实数编码化学反应优化的全局收敛性研究

作为一种新的自然计算方法,化学反应优化性能优越,适应性强,但其理论研究缺乏.针对上述问题,以实数编码化学反应优化(RCCRO)为对象,研究其收敛性和收敛速度.首先,建立RCCRO在连续时间上有限吸收的Markov链模型,并证明其为有限可吸收Markov链;然后,基于有限吸收Markov链证明RCCRO的收敛性;进而,对于采用不同初等反应组合的RCCRO,研究初等反应的有效性和算法全局收敛的必要条件;最后分析了RCCRO的收敛速度和首达时间.     

Numerical Solutions for Optimal Control of Stochastic Kolmogorov Systems

This work is concerned with controlled stochastic Kolmogorov systems. Such systems have received much attention recently owing to the wide range of applications in biology and ecology.Starting with the basic premise that the underlying system has an optimal control, this paper is devoted to designing numerical methods for approximation. Different from the existing literature on numerical methods for stochastic controls, the Kolmogorov systems take values in the first quadrant. That is, each component of the state is nonnegative. The work is designing an appropriate discrete-time controlled Markov chain to be in line with(locally consistent) the controlled diffusion. The authors demonstrate that the Kushner and Dupuis Markov chain approximation method still works. Convergence of the numerical scheme is proved under suitable conditions.     

SINGULARLY PERTURBED MARKOV DECISION PROCESSES WITH INCLUSION OF TRANSIENT STATES

1 IntroductionMarkov decision processes (MDP) have drawn much sttention because of their capabilityin dealing with a wide range of application under UnCertainty. Many problems in operationsresearch such as resource allocation, queueing networks, and maChine replaCement etc., fit wellin the framework of Markov decision processes. Classical aPProaChes of discrete-time MDPmodels can be foUnd in Dermanll], RDssIZ], and ~e[3] among others.Because most of the systems in real life are large a…     

Global Convergence Analysis of Non-Crossover Genetic Algorithm and Its Application to Optimization

Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.     

The bulk input M[X] /M/1 queue with working vacations

In this paper, we analyze a bulk input M^[X] /M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function(PGF) of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X] /M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.     

ON APPROXIMATION BY REPRODUCING KERNEL SPACES IN WEIGHTED L^p SPACES

In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.     

Inverse Center Location Problem on a Tree

This paper discusses the inverse center location problem restricted on a tree with different costs and bound constraints. The authors first show that the problem can be formulated as a series of combinatorial linear programs, then an O（｜V｜^2 log ｜V｜） time algorithm to solve the problem is presented. For the equal cost case, the authors further give an O（｜V｜） time algorithm.     

灰色正交化方法在用电量预测中的仿真研究

根据灰色正交化方法和马尔可夫链原理,应用Gauss-Chebyshev正交化思想预测时序数据的总体趋势。预测的精度是时变的,而马尔可夫链原理在处理时变的系统过程时具有较好的优势,选用该方法能更好的解决预测结果的不稳定性。基于此,提出一种用于用电量数据预测的灰色马尔可夫正交化模型,适用于中短期、数据需求量少且数据振幅较大的动态过程预测。最后用提出的方法对江苏省2007年工业用电量进行预测,其结果表明了所提方法的有效性。

Abstract：

The general trend of time series data was predicted with Gauss-Chebyshev orthogonalization theory according to the grey orthogonalization method and the Markov Chain theory.The prediction accuracy is time-varying.However,this approach will better solve the problem of unstable prediction result since Markov chain theory has greater advantages in handling time-varying system process.Based on this,the Markov grey orthogonalization model prediction was proposed for electricity consumption.It is suitable for dynamic process prediction in medium and short term with less data demand and large data fluctuations.Finally,the proposed approach was used to forecast the industrial electricity consumption of Jiangsu Province in 2007,and the results show the effectiveness of this approach.     

HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS

A fluid buffer model with Markov modulated input-output rates is considered.When traffic intensity is near its critical value, the system is known as in heavy traffic.It is shown that a suitably scaled sequence of the equilibrium buffer contents has a weakor distributional limit under heavy traffic conditions. This weak limit is a functional of adiffusion process determined by the Markov chain modulating the input and output rates.The first passage time of the reflected process is examined. It is shown that the mean firstpassage time can be obtained via a solution of a Dirichlet problem. Then the transitiondensity of the reflected process is derived by solving the Kolmogorov forward equation witha Neumann boundary condition. Furthermore, when the fast changing part of the generatorof the Markov chain is a constant matrix, the representation of the probability distributionof the reflected process is derived. Upper and lower bounds of the probability distributionare also obtained by means of asymptotic e     

Least-squares Galerkin procedure for second-order hyperbolic equations

This paper proposes the least-squares Galerkin finite element scheme to solve second-order hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in (L ²(Ω))² × L ²(Ω) norms. Moreover, the method gets the approximate solutions with second-order accuracy in time increment. A numerical example testifies the efficiency of the novel scheme.     

一种改进型遗传算法及其收敛性分析

针对解决简单遗传算法 (SimpleGeneticAlgorithm ,SGA)在应用过程中出现收敛过慢和早熟现象的问题 ,提出了一种改进型遗传算法 (ModifiedGeneticAlgorithm ,MGA) ,并利用Markov链理论证明了该算法的全局概率收敛性。最后以雷达滑窗检测器第一门限的优化设计为例 ,说明了该算法的有效性和实用性。     

REGULARITY AND RECURRENCE OF SWITCHING DIFFUSIONS

This work is concerned with switching diffusion processes, also known as regime-switching diffusions. Our attention focuses on regularity, recurrence, and positive recurrence of the underlying stochastic processes. The main effort is devoted to obtaining easily verifiable conditions for the aforementioned properties. Continuous-state-dependent jump processes are considered. First general criteria on regularity and recurrence using Liapunov functions are obtained. Then we focus on a class of problems, in which both the drift and the diffusion coefficients are ＂linearizable＂ with respect to the continuous state, and suppose that the generator of the jump part of the process can be approximated by a generator of an ergodic Markov chain. Sufficient conditions for regularity, recurrence, and positive recurrence are derived, which are linear combination of the averaged coefficients （averaged with respect to the stationary measure of the Markov chain）.     

不确定退出时间和随机市场环境下风险资产的动态投资组合选择

本文在不确定退出时间和随机市场环境下利用拉格朗日对偶方法研究了多阶段均值-方差投资组合选择问题.我们假定市场上的资产全是风险资产,且随机市场环境只有有限个自然状态,自然状态的转移过程为时变马尔可夫链,各阶段资产的随机收益率不仅与时间有关而且与市场所处的状态有关.首先利用动态规划技术和拉格朗日对偶方法得到了模型的有效投资策略及有效边界的显式表达式.然后,还给出并证明了一个多阶段版本的两基金分离定理,最后,为说明本文的结论及应用,给出了一个数值算例.     

A discontinuous Galerkin method combined with mixed finite element for seawater intrusion problem

<正> Seawater intrusion problem is considered in this paper.Its mathematical model is anonlinear coupled system of partial differential equations with initial boundary problem.It consistsof the water head equation and the salt concentration equation.A combined method is developedto approximate the water head equation by mixed finite element method and concentration equationby discontinuous Galerkin method.The scheme is continuous in time and optimal order estimates inH~1-norm and L~2-norm are derived for the errors.     

Discriminant analysis based on statistical depth

<正> In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been presented.In this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is proposed.Then aclassification rule based on the depth function family is proposed.The classification parameter b couldbe modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achievesthe convergence rate n~(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a realdata example compare the performance of the different discriminant methods.     

Multi-period mean-variance portfolio selection with Markov regime switching and uncertain time-horizon

This paper investigates a multi-period mean-variance portfolio selection with regime switching and uncertain exit time. The returns of assets all depend on the states of the stochastic market which are assumed to follow a discrete-time Markov chain. The authors derive the optimal strategy and the efficient frontier of the model in closed-form. Some results in the existing literature are obtained as special cases of our results.     

A batch arrival retrial queue with starting failures,feedback and admission control

This paper is concerned with the analysis of a feedback M^[X]/G/1 retrial queue with starting failures and general retrial times. In a batch, each individual customer is subject to a control admission policy upon arrival. If the server is idle, one of the customers admitted to the system may start its service and the rest joins the retrial group, whereas all the admitted customers go to the retrial group when the server is unavailable upon arrival. An arriving customer (primary or retrial) must turn-on the server, which takes negligible time. If the server is started successfully (with a certain probability), the customer gets service immediately. Otherwise, the repair for the server commences immediately and the customer must leave for the orbit and make a retrial at a later time. It is assumed that the customers who find the server unavailable are queued in the orbit in accordance with an FCFS discipline and only the customer at the head of the queue is allowed for access to the server. The Markov chain underlying the considered queueing system is studied and the necessary and sufficient condition for the system to be stable is presented. Explicit formulae for the stationary distribution and some performance measures of the system in steady-state are obtained. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.     

CONVERGENCE PROPERTIES OF THE DEPENDENT PRP CONJUGATE GRADIENT METHODS

In this paper, a new region of βk with respect to ;βk^PRP is given. With two Armijo-type line searches, the authors investigate the global convergence properties of the dependent PRP conjugate gradient methods, which extend the global convergence results of PRP conjugate gradient method proved by Grippo and Lucidi （1997） and Dai and Yuan （2002）.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for nonlinear stochastic Markov systems with time-delay and multiplicative noise

This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input- and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities (HJIs), the exponential mean square H_∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly, by using fuzzy T-S model approach, the H_∞ controller can be designed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.     

Neural networks and the best trigomometric approximation

With the best trigonometric polynomial approximation as a metric, the rate of approximation of the one-hidden-layer feedforward neural networks to approximate an integrable function is estimated by using a constructive approach in this paper. The obtained result shows that for any 2π-periodic integrable function, a neural networks with sigmoidal hidden neuron can be constructed to approximate the function, and that the rate of approximation do not exceed the double of the best trigonometric polynomial approximation of function.