristics and its application to optimization problems

Ranking and comparing fuzzy numbers is an important part in many fuzzy optimization problems such as intelligent control and manufacturing system production line scheduling with uncertainty environments. In this paper, based on the level characteristic function and α-average of level cut sets of fuzzy number, we establish the IMα-metric method for measuring fuzzy number as a whole, and introduce the concept of IDα-difFerence that describes the reliability of IMα-metric value. Further, the basic properties and the separability of IMα-metric and IDα-difference are discussed. Finally, we give a mathematical model to solve fuzzy optimization problems by means of IMα-metric.     

模糊性度量方法（Ⅱ）—次模糊度

《模糊性度量法（Ｉ）》给出了全平均模糊度概念，本文建立了次模糊度的概念，真平均模糊度的概念，并讨论了这些概念之间的联系。     

多阶段复合型遗传算法的结构及性能研究

针对基本遗传算法(SGA)在求解复杂优化问题时常常存在的局部收敛和不能很好地收敛到全局最优解的不足,采用逐步缩小寻优范围的策略,提出了多阶段复合型遗传算法(简记为MSC-GA),给出了MSC-GA的结构以及具体的实施策略;进而利用Markov链理论和仿真技术分析了MSC-GA的收敛性,证明了MSC-GA在最优个体保留策略下是全局收敛的;最后,通过一个实例从不同的角度分析了MSC-GA的收敛性能。结果表明,MSC-GA具有良好的收敛稳定性,可以有效地避免局部收敛现象,尤其适用于大范围、高精度的优化问题,具有广泛的应用价值。     

Fuzzy数的Fuzzy运算

首先给出了区间数的取大，取小运算，进而利用分解定理建立了Ｆｕｚｚｙ数的Ｆｕｚｚｙ运算，讨论了这种运算规则的基本性质。     

Fuzzy metric based on the distance function of plane and its application in optimal scheduling problems

Measuring the difference between fuzzy numbers is often needed in many fuzzy optimization problems such as manufacturing system production line scheduling with uncertainty environments. In this paper, based on the distance function of plane R2 and the level importance function, we establish the UID-metric and LPID-metric of measuring the difference between fuzzy numbers, and discuss the basic properties of UID-metric and LPID-metric, and prove that fuzzy number spaces are metric spaces about UID-metric and LPID-metric if and only if the level importance function I(λ)≠0 almost everywhere on [0, 1]. Further, we discuss the convergence, separability and completeness of UID-metric and LPID-metric based on the norms of plane R2. Finally, we analyze the characteristics of UID-metric and LPID-metric by some application examples.     

模糊性度量方法（Ⅲ）—λ—模糊度

引入了λ－模糊因素集，λ－模糊生成集的概念，建立了度量模糊集的模糊性的λ－模糊度，讨论了全平均模糊度，次模糊度及λ－模糊度之间的关系。