遗传算法的Markov链分析与收敛速度估计

主要利用Ｍａｒｋｏｖ链讨论一类遗传算法（简称ＧＡ）的ｒ阶收敛性与收敛速度．首先介绍了ＧＡ的Ｍａｒｋｏｖ链状态空间的分类,按此分类,证明了Ｍａｒｋｏｖ链的一步转移概率矩阵为下三角矩阵,进而分析了ＧＡ的ｒ阶收敛性及其它形式的收敛性．最后讨论了ＧＡ的收敛速度．     

Analysis of the diversity of population and convergence of genetic algorithms based on Negentropy

1.INTRODUCTION Thediversityandconvergenceofgeneticalgorithms havegainedmoreattentionbymanyspecialistsinre centyears,althoughGAhasbeenwidelyusedin manyfieldsandobtainedsomesuccess,therestill isn’tasetofcompletetheorytoexplaintheprinciple ofGA,tosomeextent,itsdevelopmentisrestricted, evenmakingsomeonedoubtfulaboutit. Holland’smodeltheoremisthemaintheoryof GA,butitjustdisclosestheaveragechangeinthe evolutionarypopulation,notsuggestinganyinforma tionofindividualdistributionwithintheevo…     

ON THE CONVERGENCE ANALYSIS OF ALGORITHMS FOR GENERALIZED SET-VALUEDVARIATIONAL INCLUSIONS IN BANACH SPACES

In this paper, we are devoted to the convergence analysis of algorithms forgeneralized set-valued variational inclusions in Banach spaces. Our results improve, extend,and develop the earlier and recent corresponding results.     

n 进制编码遗传算法的收敛速度

利用一个特殊的minorization条件给出了n进制编码的经典遗传算法收敛速度的一个上界,分析了种群的规模、编码串的长度以及变异概率等变量对算法收敛速度的影响,它推广了已有的结论,并对算法的参数设计有参考价值.     

一种改进的原子搜索算法

原子搜索算法(atom search algorithm,ASO)是模仿自然界中原子运动而提出的一种新型优化算法,针对ASO在求解复杂函数时存在易早熟及收敛速度慢的问题,提出了一种改进ASO算法(improved atomic search algorithm,IASO)。IASO加入了原子个体历史最优解产生的约束力来修正ASO的加速度,增强全局搜索能力。自适应更新2个乘数系数来协调算法的全局搜索和局部开发能力。适时采用高斯变异策略来重新更新原子位置,提高跳出早熟的能力。对14个基准函数进行仿真实验,对比其他算法,IASO在收敛速度、收敛精度方面表现出优越的性能。     

THE CONVERGENCE OF BROYDEN ALGORITHMSWITHOUT CONVEXITY ASSUMPTION

1.IatroductionWeknowthatthevariablemetricalgorithms,suchastheBroydenalgorithms[1],areveryusefulandefficientmethodsforsolvingthenonlinearprogrammingproblem:min{f(x);xERn}.(1.1)Withexactlinesearch,Powelll2]provedthattherateofconvergenceofthesealgorithmsisone-stepsuperlinearfortheuniformlyconvexobjectivefunction,andifthepoiedsgivenbythesealgorithmsareconvergeal,PnandYul3]provedthattheyaregloballyconvergelitforthecolltinuousdifferentiablefunction.Withoutexactlinesearchseveralresultshavebeenobtai…     

PARALLE DOMAIN DECOMPOSITION ALGORITHMS FOR A GENERALIZED STOKES PROBLEM

ＰＡＲＡＬＬＥＤＯＭＡＩＮＤＥＣＯＭＰＯＳＩＴＩＯＮＡＬＧＯＲＩＴＨＭＳＦＯＲＡＧＥＮＥＲＡＬＩＺＥＤＳＴＯＫＥＳＰＲＯＢＬＥＭ￥ＣＨＵＤｅｌｉｎ；ＺＨＯＵＦａｎｇｊｕｎ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔｓｉｎｇｈｕａ...     

Convergence Rate and Convergence of Genetic Algorithms

IntroductionTheanalysisfortheconvergencerateandconvergenceofthegeneticalgorithmsisveryimportanttounderstanditsproperties.Manyresultshavebeenmadeinthispield.A.E.Eib..[1]hasprovedthataclassofabstractgeneticalgorithms(AGA's)convergewithprobabilityoneunderelitistselection.G.Rudolphl']hasstudiedtileasymptoticconvergenceofthecannonicalgeneticalgorithms(CGA's),buttheresultsdonotcoverthecaseofelitistselection.SomeotherimportanttheoreticalanalysesforGA'shavebeencontributedbyD.B.Foge'[']andX.Qi['…     

平衡问题解的收敛性

利用集收敛、函数收敛建立了集值映射收敛的概念及其性质 ,并依此讨论了平衡问题解的收敛性 .     

探索曲面结构的小生境遗传算法

提出了具有适应值曲面结构自学习能力的多区域并行局部搜索算子PLS和约束交叉算子GC，定性地分析了它们的作用机制，给出了基子仿真实验数据的遗传算法收敛速度和全局收敛可靠性的定量计算方法。仿真实验数据表明，PLS能有效地提高搜索速度并维持足够的种群基因多样度，GC可有效地微调解的质量，使改进的遗传算法的全局收敛速度和收敛可靠性均显著地优于标准遗传算法，并具有良好的鲁棒性和稳定性．     

Inertial projection algorithms for convex feasibility problem

The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.     

Global Convergence of Adaptive Generalized Predictive Controller Based on Least Squares Algorithm

Some papers on stochastic adaptive control schemes have established convergence algorithm using a least-squares parameters. With the popular application of GPC, global convergence has become a key problem in automatic control theory. However, now global convergence of GPC has not been established for algorithms in computing a least squares iteration. A generalized model of adaptive generalized predictive control is presented. The global convergebce is also given on the basis of estimating the parameters of GPC by least squares algorithm.     

A VARIATION OF GOLDFARB'S METHOD FOR LINEARLY CONSTRAINED OPTIMIZATIONPROBLEMS AND ITS SUPERLINEAR CONVERGENCE RATE

1.IntroductionRosen'sgradientprojectionmethodisaveryinterestingtechniqueinoptimization(see[1,2]),butitsglobalconvergenceisalong-standingopenproblemintheliterature.Thefirstconvergentversionwasfoundbyp.l.k[3].ButPolak'sversionistoocomplicated.Du[4]alsofoundasimplerconvergentversionbydeletingPolak'sspecialprocedure.CombiningRosen'smethodwithvariablemetricmethods,Goldfarb[sl,MurtaghandSargentl'lobtainedtwoefficientalgorithms.Theconvergenceofsuchalgorithmsisstillanopenproblem.However,severalcon…     

Alternative Theorems and Sufficient Conditions of Global Convergence for a Class of Feasible Direction Algorithms

In this paper,two alternative theorems which differ from Theorem 10.2.6 in [1] andTheorem 1 in [3] are presented for a class of feasible direction algorithms.On the basis of alternativetheorems,furthermore,two sufficient conditions of global convergence of this class of algorithms areobtained.     

End-to-end rate-based congestion control with random loss: convergence and stability

The convergence and stability analysis for two end-to-end rate-based congestion control algorithms with unavoidable random loss in packets are presented, which can be caused by, for example, errors on wireless links. The convergence rates of these two algorithms are analyzed by linearizing them around their equilibrium points, since they are globally stable and can converge to their unique equilibrium points. Some sufficient conditions for local stability in the presence of round-trip delay are obtained based on the general Nyquist criterion of stability. The stability conditions can be considered to be more general. If random loss in the first congestion control algorithm is not considered, they reduce to the local stability conditions which have been obtained in some literatures. Furthermore, sufficient conditions for local stability of a new congestion control algorithm have also been obtained if random loss is not considered in the second congestion control algorithm.     

求解非线性互补问题的混合光滑型算法

光滑型算法已经成功地用来求解各种优化问题. 基于一类新的光滑函数族， 提出了一个带有混合线搜 索的光滑型算法求解非线性互补问题. 在适当的条件下， 证明了算法是适定的， 且保持全局 收敛性和局部超线性收敛性. 最后对提出的算法进行了数值计算. 数值结果显示出该算法的有效性.     

OPTIMAL VALUE FUNCTIONS IN MATHEMATICAL PROGRAMMING AND CONVERGENCE FOR GRADIENT PROJECTION METHOD

ＯＰＴＩＭＡＬＶＡＬＵＥＦＵＮＣＴＩＯＮＳＩＮＭＡＴＨＥＭＡＴＩＣＡＬＰＲＯＧＲＡＭＭＩＮＧＡＮＤＣＯＮＶＥＲＧＥＮＣＥＦＯＲＧＲＡＤＩＥＮＴＰＲＯＪＥＣＴＩＯＮＭＥＴＨＯＤ￥ＷＡＮＧＣｈａｎｇｙｕ；ＺＨＡＯＦｕａｎ（ＩｎＳｔｉｔｕｔｅｏｆＯＲ，Ｑｕ...     

基于位置感知的大规模LEO星座分布式路由算法

针对传统星座路由算法应用在大规模低地球轨道(low earth orbit, LEO)星座中, 存在鲁棒性差、资源开销大、路由效率低等缺点。根据卫星运行时的位置可预测特性, 提出了基于位置感知的分布式路由算法。考虑卫星资源受限, 大规模LEO星座具有卫星节点多、动态性大等特点, 基于位置感知提出一种路径预选机制, 初步确定数据包的传输路径。在此基础上, 考虑业务服务质量(quality of service, QoS)需求, 基于状态和传播矢量函数提出一种路径收敛机制, 无重合确定数据包传输主路径和备用路径。理论和仿真结果证明, 相比于传统路由算法, 所提算法降低了路由存储和开销, 随着中断概率的增大, 提高了星座的吞吐量, 降低了端到端时延。     

基于育种系统管理全局优化算法及其性能

针对遗传类算法收敛精度差和收敛速度慢等问题,本文将育种系统的管理运作思想引入遗传算法,构造了一种新的全局优化算法—育种算法。通过对搜索和进化操作过程进行分析,指出了算法收敛到全局最优的途径和方法,提出了利用简单的随机采样实现全局搜索和采用基因置换技术实现交叉进化的思想策略,建立了算法模型并确定了相应的控制参数和终止准则。实验表明,该算法能够实现精确搜索并实现计算精度和成本之间的平衡,可以避免遗传算法的早熟收敛问题和大量的冗余运算,提高了优化计算的速度和可靠性。     

Job Shop调度问题的遗传退火算法

针对作业车间(JobShop)调度问题,提出了一个遗传退火算法。该算法构造了基于工作的遗传算子,因而保证了遗传进程中生成个体的可行性,有效地解决了工件机器顺序的约束限制。通过对最佳个体进行模拟退火,把模拟退火机制引入到遗传进化过程中,将模拟退火和遗传算法两者的优点有机地结合起来,从而进一步提高了算法的全局寻优能力。仿真计算表明了该算法的良好收敛性和有效性。