Approximating nondominated sets in continuous multiobjective optimization problems

Many important problems in Operations Research and Statistics require the computation of nondominated (or Pareto or efficient) sets. This task may be currently undertaken efficiently for discrete sets of alternatives or for continuous sets under special and fairly tight structural conditions. Under more general continuous settings, parametric characterisations of the nondominated set, for example through convex combinations of the objective functions or ε‐constrained problems, or discretizations‐based approaches, pose several problems. In this paper, the lack of a general approach to approximate the nondominated set in continuous multiobjective problems is addressed. Our simulation‐based procedure only requires to sample from the set of alternatives and check whether an alternative dominates another. Stopping rules, efficient sampling schemes, and procedures to check for dominance are proposed. A continuous approximation to the nondominated set is obtained by fitting a surface through the points of a discrete approximation, using a local (robust) regression method. Other actions like clustering and projecting points onto the frontier are required in nonconvex feasible regions and nonconnected Pareto sets. In a sense, our method may be seen as an evolutionary algorithm with a variable population size. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A generalization of the weighted set covering problem

We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b‐matching problem. In general, we may use a polynomial‐time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256–278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383–390], and V. Chvatal [A greedy heuristic for the set‐covering problem, Math Oper Res 4(3) (1979), 233–235] to get an approximate solution for the problem. We find a worst‐case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Optimum quantiles for the linear estimation of the parameters of the extreme value distribution in complete and censored samples

The present study is concerned with the determination of a few observations from a sufficiently large complete or censored sample from the extreme value distribution with location and scale parameters μ and σ, respectively, such that the asymptotically best linear unbiased estimators (ABLUE) of the parameters in Ref. [24] yield high efficiencies among other choices of the same number of observations. (All efficiencies considered are relative to the Cramér-Rao lower bounds for regular unbiased estimators.) The study is on the asymptotic theory and under Type II censoring scheme. For the estimation of μ when σ is known, it has been proved that there exists a unique optimum spacing whether the sample is complete, right censored, left censored, or doubly censored. Several tables are prepared to aid in the numerical computation of the estimates as well as to furnish their efficiencies. For the estimation of σ when μ is known, it has been observed that there does not exist a unique optimum spacing. Accordingly we have obtained a spacing based on a complete sample which yields high efficiency. A similar table as above is prepared. When both μ and σ are unknown, we have considered four different spacings based on a complete sample and chosen the one yielding highest efficiency. A table of the efficiencies is also prepared. Finally we apply the above results for the estimation of the scale and/or shape parameters of the Weibull distribution.     

基于偏最小二乘回归的军用飞机采购价格预测

考虑到军用飞机采购价格样本数据少、难于预测的特点和偏最小二乘回归方法在处理小样本多元数据方面的优势,提出一种基于偏最小二乘回归的军用飞机价格预测方法.偏最小二乘回归首先提取第一、第二主成分对采购价格样本的特异点进行剔除;然后进行变量投影重要度分析来筛选变量;最后,偏最小二乘回归对筛选的变量进行回归建立军用飞机价格预测模型,并对军用飞机价格进行预测.结果表明,在军用飞机价格预测方面,与未筛选变量的回归模型和逐步多元回归相比,经过变量筛选的偏最小二乘回归模型预测的精度更高,更能体现采购价格与飞机性能参数之间的关系.     

基于混合矩的多输出模型确认指标研究

针对随机不确定性条件下多输出计算模型与物理实验数据之间一致性难以量化度量这一问题,本文提出一组新的基于混合矩的多输出模型确认指标。在不确定情况下,同时考虑到多维输出之间的相关关系和单输出的均值,构建了由多输出数学期望列阵和协方差矩阵组成的多输出模型确认局部混合矩指标和全局混合矩指标。其中局部混合矩指标包括绝对指标(LA-3M)和相对指标(LR-3M),它们适合固定位置的多输出局部模型确认;全局混合矩指标也包括绝对指标(GA-3M)和相对指标(GR-3M),它们适合多点位置的多输出全局模型确认。通过数字算例和工程算例,并与PIT和t-pooling 面积指标进行对比,结果表明本文所提指标可行有效,能够方便地度量计算模型和物理实验之间的差异程度。     

A model to predict the residual life of aircraft engines based upon oil analysis data

This paper reports on a study using the available oil monitoring information, such as the data obtained using the Spectrometric Oil Analysis Programme (SOAP), to predict the residual life of a set of aircraft engines. The relationship between oil monitoring information and the residual life is established using the concept of the proportional residual, which states that the predicted residual life may be proportional to the wear increment measured by the oil analysis programmes. Assuming such a relationship between wear and the residual life exists, we formulated a recursive prediction model for the item's residual life given measured oil monitoring information to date. A set of censored life data of 30 aircraft engines (right censored due to preventive overhaul) along with the history of their monitored metal concentration information are available to us. The metal concentration information includes many variables, such as Fe, Cu, Al, etc.; not all of them are useful, and some of them may be correlated. The principal component analysis (PCA) has been adopted to reduce the dimension of the original data set and to produce a new set of uncorrelated variables, which we shall use in the prediction model. The procedure associated with estimating model parameters is discussed. The model is fitted to the actual SOAP data from the aircraft engines, and the goodness‐of‐fit test has been carried out. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

基于遗传算法与最大最小原理的故障模式特征选择

在诸如液体火箭发动机等复杂动力学系统的故障诊断中，监控参数组的优选问题一直受到工程技术人员的高度重视。本文提出了综合样本矢量方向离散度概念，以此作为故障特征参数的优选准则；然后利用经过改进的遗传算法，对某液体火箭发动机常见故障的诊断进行了特征参数组的优选。在改进的遗传算法中，采用了非常简洁而高效的染色体编码，针对特征优选的组合优化类问题专门设计了一种特殊的基因迁移算子，并引进了父本个体适应值的动态调整技术与共享函数。数值实验结果表明，该算法具有理想的效果。     

Country survey III — Defence spending in West Germany

This survey article deals with defence spending in West Germany from 1960 on, and the resulting manpower levels and major weapons of the Federal Armed forces, focusing on macro‐economic aspects. Statistics compiled from a variety of published and unpublished sources are presented in 16 tables. An econometric defence‐spending function is derived for the period. For comparison, the equivalent data of East Germany from the last years is also presented. The small set of developments in the next few years that can be predicted firmly are discussed.     

基于免疫FNN算法的加热炉炉温优化控制

针对复杂钢坯加热过程,提出了一种免疫克隆进化模糊神经网络(ICE-FNN)控制算法。首先根据现场样本数据建立过程神经网络模型;然后基于该模型,采用模糊神经网络控制器(FNNC)规则优化算法,确定FNNC的最佳规则数;最后由FNNC的规则优化所得参数构造初始种群的一个解,采用免疫克隆进化(ICE)算法对FNNC参数优化。该算法具有全局寻优和局部求精能力,仿真结果证实了其有效性。     

Tests of independence of continuous random variables which guard against special alternatives

For the problem of testing the independence of a set of continuous random variables, where the test is to be based on n independent and identically distributed observations, tests are constructed that guard against all alternatives but are particularly effective against special alternatives of interest. The tests are based on the numbers of observations falling in the cells of a grid constructed using order statistics.     

语音矢量量化编码

语音矢量量化编码是一项新技术,具有很大的实用价值。本文简要地阐述矢量量化原理之后,着重介绍语音波形矢量量化编码、语音参数矢量量化编码、以及混合形式矢量量化编码,综述近年来国内外学者在这几个方面取得的一些成果,预测它们的发展动向。     

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive esti-mation algorithm is insensitive to initial conditions and of good robustness.     

IMM-Singer模型的机动目标跟踪算法

交互式多模型(IMM)算法是一种有效机动目标跟踪算法,但其性能与模型的选择、个数以及参数有关。Singer模型算法可以实现对机动目标的跟踪,但该算法存在机动频率和过程噪声大小等参数难以选取的问题。针对以上情况,利用IMM算法易于结合其他算法的特点,提出一种基于IMM-Singer模型的机动目标跟踪算法,实现Singer模型参数的自适应选择。仿真结果表明,该算法比单一的Singer模型算法或一般的IMM算法更能有效提高机动目标跟踪精度。     

Bi‐objective missile rescheduling for a naval task group with dynamic disruptions

This paper considers the rescheduling of surface‐to‐air missiles (SAMs) for a naval task group (TG), where a set of SAMs have already been scheduled to intercept a set of anti‐ship missiles (ASMs). In missile defense, the initial engagement schedule is developed according to the initial state of the defensive and attacking units. However, unforeseen events may arise during the engagement, creating a dynamic environment to be handled, and making the initial schedule infeasible or inefficient. In this study, the initial engagement schedule of a TG is assumed to be disrupted by the occurrence of a destroyed ASM, the breakdown of a SAM system, or an incoming new target ASM. To produce an updated schedule, a new biobjective mathematical model is formulated that maximizes the no‐leaker probability value for the TG and minimizes the total deviation from the initial schedule. With the problem shown to be NP‐hard, some special cases are presented that can be solved in polynomial time. We solve small size problems by the augmented ? ‐ constraint method and propose heuristic procedures to generate a set of nondominated solutions for larger problems. The results are presented for different size problems and the total effectiveness of the model is evaluated.     

‘Today we shall drink blood’: internal unrest in Nigeria

Despite some tentative internal peace agreements, Nigeria continues to face violence from multiple groups. This violence feeds upon itself, with segments of the population being mobilized both for self defense and for pressing their ideological and practical goals. These multiple sources of violence, which the Nigerian government appears unable to control to any significant degree, have a long term corrosive effect on the country's internal stability. There are few reasons to be sanguine as to any rapid changes to the level of overall violence or the relative number of armed groups, although their specific identities may shift. Nigeria represents a good case study of a country in which relatively low but persistent violence by a multiplicity of groups can have major impacts on internal security.     

A numerical study on the disturbance of explosive reactive armors to jet penetration

The disturbance of flat and V-shaped sandwich reactive armor configurations to shaped-charge jet is studied by a numerical approach. The disturbing and cutting effects of the two reactive armor configurations to the jet are successfully captured. The predicted disturbance characteristics and patterns are in fairly good agreement with the X-ray photographic observations. The residual depth of penetration into a semi-infinitive homogeneous steel target behind the reactive armor is computed for a series of jet/armor parameters. For the flat configuration, it is demonstrated that the residual penetration depth is not significantly reduced for a normal impact while it is reduced up to 75% for an oblique impact. In comparison, the V-shaped configuration reduces the penetration depth of the jet to 90%, and it is observed that the penetration depth is not sensitive to the V-shaped angle.     

Test for the extreme value and weibull distributions based on normalized spacings

Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling A² statistic calculated from a set zⁱ of values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, A² is recommended overall; the mean also gives good power in many situations, but can be nonconsistent.     

基于UKF-SOFNN的近距机动目标跟踪滤波算法

对于多目标杂波环境中的机动目标跟踪,由于目标集群中各个目标间的空间距离可能小于探测器的空间分辨率,因而可能出现误跟、诱饵欺骗与杂波虚警等一系列严重后果。对此,提出一种综合运用UKF(不敏卡尔曼滤波)和SOFNN(自组织模糊神经网络)的UKF-SOFNN滤波跟踪算法,将机动目标模型视作严格的非线性系统,利用UKF-SOFNN对非线性参数的辨识能力提高对锁定机动目标的跟踪能力。仿真实例表明,该算法能有效地辨识目标群中的目标,并进行可靠的跟踪。     

Neutrino-Based Tools for Nuclear Verification and Diplomacy in North Korea

We present neutrino-based options for verifying that the nuclear reactors at North Korea’s Yongbyon Nuclear Research Center are no longer operating or that they are operating in an agreed manner, precluding weapons production. Neutrino detectors may be a mutually agreeable complement to traditional verification protocols because they do not require access inside reactor buildings, could be installed collaboratively, and provide persistent and specific observations. At Yongbyon, neutrino detectors could passively verify reactor shutdowns or monitor power levels and plutonium contents, all from outside the reactor buildings. The monitoring options presented here build on recent successes in basic particle physics. Following a dedicated design study, these tools could be deployed in as little as one year at a reasonable cost. In North Korea, cooperative deployment of neutrino detectors could help redirect a limited number of scientists and engineers from military applications to peaceful technical work in an international community. Opportunities for scientific collaboration with South Korea are especially strong. We encourage policymakers to consider collaborative neutrino projects within a broader program of action toward stability and security on the Korean Peninsula.     

Asymptotic joint normality of an increasing number of multivariate order statistics and associated cell frequencies

Take n independent identically distributed (IID) observations from a continuous r-variate population, and choose some order statistics from each of the r variates. These order statistics are used to construct a grid in r-dimensional space. Under certain conditions, it is shown that as n increases we can choose an increasing number of order statistics in such a way that the asymptotic joint distribution of the chosen order statistics and of the frequencies of sample points falling in the cells of the grid can be assumed to be a normal distribution. An application to testing independence of random variables is given.