基于GO法的多阶段共因失效任务系统可靠性评估

为了解决部件阶段依赖性与共因失效给系统可靠性分析带来的复杂性,针对多阶段共因失效任务系统,结合GO法易于处理有时序、含共因失效系统可靠性分析的特点,首先,将前一阶段的输出信号作为后一阶段的输入信号,建模时首尾连接各阶段模型,建立整个任务系统的隐性GO模型;其次,在进行各信号流状态组合运算时,融入阶段代数处理部件的阶段依赖性;再次,用隐性共因失效分析,将共因失效对系统的影响在状态组合的定量分析中表达出来,得到所需系统可靠性指标;最后,与基于二元决策图的算法进行对比验证。结果表明:GO法可以简捷、准确地处理多阶段共因失效任务系统可靠性评估问题。     

一类非线性系统的自适应模糊反推近似滑模控制

针对一类含有未知非线性函数项和外界干扰的不确定纯反馈非线性系统,提出了一种自适应模糊反推近似滑模变结构控制方法。采用中值定理和隐函数定理使未知非仿射输入函数拥有显式的控制输入,利用模糊系统逼近未知非线性函数,动态面控制技术解决了反推设计中出现的"微分爆炸"问题。所提出的自适应近似滑模控制方案削弱了传统滑模控制中的抖振现象。从理论上证明了所设计的控制器能够保证闭环系统所有信号半全局一致终结有界。仿真算例验证了算法的有效性。     

本质流形上的自适应运动估计

分析了计算机视觉中一种新的运动估计模型,将运动估计作为一个参数定义在"本质流形"上的非线性系统参数辨识问题。针对基于离散处理和连续处理方法得到的"本质流形",提出了一种新的、统一的自适应推广卡尔曼滤波算法,在"本质流形"的局部坐标系上进行运动估计。仿真结果验证了该算法的正确性。     

Replacing continuous demand with discrete demand in a competitive location model

Location models commonly represent demand as discrete points rather than as continuously spread over an area. This modeling technique introduces inaccuracies to the objective function and consequently to the optimal location solution. In this article this inaccuracy is investigated by the study of a particular competitive facility location problem. First, the location problem is formulated over a continuous demand area. The optimal location for a new facility that optimizes the objective function is obtained. This optimal location solution is then compared with the optimal location obtained for a discrete set of demand points. Second, a simple approximation approach to the continuous demand formulation is proposed. The location problem can be solved by using the discrete demand algorithm while significantly reducing the inaccuracies. This way the simplicity of the discrete approach is combined with the approximated accuracy of the continuous-demand location solution. Extensive analysis and computations of the test problem are reported. It is recommended that this approximation approach be considered for implementation in other location models. © 1997 John Wiley & Sons, Inc.     

Machine sequencing: Disjunctive graphs and degree-constrained subgraphs

In two earlier papers, we proposed algorithms for finding an optimal sequence of processing m items on q machines, by finding a minimaximal path in a disjunctive network. In a third paper, this latter model was generalized (from 2-state to 3-state disjunctive graphs) so as to accommodate project scheduling with resource constraints. In this paper, we discuss another algorithm for the (2-state) disjunctive network problem, closely related to those mentioned above. To make the paper self-contained, section 2 briefly describes the problem. Section 3 introduces a class of constraints which forms the basis of the algorithm discussed in section 4. The constraints have only 1, ?1, or 0 as coefficients on the left-hand side, integers on the right-hand side. The whole procedure of generating these constraints and finding a feasible solution whenever a new constraint is added, can be interpreted (section 5) as a process of generating a graph with degree-constraints on its nodes, and then finding a subgraph satisfying the degree-constraints. The nodes of the graph are generated by solving a critical-path-problem, the feasible subgraphs are found by implicit enumeration.     

Comparative evaluation of prior versus progressive articulation of preference in bicriterion optimization

Procedures for solving multiple criteria problems are receiving increasing attention. Two major solution approaches are those involving prior articulation and progressive articulation of preference information. A progressive articulation (interactive) optimization approach, called the Paired Comparison Method (PCM) is compared to the prior articulation approach of a priori utility function measurement in a quality control decision environment from the perspective of the decision maker. The three major issues investigated included: (1) the ease of use of each method, (2) the preferences of solutions obtained, and (3) the insight provided by the methodology into the nature and structure of the problem. The problem setting involved management students who were rquired to determine an acceptance sampling plan using both methods. The PCM provided the most preferred solutions and was considered easier to use and understand. The prior articulation of preference method was found to give more insight into the problem structure. The results suggest that a hybrid approach, combining both prior preference assessment and an interactive procedure exploiting the advantages of each, should be employed to solve multiple criteria problems.     

The one-period,N-location distribution problem

This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. This method is not directly suitable for the solution for large problems, but the exact solution for small problems can be obtained. For the numerical solutions of large problems, the problem has been formulated as a linear program with column generation. This latter approach is quite robust in the sense that it is easily extended to incorporate capacity constraints and the multiproduct case.     

Single-machine scheduling with dynamic arrivals: Decomposition results and an improved algorithm

This article considers the single-machine dynamic scheduling problem where the jobs have different arrival times and the objective is to minimize the sum of completion times. This problem is known to be strongly NP-hard. We develop decomposition results for this problem such that a large problem can be solved by combining optimal solutions for several smaller problems. The decomposition results can be used with any implicit enumeration method to develop an optimal algorithm. Our computational experiment indicates that the computational efficiency of the currently best available branch-and-bound algorithm can be improved with the use of our decomposition results. © 1996 John Wiley & Sons, Inc.     

航天测控调度问题的拉格朗日启发式算法

通过分析航天测控调度问题的测控需求,建立了航天测控调度0-1整数规划模型,运用拉格朗日松弛方法对模型中的任务约束和设备约束进行了松弛,运用次梯度优化算法求得了航天测控调度问题上界,同时得到了决策变量对应的拉格朗日权重,可以作为决策变量在最优解中是否被调度的启发式信息,对拉格朗日权重进行分析,提出了求解问题可行解的拉格朗日启发式算法。最后,通过对两个场景的试验分析验证了拉格朗日启发式算法所求可行解的优越性。     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.     

Class scheduling algorithms for Navy training schools

The problem of developing good schedules for Navy C-Schools has been modeled as a combinatorial optimization problem. The only complicating feature of the problem is that classes must be grouped together into sequences known as pipelines. An ideal schedule will have all classes in a pipeline scheduled in consecutive weeks. The objective is to eliminate the nonproductive time spent by sailors at C-Schools who are waiting for the next class in a pipeline. In this investigation an implicit enumeration procedure for this problem was developed. The key component of our algorithm is a specialized greedy algorithm which is used to obtain a good initial incumbent. Often this initial incumbent is either an optimal schedule or a near optimal schedule. In an empirical analysis with the only other competing software system, our greedy heuristic found equivalent or better solutions in substantially less computer time. This greedy heuristic was extended and modified for the A-School scheduling problem and was found to be superior to its only competitor. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 533–551, 1998     

Diffusion approximation to the G/G/R machine repair problem with warm standby spares

The G/G/R machine repair problem with M operating machines, S warm standby spares, and R repairmen is studied as a diffusion process. The steady-state equations are formulated as diffusion equations subject to two reflecting barriers. The approximate diffusion parameters of the diffusion equations are obtained (1) under the assumption that the input characteristics of the problem are defined only by their first two moments rather than their probability distribution function, (2) under the assumption of heavy traffic approximation, that is, when queues of failed machines in the repair stage are almost always nonempty, and (3) using well-known asymptotic results from renewal theory. Expressions for the probability density functions of the number of failed machines in the system are obtained. A study of the derived approximate results, compared to some of the exact results, suggests that the diffusion approach provides a useful method for solving complex machine-repair problems.     

高超音速流场的隐式TVD格式并行计算

本文采用区域分割技术和拼接网格的并行策略，发展了一个适合于分布式存贮多机系统的ＴＶＤ隐式有限体积并行算法；并在ＰＶＭ并行环境下，对三维高超音速绕流流场实现了多机并行计算，通过负载平衡等方法得到了较高的加速比（在二处理机系统上加速比为１∶８４，在四处理机系统上为３∶４４）。     

常微分方程的不动点迭代格式

在常微分方程的数值解法中,Euler的隐式格式稳定性较好,但由于它为隐式,因而给计算带来了极大地不方便。为了解决此问题,本文给出了一种数值解法———常微分方程的不动点迭代格式。     

过椭圆外一定点作其法线的计算机实现

对过椭圆外一定点的法线作图问题给出了一种计算机实现的几何逼近方法。该方法以几何迭代逼近作图原理为基础,建立了新的逼近法线方程,从而避免了手工作图的低精度及实际操作时的繁琐,使过椭圆外一定点的法线作图问题得以在计算机上迅速获得解决,且可达到足够的精度要求。     

The procurement problem: An integer programming problem well suited to a solution using duality

A procurement problem, as formulated by Murty [10], is that of determining how many pieces of equipment units of each of m types are to be purchased and how this equipment is to be distributed among n stations so as to maximize profit, subject to a budget constraint. We have considered a generalization of Murty's procurement problem and developed an approach using duality to exploit the special structure of this problem. By using our dual approach on Murty's original problem, we have been able to solve large problems (1840 integer variables) with very modest computational effort. The main feature of our approach is the idea of using the current evaluation of the dual problem to produce a good feasible solution to the primal problem. In turn, the availability of good feasible solutions to the primal makes it possible to use a very simple subgradient algorithm to solve the dual effectively.     

Damage accumulation and probability of kill for gun and target engagements

Determination of the gunfire probability of kill against a target requires two parameters to be taken into consideration: the likelihood of hitting the target (susceptibility) and the conditional probability of kill given a hit (vulnerability). Two commonly used methods for calculating the latter probability are (1) treating each hit upon the target independently, and (2) setting an exact number of hits to obtain a target kill. Each of these methods contains an implicit assumption about the probability distribution of the number of hits‐to‐kill. Method (1) assumes that the most likely kill scenario occurs with exactly one hit, whereas (2) implies that achieving a precise number of hits always results in a kill. These methods can produce significant differences in the predicted gun effectiveness, even if the mean number of hits‐to‐kill for each distribution is the same. We therefore introduce a new modeling approach with a more general distribution for the number of hits‐to‐kill. The approach is configurable to various classes of damage mechanism and is able to match both methods (1) and (2) with a suitable choice of parameter. We use this new approach to explore the influence of various damage accumulation models on the predicted effectiveness of weapon‐target engagements.     

A selective newsvendor approach to order management

Consider a supplier offering a product to several potential demand sources, each with a unique revenue, size, and probability that it will materialize. Given a long procurement lead time, the supplier must choose the orders to pursue and the total quantity to procure prior to the selling season. We model this as a selective newsvendor problem of maximizing profits where the total (random) demand is given by the set of pursued orders. Given that the dimensionality of a mixed‐integer linear programming formulation of the problem increases exponentially with the number of potential orders, we develop both a tailored exact algorithm based on the L‐shaped method for two‐stage stochastic programming as well as a heuristic method. We also extend our solution approach to account for piecewise‐linear cost and revenue functions as well as a multiperiod setting. Extensive experimentation indicates that our exact approach rapidly finds optimal solutions with three times as many orders as a state‐of‐the‐art commercial solver. In addition, our heuristic approach provides average gaps of less than 1% for the largest problems that can be solved exactly. Observing that the gaps decrease as problem size grows, we expect the heuristic approach to work well for large problem instances. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

常微分方程的割线迭代格式

在常微分方程的数值解法中,Euler的隐式格式稳定性较好,但由于它为隐式,因而给计算带来了极大地不方便。为了解决此问题,本文给出了一种数值解法——常微分方程的割线迭代格式。     

Scheduling a production–distribution system to optimize the tradeoff between delivery tardiness and distribution cost

We consider a make‐to‐order production–distribution system with one supplier and one or more customers. A set of orders with due dates needs to be processed by the supplier and delivered to the customers upon completion. The supplier can process one order at a time without preemption. Each customer is at a distinct location and only orders from the same customer can be batched together for delivery. Each delivery shipment has a capacity limit and incurs a distribution cost. The problem is to find a joint schedule of order processing at the supplier and order delivery from the supplier to the customers that optimizes an objective function involving the maximum delivery tardiness and the total distribution cost. We first study the solvability of various cases of the problem by either providing an efficient algorithm or proving the intractability of the problem. We then develop a fast heuristic for the general problem. We show that the heuristic is asymptotically optimal as the number of orders goes to infinity. We also evaluate the performance of the heuristic computationally by using lower bounds obtained by a column generation approach. Our results indicate that the heuristic is capable of generating near optimal solutions quickly. Finally, we study the value of production–distribution integration by comparing our integrated approach with two sequential approaches where scheduling decisions for order processing are made first, followed by order delivery decisions, with no or only partial integration of the two decisions. We show that in many cases, the integrated approach performs significantly better than the sequential approaches. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005