Optimal arrangement of components via pairwise rearrangements

We introduce the notion of comparison of the criticality of two nodes in a coherent system, and devlop a monotonicity property of the reliability function under component pairwise rearrangement. We use this property to find the optimal component arrangement. Worked examples illustrate the methods proposed.     

Optimal arrangement of systems

To location L_i we are to allocate a “generator” and n_i “machines” for i = 1, …,k, where n₁ … n₁ ≧ … ≧ n_k. Although the generators and machines function independently of one another, a machine is operable only if it and the generator at its location are functioning. The problem we consider is that of finding the arrangement or allocation optimizing the number of operable machines. We show that if the objective is to maximize the expected number of operable machines at some future time, then it is best to allocate the best generator and the n₁ best machines to location L₁, the second-best generator and the n₂-next-best machines to location L₂, etc. However, this arrangement is not always stochastically optimal. For the case of two generators we give a necessary and sufficient condition that this arrangement is stochastically best, and illustrate the result with several examples.     

基于虚拟力驱动的传感器网络节点定位

为了解决传感器网络节点三边测量定位的全局优化问题,提出了一种基于虚拟力驱动的节点最优相对定位方法。该方法建立了满足节点位置最优最小二乘估计需要的虚拟势能场模型,给出了一种基于虚拟势能场梯度的虚拟力定义新方法,证明了利用该虚拟力驱动节点定位的收敛性,提供了保证节点定位结果全局最优的方法。仿真分析表明,基于虚拟力驱动的节点相对定位方法能够解决节点相对位置的最优估计问题。     

临近空间拦截弹最优弹道跟踪制导律

针对拦截临近空间高超声速飞行器的弹道跟踪过程,基于线性二次型调节器理论和高斯伪谱法设计一种跟踪制导律。为了对标称弹道进行精确跟踪,考虑线性二次型跟踪问题,应用最优控制理论推导最优解的充要条件,得到带时变增益的线性状态反馈控制量的表达式;基于高斯伪谱法,在离散的勒让德-高斯点上利用标称弹道数据计算差分矩阵和系数矩阵,求得状态扰动反馈控制律。仿真结果表明,与基于求解矩阵黎卡提方程的方法相比,该方法选取较少的节点即可获得高精度的反馈控制量,且运算效率大幅提高,满足在线实施要求。     

Bounds on optimal cost for a replacement problem with partial observations

This paper characterizes the structure of optimal strategies for a replacement problem for two special cases of observation quality. It is shown that when the state of the system is either completely observed or completely unobserved at every decision epoch by the controller, reasonable assumptions are sufficient for the existence of optimal replacement strategies composed of policies having a generalized, control-limit form. These structural results are of particular interest since the optimal cost functions for the two special cases represent bounds on the optimal cost function for the general partially observed case, significant computational simplification can result for the two special cases due to their optimal strategy structure, and optimal strategies possessing a control-limit structure do not necessarily exist for the general partially observed case.     

On allocating one active redundancy to coherent systems with dependent and heterogeneous components' lifetimes

This article studies coherent systems of heterogenous and statistically dependent components' lifetimes. We present a sufficient and necessary condition for a stochastically longer system lifetime resulted by allocating a single active redundancy. For exchangeable components' lifetimes, allocating the redundancy to the component with more minimal path sets is proved to produce a more reliable system, and for systems with stochastic arrangement increasing components' lifetimes and symmetric structure with respect to two components, allocating the redundancy to the weaker one brings forth a larger reliability. Several numerical examples are presented to illustrate the theoretical results as well. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 335–345, 2016     

The maximum collection problem with time-dependent rewards

We consider a routing problem where the objective is to maximize the sum of the rewards collected at the nodes visited. Node rewards are decreasing linear functions of time. Time is spent when traveling between pairs of nodes, and while visiting the nodes. We propose a penalty-based greedy (heuristic) algorithm and a branch-and-bound (optimal) algorithm for this problem. The heuristic is very effective in obtaining good solutions. We can solve problems with up to 20 nodes optimally on a microcomputer using the branch-and-bound algorithm. We report our computational experience with this problem. © 1996 John Wiley & Sons, Inc.     

雷达组网系统责任区抗干扰优化部署

针对有源压制干扰对雷达组网系统的威胁,深入分析了雷达组网系统的抗干扰优化部署问题,建立了雷达组网系统责任区抗干扰优化布站决策模型,并给出了具体的算法和求解分析.仿真结果验证了该方法的有效性,可为雷达组网系统的实际优化部署提供参考.     

Using hybrid metaheuristics for the one‐way and two‐way network design problem

A network with traffic between nodes is known. The links of the network can be designed either as two‐way links or as one‐way links in either direction. The problem is to find the best configuration of the network which minimizes total travel time for all users. Branch and bound optimal algorithms are practical only for small networks (up to 15 nodes). Effective simulated annealing and genetic algorithms are proposed for the solution of larger problems. Both the simulated annealing and the genetic algorithms propose innovative approaches. These innovative ideas can be used in the implementation of these heuristic algorithms for other problems as well. Additional tabu search iterations are applied on the best results obtained by these two procedures. The special genetic algorithm was found to be the best for solving a set of test problems. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 449–463, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10026     

Optimal design of accelerated life tests with two stresses

Most of the previous works on designing accelerated life test plans were concerned with the case where a single stress is employed for acceleration. In this article we develop optimal accelerated life test plans when two stresses are involved with possible interaction between them. The lifetimes of test items are assumed to follow an exponential distribution, the mean of which depends on the stresses according to the generalized Eyring law. A factorial arrangement of test points is considered for an efficient utilization of equipment, and the low level of each stress and the proportion of test items allocated to each test point are determined such that the asymptotic variance of the maximum-likelihood estimator of the mean lifetime at the use condition or of an acceleration factor is minimized. Patterns of optimal plans are identified and their efficiencies are compared with the corresponding single-stress accelerated life test plans. © 1996 John Wiley & Sons, Inc.     

A search game on a cyclic graph

There is a finite cyclic graph. The hider chooses one of all nodes except the specified one, and he hides an (immobile) object there. At the beginning the seeker is at the specified node. After the seeker chooses an ordering of the nodes except the specified one, he examines each nodes in that order until he finds the object, traveling along edges. It costs an amount when he moves from a node to an adjacent one and also when he checks a node. While the hider wishes to maximize the sum of the traveling costs and the examination costs which are required to find the object, the seeker wishes to minimize it. The problem is modeled as a two‐person zero‐sum game. We solve the game when unit costs (traveling cost + examination cost) have geometrical relations depending on nodes. Then we give properties of optimal strategies of both players. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Equalities in transportation problems and characterizations of optimal solutions

This paper considers the classical finite linear transportation Problem (I) and two relaxations, (II) and (III), of it based on papers by Kantorovich and Rubinstein, and Kretschmer. Pseudo-metric type conditions on the cost matrix are given under which Problems (I) and (II) have common optimal value, and a proper subset of these conditions is sufficient for Problems (II) and (III) to have common optimal value. The relationships between the three problems provide a proof of Kantorovich's original characterization of optimal solutions to the standard transportation problem having as many origins as destinations. The result are extended to problems having cost matrices which are nonnegative row-column equivalent.     

On equivalence between the proportionate flow shop and single‐machine scheduling problems

We derive sufficient conditions which, when satisfied, guarantee that an optimal solution for a single‐machine scheduling problem is also optimal for the corresponding proportionate flow shop scheduling problem. We then utilize these sufficient conditions to show the solvability in polynomial time of numerous proportionate flow shop scheduling problems with fixed job processing times, position‐dependent job processing times, controllable job processing times, and also problems with job rejection. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 595–603, 2015     

Solving min-max shortest-path problems on a network

In this article we consider the problem of determining a path between two nodes in a network that minimizes the maximum of r path length values associated with it. This problem has a direct application in scheduling. It also has indirect applications in a class of routing problems and when considering multiobjective shortest-path problems. We present a label-correcting procedure for this problem. We also develop two pruning techniques, which, when incorporated in the label-correcting algorithm, recognize and discard many paths that are not part of the optimal path. Our computational results indicate that these techniques are able to speed up the label-correcting procedure by many orders of magnitude for hard problem instances, thereby enabling them to be solved in a reasonable time. © 1992 John Wiley & Sons, Inc.     

基于Gauss伪谱法和直接打靶法结合的月球定点着陆轨道优化

将一种求解最优控制问题的新方法—高斯伪谱法( Gauss Pseudospectral Method-GPM)和传统的直接打靶法有效结合,对月球着陆器定点软着陆轨道快速优化问题做出了研究.推导了高精度模型下着陆动力学方程.针对优化方法各自的特点和多约束条件下最优月球软着陆轨道设计的难点,提出了问题求解的串行优化策略:将控制变量和终端时间一同作为优化变量,同时离散控制变量与状态变量,取较少的Gauss节点,利用GPM求解初值,初值的求解采用从可行解到最优解的串行优化策略;在Gauss节点上离散控制变量,利用直接打靶法求解精确最优解.仿真结果表明,本文提出的轨道优化方法具有较强的鲁棒性和快速收敛性.     

Minimizing logistic costs in multistage supply chains

We consider the problem in which a set of products has to be shipped from a common origin to a common destination through one or several intermediate nodes with the objective of minimizing the sum of inventory and transportation costs when a set of possible shipping frequencies is given on each link. From the theoretical point of view, the main issue is the computation of the inventory cost in the intermediate nodes. From the computational point of view, given that the simpler single link problem is known to be NP-hard, we present four classes of heuristic algorithms. The first two classes are based on the decomposition of the sequence in links, the third class on the adaptation of the EOQ-type solution known for the continuous case, and the fourth on the optimal solution of a simpler problem through dynamic programming techniques. Finally, we compare them on a set of randomly generated problem instances. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 399–417, 1999     

Optimality of control limit policies in replacement models

We study a class of replacement models for systems subject to deterioration. The objective is to determine an optimal replacement policy that minimizes the average operating costs of the system. We use a parametric analysis to establish sufficient conditions for the optimality of control limit policies. This work generalizes several existing results for optimal replacement models in the literature. © 1992 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.     

Determining newspaper marketing zones using contiguous clustering

We develop a heuristic procedure for partitioning graphs into clusters of nodes such that each cluster of nodes induces a connected subgraph with the objective of minimizing the differences within clusters as measured by the total differences between all pairs of nodes of a cluster. We apply our procedure to determine optimal delivery zones for community sections of a major newspaper while including a number of operational constraints. Our results demonstrate a 18–56% improvement in the total differences within the zones designed over the usual intuitive heuristics. Given the magnitude of the revenue generated by larger local newspapers through zoning, our method demonstrates how better zoning can significantly enhance the value of segmentation. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

船用核反应堆提棒外推临界优化研究

因稳定时间受限,传统的倍增公式导出的外推临界公式计算结果大于实测值,偏危险;文中根据新的中子倍增公式导出了外推临界计算的新公式,实例计算表明,该公式比传统的外推临界公式精确且偏安全.