修正积分水平集方法的随机实现算法

本文提出了一个从随机到确定性的变测度算法，通过对不同的箱子采用不同的测度，将Monte-Carlo随机投点与确定性数论方法相结合的策略，使水平值充分地下降．最后，给出了实现算法收敛性并通过数值实验验证了其有效性．     

变测度的积分型全局优化算法

郑权等首先提出积分-水平集求总极值的方法,实现算法中采用Monte-Carlo 随机投点产生近似水平集来缩小搜索区域范围,但这一算法可能失去总极值点．此后,邬 冬华等给出了一种修正的积分－水平集的方法,一种区域不收缩的分箱方法以保证总极 值点不被丢失．本文在此基础上采取对不同的箱子采用不同的测度这一策略,使水平值 更充分的下降,更快的达到全局极小值,以提高修正算法的计算效率．最后给出的数值算 例说明了算法是有效的．     

有约束的变测度积分——水平集算法

提出了一种有约束的变测度积分-水平集的算法,对不同的箱子采用不同的测度,结合确定性数论方法选取一致分布佳点集来代替Monte-Carlo随机投点,使水平值充分地下降,更快地到达全局最小,从而提高算法的计算效率.给出了算法的收敛性证明,并通过数值算例验证了它的有效性.     

四阶R-K方法中一类新算法的分析

对常微分方程初值问题数值计算中的四阶R-K方法首次具体给出了一般格式中的参数所满足的方程,并提出了新的计算格式,这些新算法对某些初值问题其整体截断误差有明显的减少.这对常微分方程初值问题在社会、经济、生态等领域中的广泛应用将提供有益的新算法.     

The global and superlinear convergence of a new nonmonotone MBFGS algorithm on convex objective functions

In this paper, a new nonmonotone MBFGS algorithm for unconstrained optimization will be proposed. Under some suitable assumptions, the global and superlinear convergence of the new nonmonotone MBFGS algorithm on convex objective functions will be established. Some numerical experiments show that this new nonmonotone MBFGS algorithm is competitive to the MBFGS algorithm and the nonmonotone BFGS algorithm.     

求解全局最优问题的多重点样本水平值估计的相对熵算法

研究有界闭箱约束下的全局最优化问题,利用相对熵及广义方差函数方程的最大根与全局最小值之间的等价关系,设计求解全局最优值的积分型水平值估计算法.对采用重点样本采样技巧产生的函数值按一定规则进行聚类,从而在各聚类中产生的若干新重点样本,结合相对熵算法,构造出多重点样本进行全局搜索的新算法.该算法的优点在于每次迭代选用当前较好的函数值信息,以达到随机搜索到更好的函数值信息.同时多重点样本可有利挖掘出更好的全局信息.一系列的数值实验表明该算法是非常有效的.     

An algorithm to solve boundary value problems for differential iinclusions and applications in optimal control

Convergence results for simplicia1 fixed point algorithms applied to problems in Banach-spaces enable constructive proofs of the existence of fixed points for set valued operators [14]. Boundary value problems for differential inclusions will be interpreted in this context. The resulting new algorithm allows numerical treatment of boundary value problems with Peano-typedynamics. The necessary conditions of the Pontryagin Maximum Principle are discussed in this framework, leading to a new indirect method for the computation of optimal trajectories with its focus on global convergence conditions for compact control domains.     

QRS complex detection based on multi wavelet packet decomposition

We present in this paper a wavelet packet based QRS complex detection algorithm. Our proposed algorithm consists of a particular combination of two vectors obtained by applying a designed routine of QRS detection process using ‘haar’ and ‘db10’ wavelet functions respectively. The QRS complex detection routine is based on the histogram approach where our key idea was to search for the node with highest number of histogram coefficients, at center, which we assume that they are related to the iso-electric baseline whereas the remaining least number coefficients reflect the R waves peaks. Following a classical approach based of a calculated fixed threshold, the possible QRS complexes will be determined. The QRS detection complex algorithm has been applied to the whole MIT-BIH arrhythmia Database to assess its robustness. The algorithm reported a global sensitivity of 98.68%, positive predictive value of 97.24% and a percentage error of 04.12%. Eventhough, the obtained global results are not as excellent as expected, we have demonstrate that our designed QRS detection algorithm performs good on a partial selected high percentage of the whole database, e.g., the partial results, obtained when applying the algorithm on 85.01% of the whole MIT-BIH arrhythmia Database, are 99.14% of sensitivity, 98.94% of positive predictive value and 01.92% of percentage error.     

一种具有非线性约束线性规划全局优化算法

本文提出了一种新的适用于处理非线性约束下线性规划问题的全局优化算法。该算法通过构造子问题来寻找优于当前局部最优解的可行解。该子问题可通过模拟退火算法来解决。通过求解一系列的子问题,当前最优解被不断地更新,最终求得全局最优解。最后,本算法应用于几个典型例题,并与罚函数法相比较,数值结果表明该算法是可行的,有效的。     

变测度的积分-水平集确定性算法

提出了一个求总极值的变测度确定性算法,对不同的箱子采用不同的测度,结合确定性数论方法选取一致分布佳点集来代替Monte-Carlo随机投点,使水平值充分地下降,更快地到达全局最小,从而提高算法的计算效率.在文中给出了算法的收敛性证明,并通过数值算例验证了它的有效性.     

服务台不可靠的重试排队系统均衡分析

本文研究服务台不可靠的M/M/1常数率重试排队系统中顾客的均衡进队策略, 其中服务台在正常工作和空闲状态下以不同的速率发生故障。在该系统中, 服务台前没有等待空间, 如果到达的顾客发现服务台处于空闲状态, 该顾客可占用服务台开始服务。否则, 如果服务台处于忙碌状态, 顾客可以选择留下信息, 使得服务台在空闲时可以按顺序在重试空间中寻找之前留下信息的顾客进行服务。当服务台发生故障时, 正在被服务的顾客会发生丢失, 且系统拒绝新的顾客进入系统。根据系统提供给顾客的不同程度的信息, 研究队长可见和不可见两种信息情形下系统的稳态指标, 以及顾客基于收入-支出函数的均衡进队策略, 并建立单位时间内服务商的收益和社会福利函数。比较发现, 披露队长信息不一定能提高服务商收益和社会福利。     

Global optimization of fractional programs

Dinkelbach's global optimization approach for finding the global maximum of the fractional programming problem is discussed. Based on this idea, a modified algorithm is presented which provides both upper and lower bounds at each iteration. The convergence of the lower and upper bounds to the global maximum function value is shown to be superlinear. In addition, the special case of fractional programming when the ratio involves only linear or quadratic terms is considered. In this case, the algorithm is guaranteed to find the global maximum to within any specified tolerance, regardless of the definiteness of the quadratic form.     

A new hybrid classical-quantum algorithm for continuous global optimization problems

Grover’s algorithm can be employed in global optimization methods providing, in some cases, a quadratic speedup over classical algorithms. This paper describes a new method for continuous global optimization problems that uses a classical algorithm for finding a local minimum and Grover’s algorithm to escape from this local minimum. Such algorithms will be useful when quantum computers of reasonable size are available. Simulations with testbed functions and comparisons with algorithms from the literature are presented.     

A Modified BFGS Algorithm for Unconstrained Optimization

In this paper we present a modified BFGS algorithm for unconstrainedoptimization. The BFGS algorithm updates an approximate Hessianwhich satisfies the most recent quasi-Newton equation. The quasi-Newtoncondition can be interpreted as the interpolation conditionthat the gradient value of the local quadratic model matchesthat of the objective function at the previous iterate. Ourmodified algorithm requires that the function value is matched,instead of the gradient value, at the previous iterate. Themodified algorithm preserves the global and local superlinearconvergence properties of the BFGS algorithm. Numerical resultsare presented, which suggest that a slight improvement has beenachieved.     

A matrix rational Lanczos method for model reduction in large‐scale first‐ and second‐order dynamical systems

In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model‐order reduction problems using multipoint moment matching‐based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos‐like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second‐order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given.     

Pseudo expected improvement criterion for parallel EGO algorithm

The efficient global optimization (EGO) algorithm is famous for its high efficiency in solving computationally expensive optimization problems. However, the expected improvement (EI) criterion used for picking up candidate points in the EGO process produces only one design point per optimization cycle, which is time-wasting when parallel computing can be used. In this work, a new criterion called pseudo expected improvement (PEI) is proposed for developing parallel EGO algorithms. In each cycle, the first updating point is selected by the initial EI function. After that, the PEI function is built to approximate the real updated EI function by multiplying the initial EI function by an influence function of the updating point. The influence function is designed to simulate the impact that the updating point will have on the EI function, and is only corresponding to the position of the updating point (not the function value of the updating point). Therefore, the next updating point can be identified by maximizing the PEI function without evaluating the first updating point. As the sequential process goes on, a desired number of updating points can be selected by the PEI criterion within one optimization cycle. The efficiency of the proposed PEI criterion is validated by six benchmarks with dimension from 2 to 6. The results show that the proposed PEI algorithm performs significantly better than the standard EGO algorithm, and gains significant improvements over five of the six test problems compared against a state-of-the-art parallel EGO algorithm. Furthermore, additional experiments show that it affects the convergence of the proposed algorithm significantly when the global maximum of the PEI function is not found. It is recommended to use as much evaluations as one can afford to find the global maximum of the PEI function.     

Identification of mechanical properties of arteries with certification of global optimality

In this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.

     

Global Optimization Using Diffusion Perturbations with Large Noise Intensity

This work develops an algorithm for global optimization.The algorithm is of gradient ascent typeand uses random perturbations.In contrast to the annealing type procedurcs,the perturbation noise intensityis large.We demonstrate that by properly varying the noise intensity,approximations to the global maximumcan be achieved.We also show that the expected time to reach the domain of attraction of the global maximum,which can be approximated by the solution of a boundary value problem,is finite.Discrete-time algorithmsare proposed;recursive algorithms with occasional perturbations involving large noise intensity are developed.Numerical examples are provided for illustration.     

解带有二次约束二次规划的一个整体优化方法

在本文中，我们提出了一种解带有二次约束二次规划问题（QP）的新算法，这种方法是基于单纯形分枝定界技术，其中包括极小极大问题和线性规划问题作为子问题，利用拉格朗日松弛和投影次梯度方法来确定问题（QP）最优值的下界，在问题（QP）的可行域是n维的条件下，如果这个算法有限步后终止，得到的点必是问题（QP）的整体最优解；否则，该算法产生的点的序列{v^k}的每一个聚点也必是问题（QP）的整体最优解。     

A rank based particle swarm optimization algorithm with dynamic adaptation

The particle swarm optimization (PSO) technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space. This paper presents a variation on the standard PSO algorithm called the rank based particle swarm optimizer, or PSO_rank, employing cooperative behavior of the particles to significantly improve the performance of the original algorithm. In this method, in order to efficiently control the local search and convergence to global optimum solution, the γ best particles are taken to contribute to the updating of the position of a candidate particle. The contribution of each particle is proportional to its strength. The strength is a function of three parameters: strivness, immediacy and number of contributed particles. All particles are sorted according to their fitness values, and only the γ best particles will be selected. The value of γ decreases linearly as the iteration increases. A time-varying inertia weight decreasing non-linearly is introduced to improve the performance. PSO_rank is tested on a commonly used set of optimization problems and is compared to other variants of the PSO algorithm presented in the literature. As a real application, PSO_rank is used for neural network training. The PSO_rank strategy outperformed all the methods considered in this investigation for most of the functions. Experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness.