The fractional fixed-charge problem

Fractional fixed-charge problems arise in numerous applications, where the measure of economic performance is the time rate of earnings or profit (equivalent to an interest rate on capital investment). This paper treats the fractional objective function, after suitable transformation, as a linear parametric fixed-charge problem. It is proved, with wider generality than in the case of Hirsch and Dantzig, that some optimal solution to the generalized linear fixed-charge problem is an extreme point of the polyhedral set defined by the constraints. Furthermore, it is shown that the optimum of the generalized fractional fixed-charge problem is also a vertex of this set. The proof utilizes a suitable penalty function yielding an upper bound on the optimal value of the objective function; this is particularly useful when considering combinations of independent transportation-type networks. Finally, it is shown that the solution of a fractional fixed-charge problem is obtainable through that of a certain linear fixed-charge one.     

高可靠性软件的极值统计分析

提出了极值统计分析的方法.对于失效数据极值分布函数的拟合检验,采用了相关系数法;对于母体分布的参数估计,则分别采用了最小二乘估计(LSE)和极大似然估计(MLE);最后通过一个实例说明了统计过程,并用模拟的方法证明了最小二乘估计较好.     

Distribution of a linear function and the ratio of two independent linear functions of independent generalized gamma variables

In this paper the exact distribution of a linear function and the ratio of two independent linear functions of independent generalized gamma variables is given.     

Approximate probability distributions for the extreme spread

The extreme spread, or greatest distance between all pairs of impact points on a target, is often used as a rapid measure of dispersion or precision of shot groups on a target. It is therefore desirable to know its statistical properties. Since the exact theoretical distribution has not yet been worked out, this paper examines the accuracy of several approximations which are checked against large sample monte carlo values. We find in particular that for the sample sizes considered the extreme spread can be approximated well by a Chi variate.     

关于正规变换函数性质的研究

正规变换函数是研究估计量的各类渐近性质的重要工具,在估计量的渐近性质研究中起着非常重要的作用。通过对正规变换函数性质的研究,利用概率统计的分析方法,对正规变换函数的性质做出更为深刻的刻画,推广了正规变换函数的性质,得到了正规变换函数的一系列好的性质,为极值理论领域中估计量及估计量各类性质的研究提供了有力的工具。     

Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring

Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring, Commun Statist Theory Methods 17 (1988), 1857–1870] considered a hybrid censoring scheme and obtained the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution along with an exact lower confidence bound. Childs et al. [Exact likelihood inference based on Type‐I and Type‐II hybrid censored samples from the exponential distribution, Ann Inst Statist Math 55 (2003), 319–330] recently derived an alternative simpler expression for the distribution of the MLE. These authors also proposed a new hybrid censoring scheme and derived similar results for the exponential model. In this paper, we propose two generalized hybrid censoring schemes which have some advantages over the hybrid censoring schemes already discussed in the literature. We then derive the exact distribution of the maximum likelihood estimator as well as exact confidence intervals for the mean of the exponential distribution under these generalized hybrid censoring schemes. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Optimal betting strategies for favorable games

We examine the problem of a gambler interested in maximizing the expected value of a convex utility function of his fortune after n plays of a game. We allow any probability distribution to rule the outcome of each play, and this distribution may change from play to play according to a Markov process. We present results regarding the existence of an optimal policy and its structural dependence on the gambler's fortune. The well-known results of Bellman and Kalaba for exponential and logarithmic utility functions and coin-tossing games are generalized. We also examine the situation of general stale spaces and show that the same structural results hold.     

基于时延的宽带LFM信号DOA估计算法

针对常用宽带LFM信号DOA估计算法采样数据量大、运算量大的特点,提出了一种基于时延的宽带LFM信号DOA估计算法。先把阵元接收到的信号变换到频域,而后用极值频率点进行时延估计,并对各极值频率点的时延估计值进行加权平均,进而估计出宽带LFM信号的来波方位。仿真验证了该算法的合理性和有效性。     

一种基于遗传算法的防空兵火力分配方法

在建立了防空兵火力分配的遗传算法模型基础上,阐述了遗传算法在防空兵火力分配中的应用情况,并通过在计算机上仿真运行实例,得出了火力分配方案。分析了此方法与威胁估计模型火力分配方法的优缺点,是一种有益的尝试与探索,对防空兵指挥决策和理论研究有一定的参考价值。     

灰色关联投影法的威胁排序算法

威胁评估与排序是作战系统和C4I系统必须具备的重要功能.结合多指标决策理论和灰色系统理论,提出了基于多指标决策灰色关联投影法的威胁排序算法.首先通过建立灰色关联判断矩阵将威胁排序转化为多指标决策问题;其次为缩小极端值的影响提出了基于信息熵的威胁指标权重算法;最后从矢量投影角度应用灰色关联投影值进行威胁排序;并分别研究了分辨系数和指标权重对威胁排序的影响.通过现代防空作战实例验证了算法的有效性和工程实用性.     

Bounds and elimination in generalized markov decisions

In discounted Markov decision processes bounds on the optimal value function can be computed and used to eliminate suboptimal actions. In this paper we extend these procedures to the generalized Markov decision process. In so doing we forfeit the contraction property and must base our analysis on other procedures. Duality theory and the Perron-Frobenius theorem are the main tools.     

A versatile scheme for ranking the extreme points of an assignment polytope

A cutting plane scheme embedded in an implicit enumeration framework is proposed for ranking the extreme points of linear assignment problems. This method is capable of ranking any desired number of extreme points at each possible objective function value. The technique overcomes storage difficulties by being able to perform the ranking at any particular objective function value independently of other objective values. Computational experience on some test problems is provided.     

Expansion planning for waste‐to‐energy systems using waste forecast prediction sets

We consider an expansion planning problem for Waste‐to‐Energy (WtE) systems facing uncertainty in future waste supplies. The WtE expansion plans are regarded as strategic, long term decisions, while the waste distribution and treatment are medium to short term operational decisions which can adapt to the actual waste collected. We propose a prediction set uncertainty model which integrates a set of waste generation forecasts and is constructed based on user‐specified levels of forecasting errors. Next, we use the prediction sets for WtE expansion scenario analysis. More specifically, for a given WtE expansion plan, the guaranteed net present value (NPV) is evaluated by computing an extreme value forecast trajectory of future waste generation from the prediction set that minimizes the maximum NPV of the WtE project. This problem is essentially a multiple stage min‐max dynamic optimization problem. By exploiting the structure of the WtE problem, we show this is equivalent to a simpler min‐max optimization problem, which can be further transformed into a single mixed‐integer linear program. Furthermore, we extend the model to optimize the guaranteed NPV by searching over the set of all feasible expansion scenarios, and show that this can be solved by an exact cutting plane approach. We also propose a heuristic based on a constant proportion distribution rule for the WtE expansion optimization model, which reduces the problem into a moderate size mixed‐integer program. Finally, our computational studies demonstrate that our proposed expansion model solutions are very stable and competitive in performance compared to scenario tree approaches. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 47–70, 2016     

基于神经网络的广义两点边值问题

在航天领域中 ,多数制导问题均可以抽象为广义两点边值问题。本文探讨了神经网络在广义两点边值问题求解中的应用。首先讨论了离线制导这一类静态两点边值问题的求解 ,在此基础上 ,对在线制导这一类动态两点边值问题进行了分析 ,并给出了有效的解决方法     

A method to determine the shell layout scheme for equipment battlefield damage tests under artillery fire

In this paper,a new method for determining the shell layout scheme is proposed,which can make the equipment damage data by the battlefield damage test resemble as close as possible the actual combat data.This method is based on the analysis of the impact point distribution and effective damage area of equipment.In order to obtain the position of the impact points,an impact point distribution model under artillery fire was established.Similarly,in order to obtain the effective damage area of equipment,the concepts of generalized damage area and task-based equipment functional damage probability were demonstrated,and the corresponding calculation model was established.Through case analysis,the shell layout scheme was effectively obtained,verifying the correctness of the proposed method.     

Robust regression with censored data

The properties of robust M estimators with randomly right-censored response variables in linear regression models are considered. The most robust and the optimal robust M estimators of the regression parameters are derived within a class of η functions considered in James [5] as well as for a class of η functions corresponding to the general unrestricted class. The usefulness of the estimators corresponding to these two classes are examined. From the computational point of view the James-type η functions are readily obtainable from the η functions in the uncensored case. However, it is found that the breakdown point of the optimal James-type estimators can be lower than the breakdown point of the corresponding optimal robust estimators for nonsymmetric parent distribution functions such as the extreme value distribution. In addition, the efficiency of the optimal James-type estimators is somewhat lower than the efficiency of the optimal robust estimators.     

空降兵师(团)登岛作战兵力分配模型

通过结合空降兵师(团)级登岛作战的战术特点,确立了遮断点的单点和联合价值的指标体系,建立了以联盟博弈为基础的兵力分配初步模型,然后以Shapley值作为此联盟博弈的解,结合投放过程中的兵力损耗,得到一个合理的兵力分配方案,从而建立了师(团)级空降登岛作战的兵力分配模型和算法.     

两种数字水印算法的比较

分别介绍迭加水印方案和量化水印方案,对每种方案一些常见算法予以说明,阐明其优缺点,对两种水印方案的相同点和不同点进行了研究。通过实验证明,两种水印方案的PSNR比较相似：迭加水印检测的相关值分布比较扩散,受高斯影响大;量化水印检测的相关值比较稳定,受高斯噪声的影响小。     

自反Banach空间一类完全广义集值强非线性混合似变分不等式问题

研究了一类完全广义集值强非线性混合似变分不等式在自反Banach空间下的问题,借助一个极大极小不等式,证明了这类完全广义集值强非线性混合似变分不等式的解的存在唯一性定理。     

A nonparametric approach to accelerated life testing under multiple stresses

Accelerated life testing (ALT) is concerned with subjecting items to a series of stresses at several levels higher than those experienced under normal conditions so as to obtain the lifetime distribution of items under normal levels. A parametric approach to this problem requires two assumptions. First, the lifetime of an item is assumed to have the same distribution under all stress levels, that is, a change of stress level does not change the shape of the life distribution but changes only its scale. Second, a functional relationship is assumed between the parameters of the life distribution and the accelerating stresses. A nonparametric approach, on the other hand, assumes a functional relationship between the life distribution functions at the accelerated and nonaccelerated stress levels without making any assumptions on the forms of the distribution functions. In this paper, we treat the problem nonparametrically. In particular, we extend the methods of Shaked, Zimmer, and Ball [7] and Strelec and Viertl [8] and develop a nonparametric estimation procedure for a version of the generalized Arrhenius model with two stress variables assuming a linear acceleration function. We obtain consistent estimates as well as confidence intervals of the parameters of the life distribution under normal stress level and compare our nonparametric method with parametric methods assuming exponential, Weibull and lognormal life distributions using both real life and simulated data. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 629–644, 1998