遗传算法收敛率的下鞅分析

通过鞅论分析来给出遗传算法的收敛率 ,这种分析方法的优势在于它不依赖于染色体的编码形式如常用的二进制形式 ,也不依赖于转移矩阵及其特征值的分析 ,它只以概率来给出遗传算法的收敛率 ,在形式上更加简单明了 ,这是鞅分析优于其它分析如马尔可夫链分析的独特优势 .本文分别对在一定条件下收敛的杰出遗传算法和整体退火遗传算法给出了收敛率的概率形式o( 1- mNn · sNn)和o 1N +N0+( 2 - cN0n - mN0n)e(Δ-δ) /Tn .     

遗传算法基础理论研究的新近发展

本文综述了有关遗传算法收敛性及收敛速度估计的近期研究结果,在分类概述相关的Ｖｏｓｅ－Ｌｉｅｐｉｎｓ模型、Ｍａｒｋｏｖ链模型、公理化模型、连续（积分算子）模型及收敛速度估计、迭代次数估计与时间复杂性估计的基础上,指出遗传算法理论研究存在的其它亟待解决的问题。     

关于一类遗传算法收敛速度的研究

遗传算法收敛速度的研究是进化计算领域中一个复杂而重要的问题,但是有关收敛速度的研究结果还相对较少．目前有关遗传算法的收敛速度的结果可分为两类,一类是利用Doeblin条件来估计,但其结论中含有需要进一步估计的常量;另一类是利用状态转移矩阵的特征值来估计,然而同样需要进一步恰当地估计特征值的大小．本文首先给出一类遗传算法的框架,讨论了其全局收敛性,并且利用马尔可夫链的性质,估计了这类遗传算法的收敛速度．     

求解旅行商问题的搜寻者遗传算法

针对简单遗传算法易陷入局部最优及收敛速度慢的不足,提出一种改进遗传算法-基于启发式策略的搜寻者遗传算法.首先将搜寻者优化算法中的模糊思想和近邻策略相结合改进变异算子,增强种群多样性,避免陷入局部最优;然后针对路径优化问题基于启发式策略设计反转算子,使得路径中不存在交叉边,加快收敛速度;最后将改进遗传算法用于求解旅行商问题.结果表明,改进遗传算法的求解精度和求解效率明显优于基本遗传算法.     

基于云自适应遗传算法的K-means聚类分析

现有的基于遗传算法的K-means聚类算法,利用遗传算法的全局优化性提高了K-means算法的寻优能力,收敛速度却过慢.为了解决上述问题,提出基于云自适应遗传算法的K-means聚类算法,利用云模型云滴的随机性和稳定趋向性设计遗传算法的交叉和变异概率,并在进化过程中引入K均值算子,以克服算法收敛速度过慢的问题.实验比较表明,算法具有较好的全局优化性,且收敛速度较快,提高了聚类算法解决物流管理中数据聚类工作的能力.     

改进伪并行遗传算法求解作业车间调度问题

针对遗传算法在求解极复杂优化问题中出现的过早收敛、执行效率差的缺点,提出了一种改进的伪并行遗传算法.该算法将并行进化与串行搜索相结合,提高了算法的收敛速度.同时该算法通过种群因子控制伪并行算法中的各子种群的规模,不仅保证了搜索过程中勘探和开采的平衡,克服过早收敛,而且减少了计算的复杂性,特别是在处理复杂优化问题上具有较高的性能.实验结果证明了该算法的有效性.     

阶梯状黄土边坡稳定性分析的改进遗传算法及应用

阶梯状黄土边坡稳定性分析的关键是估算其稳定系数的最小值.稳定系数的求解涉及诸多因素且计算过程繁杂,传统优化算法往往不能有效地搜索到其全局最小解.为此,提出一种改进的自适应遗传算法.算法对基因变量空间进行网格状划分,采用迭代选优法建立均匀分布的初始种群,运用优质个体保留遗传策略,并按照特定的准则自适应地调整交叉概率和变异概率,提高算法的全局搜索能力和收敛速度.实例应用表明算法能够快速有效地收敛于土坡稳定系数的全局最小解,且计算结果与实际情况更加吻合.     

整体退火遗传算法的几乎处处强收敛性

本文通过鞍论来分析整体退火遗传算法收敛的特性，得出整体退火遗传算法几乎处处强收敛的条件∑n=1^∞e^-δ,Tn＜ ∞，并且给出其收敛率0（1/N N0 （2-Cn^-^N0-mn^-^N0)e^(△-d)/Tm)。     

连续时间遗传算法模型及其强收敛性分析

本文在隐马尔可夫链的框架下利用隐马尔可夫链{Xt:t∈[0,∞)}的观测链的概率分布提出一个连续化遗传算法模型，并给出其一个强收敛结果，讨论了其离散骨架的性质。     

一种改进适应度函数的遗传算法

针对遗传算法搜索导优中适应度函数的设计不当,将难以体现个体差异和选择操作的作用,从而造成早熟收敛的问题,构建了两种基于顺序的适应度函数的模型.适应度函数的设计使得在进化过程中控制选择压力,种群竞争力得到增强,早熟现象得到改善.并将改进的算法应用在复杂函数优化问题上,MATLAB优化结果表明,算法在种群多样性、搜索速度、计算精度上均有改善,推动遗传算法在工程领域的应用.     

A chaos-based evolutionary algorithm for general nonlinear programming problems

In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.     

遗传算法过早收敛现象的马氏链分析

GeneticAlgorithmsarealtitudeparalleling ,self_adaptingandrandomsearchmethodsthatbasedonideasfromnaturalchoiceandnaturalgenetics.Theyarealsobionicoptimumalgo rithmsdrewonbiologicalevolutionespeciallygenetictermsandprincipal.ThedefinitionofconvergenceofGAshadmayvarieties ,includingconvergenceindistribution ,inprobability ,inprobability 1andconvergencealmosteverywhere ,etc ..EvenforGAsmodel,differentdefini tionhaddifferentlimit.Itmightbeglobaloptimalsolution ,localoptimalsolutionornonopti malso…     

Multiple parents crossover operators: A new approach removes the overlapping solutions for sequencing problems

Maintaining population diversity throughout generations of Genetic Algorithms (GAs) is key to avoid premature convergence. Redundant solutions is one cause for the decreasing population diversity. To prevent the negative effect of redundant solutions, we propose a framework that is based on the multi-parents crossover (MPX) operator embedded in GAs. Because MPX generates diversified chromosomes with good solution quality, when a pair of redundant solutions is found, we would generate a new offspring by using the MPX to replace the redundant chromosome. Three schemes of MPX will be examined and will be compared against some algorithms in literature when we solve the permutation flowshop scheduling problems, which is a strong NP-Hard sequencing problem. The results indicate that our approach significantly improves the solution quality. This study is useful for researchers who are trying to avoid premature convergence of evolutionary algorithms by solving the sequencing problems.     

A hybrid evolutionary learning algorithm for TSK-type fuzzy model design

In this paper, a TSK-type fuzzy model (TFM) with a hybrid evolutionary learning algorithm (HELA) is proposed. The proposed HELA method combines the compact genetic algorithm (CGA) and the modified variable-length genetic algorithm (MVGA). Both the number of fuzzy rules and the adjustable parameters in the TFM are designed concurrently by the HELA method. In the proposed HELA method, individuals of the same length constitute the same group, and there are multiple groups in a population. Moreover, the proposed HELA adopts the compact genetic algorithm (CGA) to carry out the elite-based reproduction strategy. The CGA represents a population as a probability distribution over the set of solutions and is operationally equivalent to the order-one behavior of the simple GA. The evolution processes of a population consist of three major operations: group reproduction using the compact genetic algorithm, variable two-part individual crossover, and variable two-part mutation. Computer simulations have demonstrated that the proposed HELA method gives a better performance than some existing methods.     

Scatter Search and Genetic Algorithms for MAX-SAT Problems

In this paper, both scatter search (SS) and genetic algorithms (GAs) are studied for the NP-Hard optimization variant of the satisfiability problem, namely MAX-SAT. First, we investigate a new selection strategy based on both fitness and diversity to choose individuals to participate in the reproduction phase of a genetic algorithm. The resulting algorithm is enhanced in two ways leading to two genetic algorithm variants: the first one uses a uniform crossover. The second one uses a specific crossover operator (to MAX-SAT). The crossover operator is combined with an improved stochastic local search (SLS). The crossover operator is used to identify promising regions while the stochastic local search performs an intensified search of solutions around these regions. Secondly, we propose a scatter search variant for MAX-SAT. Both the SS and the GAs implementations share the solution selection strategy, the improved SLS method and the combination operator. Experiments on several instances from MAX-SAT libraries are performed to show and compare the effectiveness of our approaches. The computational experiments show that both (SS) and (GAs) with a stochastic local search (SLS) improvement technique outperform a classical genetic algorithm (without SLS). The two metaheuristics are able of balancing search diversification and intensification which leads to good results. In general, the specific genetic algorithm with a (SLS) improvement technique and a specific combination method provides competitive results and finds solutions of a higher quality than a scatter search.     

遗传-人工蜂群融合算法及其Markov收敛性分析

本文研究了遗传算法易发生"早熟"以及人工蜂群算法在搜索初期寻优速度慢的问题.基于将遗传算法与人工蜂群算法融合以实现二者互补的思想,提出遗传-人工蜂群融合算法(G-ABCA),利用马尔可夫理论对其收敛性进行了理论分析,证明其适应度函数值序列(即优化解满意值序列)是单调且收敛的,并利用四个经典的多峰测试函数对遗传-人工蜂群融合算法、改进的遗传算法以及人工蜂群算法进行了对比实验分析,结果表明:遗传-人工蜂群融合算法不仅收敛,而且其寻优性能显著优于其它两种算法.     

基于存档策略的多目标优化的遗传算法及其收敛性分析

设计了一种用遗传算法求解多目标优化问题的有效方法——基于存档策略的多目标优化的遗传算法,并讨论了此算法的收敛性.首先给出档案的定义,设计出基于支配关系下的带有存档策略遗传算法,并通过算例检验了算法的有效性;然后引入了两档案间的距离的概念,在此距离定义的基础上证明了算法在概率意义下是收敛的.     

改进的群搜索优化算法

标准的群搜索优化算法(GSO)是一种新的群智能优化算法,适用于解决高维函数的优化问题,而且简单高效,易于实现,但在其优化的后期容易陷入局部最优.为进一步提高其收敛速度和精度,对GSO算法进行了改进.保留其"发现者-加入者"模型,针对GSO算法发现者和游荡者搜索的无目的性,引进最大下降方向和杂交策略,发现者按角度搜索的同时也按最大下降方向进行搜索,游荡者通过基因突变策略的方式生成.通过23个基准测试函数对GSO算法和改进的GSO算法进行测试,结果表明改进的GSO算法在收敛速度和收敛精度上优于标准GSO算法.     

Henstock-Kurzweil可积函数空间的紧性特征

本文研究Henstock-Kurzweil可积(HK可积)函数空间中的一个经典问题.文章通过研究分布Henstock-Kurzweil积分(DHK积分)的性质,给出了该问题的否定答案.进一步,利用收敛性获得了函数HK可积的一个充分必要条件.最后,在上述结论的基础上刻画了HK可积函数空间的紧性.所得结果丰富和推广了HK可积函数空间理论.