基于序贯决策的航班恢复方法

针对枢纽机场临时关闭后的航班恢复问题,提出了一种新的调度方法,为实时航班恢复提供了新思路.通过重新定义恢复操作,将多变量复杂约束的航班规划问题转化为约束条件简单的序贯决策问题.新方法以原始航班计划为基础,按时间顺序对各时刻的机场起降航班流量约束进行冲突消解.在每一决策时刻,推理计算各航班推迟成本,优先安排成本高的航班起降.测试用例表明,新方法能够为繁忙枢纽机场临时关闭后的多机型航班恢复问题快速地给出最优调整方案.将模型拓展应用于飞机旅客一体化恢复问题,也能够迅速获得调整方案.     

关于一类连续最优控制问题的一种可实现的离散方法

本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法，此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象，文中给出这种做法的理论证明和实现方案。     

线性规划的对偶理论在图解法中的应用

对于多个变量两个约束的线性规划,首先利用线性规划的对偶理论,写出其对偶问题;其次利用图解法求出对偶问题的最优解,最后利用互补松弛条件求出原问题的最优解.     

一类受时间约束的广义运输问题的求解

研究一类受时间约束的广义运输问题,将时间约束转化为容量约束,并将该问题转化为标准的最小费用流问题进而求解.该方法能够较快地找到最优运输方案.     

基于离散型荧火虫算法的高校智能排课的研究

针对传统排课方法排课效率低、成功率低、冲突率高等无法满足现代高校教务管理要求的现状,提出一种基于离散型荧火虫算法的智能排课模型.首先,根据教师、班级、课程、教室及授课时间要求建立一个多目标、多约束的排课数学模型,采用二分图完美匹配操作初始可行排课方案;然后,利用离散型荧火虫优化算法在可行方案中寻找最优排课方案;最后,通过Matlab仿真实验验证其可行性与有效性.     

基于模糊不确定性理论的Bernardo方法

Bernardo方法是一种多属性群决策方法。针对Bernardo方法，本文结合模糊不确定性理论，提出“模糊Bernardo”方法；利用模糊变量表示决策者对多方案排序的模糊目标值，给出其Bernardo方法的模糊混合0-1规划模型和模糊机会约束混合0-1规划模型。该方法为群决策提供了一种多方案排序问题的实用且有效的理论依据和计算方法。最后通过实例对此方法予以验证。     

带时间窗车辆路径问题的改进节约算法

对节约算法进行了改进,并利用改进的节约算法解决了带时间窗约束的多类型车辆路径问题．首先讨论了带时间窗约束的单类型车辆路径问题,给出其模型,并归纳了几种通过改进传统的节约算法得到的用于求解带有具体约束车辆路径问题的改进节约算法．     

拟线性椭圆变分不等式组的特征问题

该文考虑泛函在约束（其中，Ｋ是Ｒ￣Ｎ中的闭凸锥）下的小化问题，得到了解的存在性和正则性，并给出ｐ＝２，Ｋ为双障碍约束的闭凸集时的一个多解结果．泛函Ｉ（ｕ）在约束下的变分对应于一个拟线性椭圆型变分不等式组的特征问题．     

建立运输问题初始调运方案的探讨

用表上作业法求解平衡运输问题时，我们希望编制初始方案的方法既具有操作简单的特点，又能使编制出的初始方案较优（即对应的总运费较接近或等于最小总运费），以便减少调整次数．目前，建立初始调运方案常用的方法有西北角法和最小元素法．西北角法是从产销平衡表的西北...     

一些类型的数学规划问题的全局最优解

本文对严格单调函数给出了几个凸化和凹化的方法，利用这些方法可将一个严格单调的规划问题转化为一个等价的标准D．C．规划或凹极小问题．本文还对只有一个严格单调的约束的非单调规划问题给出了目标函数的一个凸化和凹化方法，利用这些方法可将只有一个严格单调约束的非单调规划问题转化为一个等价的凹极小问题．再利用已有的关于D．C．规划和凹极小的算法，可以求得原问题的全局最优解．     

On decomposition-based block preconditioned iterative methods for half-quadratic image restoration

Image restoration is a fundamental problem in image processing. Except for many different filters applied to obtain a restored image in image restoration, a degraded image can often be recovered efficiently by minimizing a cost function which consists of a data-fidelity term and a regularization term. In specific, half-quadratic regularization can effectively preserve image edges in the recovered images and a fixed-point iteration method is usually employed to solve the minimization problem. In this paper, the Newton method is applied to solve the half-quadratic regularization image restoration problem. And at each step of the Newton method, a structured linear system of a symmetric positive definite coefficient matrix arises. We design two different decomposition-based block preconditioning matrices by considering the special structure of the coefficient matrix and apply the preconditioned conjugate gradient method to solve this linear system. Theoretical analysis shows the eigenvector properties and the spectral bounds for the preconditioned matrices. The method used to analyze the spectral distribution of the preconditioned matrix and the correspondingly obtained spectral bounds are different from those in the literature. The experimental results also demonstrate that the decomposition-based block preconditioned conjugate gradient method is efficient for solving the half-quadratic regularization image restoration in terms of the numerical performance and image recovering quality.     

A special Hermitian and skew-Hermitian splitting method for image restoration

In this paper, we consider an ill-posed image restoration problem with a noise contaminated observation, and a known convolution kernel. A special Hermitian and skew-Hermitian splitting (HSS) iterative method is established for solving the linear systems from image restoration. Our approach is based on an augmented system formulation. The convergence and operation cost of the special HSS iterative method for image restoration problems are discussed. The optimal parameter minimizing the spectral radius of the iteration matrix is derived. We present a detailed algorithm for image restoration problems. Numerical examples are given to demonstrate the performance of the presented method. Finally, the SOR acceleration scheme for the special HSS iterative method is discussed.     

生命线网络系统多节点失效的应急抢修队伍派遣模型研究

针对生命线网络系统中多个节点失效的应急抢修问题,给出了抢修队伍派遣优化模型以及模型的求解方法。在本文中,首先考虑应急修复所需时间、各节点失效所造成的损失和应急修复所需成本等因素,构建了以节点失效损失最小和应急修复成本最低为目标的抢修队伍派遣优化模型;然后针对优化模型的特点,给出了模型的求解方法。最后,通过一个算例分析说明了构建的模型的可行性和有效性。     

Quasi-Newton projection methods and the discrepancy principle in image restoration

In this work, the problem of the restoration of images corrupted by space invariant blur and noise is considered. This problem is ill-posed and regularization is required. The image restoration problem is formulated as a nonnegatively constrained minimization problem whose objective function depends on the statistical properties of the noise corrupting the observed image. The cases of Gaussian and Poisson noise are both considered. A Newton-like projection method with early stopping of the iterates is proposed as an iterative regularization method in order to determine a nonnegative approximation to the original image. A suitable approximation of the Hessian of the objective function is proposed for a fast solution of the Newton system. The results of the numerical experiments show the effectiveness of the method in computing a good solution in few iterations, when compared with some methods recently proposed as best performing.     

Multiobjective service restoration in electric distribution networks using a local search based heuristic

Contingency situations may cause emergency states in distribution systems; these states are defined as the interruption of power supply. Such situations should be avoided whenever possible in order to maintain certain quality limits related to frequency and duration of interruptions. The main objective of service restoration is to minimize the number of consumers affected by the fault, by transferring them to energized support feeders. Electrical and operational conditions, such as radial network configuration, equipment and voltage drop limits, must be respected. This paper presents a new multiobjective local search based heuristic for the restoration of service which considers the minimization of two conflicting criteria: the load not supplied and the number of switching operations involved. Computational experiments with three network systems have shown the flexibility and effectiveness of the proposed method.     

Uniqueness Theorems for Series by Vilenkin System

In this paper, we prove uniqueness theorems and restoration formulas for coefficients of series by Vilenkin system. The series is assumed to be convergent in measure and the distribution function of the majorant of partial sums satisfies some necessary condition.     

Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems

It is well recognized that using the hot standby redundancy provides fast restoration in the case of failures. However the redundant elements are exposed to working stresses before they are used, which reduces the overall system reliability. Moreover, the cost of maintaining the hot redundant elements in the operational state is usually much greater than the cost of keeping them in the cold standby mode. Therefore, there exists a tradeoff between the cost of losses associated with the restoration delays and the operation cost of standby elements. Such a trade-off can be obtained by designing both hot and cold redundancy types into the same system. Thus a new optimization problem arises for the standby system design. The problem, referred to in this work as optimal standby element distributing and sequencing problem (SE-DSP) is to distribute a fixed set of elements between cold and hot standby groups and select the element initiation sequence so as to minimize the expected mission operation cost of the system while providing a desired level of system reliability. This paper first formulates and solves the SE-DSP problem for 1-out-of-N: G heterogeneous non-repairable standby systems. A numerical method is proposed for evaluating the system reliability and expected mission cost simultaneously. This method is based on discrete approximation of time-to-failure distributions of the system elements. A genetic algorithm is used as an optimization tool for solving the formulated optimization problem. Examples are given to illustrate the considered problem and the proposed solution methodology.     

Fraction-order total variation blind image restoration based on L1-norm

A fraction-order total variation blind image restoration algorithm based on L1-norm was proposed for restoring the images blurred by unknown point spread function (PSF) during imaging. According to the form of total variation, this paper introduced an arithmetic operator of fraction-order total variation and generated a mathematical model of cost. Semi-quadratic regularization was used to solve the model iteratively so that the solution of this algorithm became easier. This paper also analyzed the convergence of this algorithm and then testified its feasibility in theory. The experimental results showed the proposed algorithm can increase the PSNR of the restored image by 1 dB in relation to the first order total variation blind restoration method and Bayesian blind restoration method. The details in real blurred image were also pretty well restored. The effectiveness of the proposed algorithm revealed that it was practical in the blind image restoration.     

A contractive operator solution of an airfoil design inverse problem

This paper deals with a numerical method for an airfoil design which was presented in [3, 5]. This method is intended for design of an airfoil from a given velocity distribution along a mean camber line. The method is based on searching for a fixed point of a contractive operator. This operator combines an inexact inverse operator and equations describing the flow. A subsonic flow is assumed, the flow is described by a system of the Euler equations which is solved by an implicit finite volume method. The Newton method is applied to the solution of the nonlinear system. The resulting system of linear algebraic equations is solved by GMRES method, the Jacobian-free version is described. The inexact inverse operator consists of a middle curve function and a thickness function, both depending on the given velocity distribution. In addition to the velocity distribution the velocity in infinity is given. The angle of attack is determined so that the stagnation point is in a specific position. Successful numerical results are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-Phase Model Algorithm with Global Convergence for Nonlinear Programming

The family of feasible methods for minimization with nonlinear constraints includes the nonlinear projected gradient method, the generalized reduced gradient method (GRG), and many variants of the sequential gradient restoration algorithm (SGRA). Generally speaking, a particular iteration of any of these methods proceeds in two phases. In the restoration phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, generally a nonlinear system of equations. In the minimization phase, optimality is improved by means of the consideration of the objective function, or its Lagrangian, on the tangent subspace to the constraints. In this paper, minimal assumptions are stated on the restoration phase and the minimization phase that ensure that the resulting algorithm is globally convergent. The key point is the possibility of comparing two successive nonfeasible iterates by means of a suitable merit function that combines feasibility and optimality. The merit function allows one to work with a high degree of infeasibility at the first iterations of the algorithm. Global convergence is proved and a particular implementation of the model algorithm is described.