Shortest path interdiction problem with arc improvement recourse: A multiobjective approach

We consider the shortest path interdiction problem involving two agents, a leader and a follower, playing a Stackelberg game. The leader seeks to maximize the follower's minimum costs by interdicting certain arcs, thus increasing the travel time of those arcs. The follower may improve the network after the interdiction by lowering the costs of some arcs, subject to a cardinality budget restriction on arc improvements. The leader and the follower are both aware of all problem data, with the exception that the leader is unaware of the follower's improvement budget. The effectiveness of an interdiction action is given by the length of a shortest path after arc costs are adjusted by both the interdiction and improvement. We propose a multiobjective optimization model for this problem, with each objective corresponding to a different possible improvement budget value. We provide mathematical optimization techniques to generate a complete set of strategies that are Pareto‐optimal. Additionally, for the special case of series‐parallel graphs, we provide a dynamic‐programming algorithm for generating all Pareto‐optimal solutions.     

A problem in network interdiction

Suppose we are given a network G=(V,E) with arc distances and a linear cost function for lengthening arcs. In this note, we consider a network-interdiction problem in which the shortest path from source node s to sink node t is to be increased to at least τ units via a least-cost investment strategy. This problem is shown to reduce to a simple minimum-cost-flow problem. Applications and generalizations are discussed, including the multiple-destination case.     

Iterative methods for dynamic stochastic shortest path problems

We consider a routing policy that forms a dynamic shortest path in a network with independent, positive and discrete random arc costs. When visiting a node in the network, the costs for the arcs going out of this node are realized, and then the policy will determine which node to visit next with the objective of minimizing the expected cost from the current node to the destination node. This paper proposes an approach, which mimics the classical label-correcting approach, to compute the expected path cost. First, we develop a sequential implementation of this approach and establish some properties about the implementation. Next, we develop stochastic versions of some well-known label-correcting methods, including the first-in-first-out method, the two-queue method, the threshold algorithms, and the small-label-first principle. We perform numerical experiments to evaluate these methods and observe that fast methods for deterministic networks can become very slow for stochastic networks. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 769–789, 1998     

Estimating critical path and arc probabilities in stochastic activity networks

This article describes a new procedure for estimating parameters of a stochastic activity network of N arcs. The parameters include the probability that path m is the longest path, the probability that path m is the shortest path, the probability that arc i is on the longest path, and the probability that arc i is on the shortest path. The proposed procedure uses quasirandom points together with information on a cutset ? of the network to produce an upper bound of O[(log K)^N?|?|+1/K] on the absolute error of approximation, where K denotes the number of replications. This is a deterministic bound and is more favorable than the convergence rate of 1/K^1/2 that one obtains from the standard error for K independent replications using random sampling. It is also shown how series reduction can improve the convergence rate by reducing the exponent on log K. The technique is illustrated using a Monte Carlo sampling experiment for a network of 16 relevant arcs with a cutset of ? = 7 arcs. The illustration shows the superior performance of using quasirandom points with a cutset (plan A) and the even better performance of using quasirandom points with the cutset together with series reduction (plan B) with regard to mean square error. However, it also shows that computation time considerations favor plan A when K is small and plan B when K is large.     

时变道路网最短路径算法的研究

道路或区域通行限制在日常交通和部队兵力机动过程中普遍存在。通行限制情况下的最短路径问题属于时变道路网最短路径研究的范畴,对时变道路网最短路径算法及算法效率的研究有着广泛而现实的意义。重点讨论了道路网的模型描述、时变道路网拓扑结构的构建技术,最短路径算法的高效实现等内容,并给出了该算法的应用实例。试验结果显示,该算法有效可行。     

Optimal interdiction of a supply network

Under certain conditions, the re-supply capability of a combatant force may be limited by the characteristics of the transportation network over which supplies must flow. Interdiction by an opposing force may be used to reduce the capacity of that network. The effects of such efforts vary for differing missions and targets. With only a limited total budget available, the interdictor must decide which targets to hit, and with how much effort. An algorithm is presented for determining the optimum interdiction plan for minimizing network flow capacity when the minimum capacity on an arc is positive and the cost of interdiction is a linear function of arc capacity reduction.     

一类有增益网络的最大流模型

一般带容量限制的网络图中流出源点与流入汇点的流量相等,但在实际应用中,存在一类流量经过弧发生变化的网络,使得流出源点与流入汇点的流量不相等。针对此类问题,建立了增益网络最大流模型,并通过增设虚弧将增益网络转换成循环网络,利用循环网络中汇点流量瞬间平衡的优点简化了模型。最后,结合实例进行分析,编写程序对实例进行了计算,计算结果验证了该模型的有效性。     

Time minimizing flows in directed networks

An important class of network flow problems is that class for which the objective is to minimize the cost of the most expensive unit of flow while obtaining a desired total flow through the network. Two special cases of this problem have been solved, namely, the bottleneck assignment problem and time-minimizing transportation problem. This paper addresses the more general case which we shall refer to as the time-minimizing network flow problem. Associated with each arc is an arc capacity (static) and a transferral time. The objective is to find a maximal flow for which the length (in time) of the longest path carrying flow is minimized. The character of the problem is discussed and a solution algorithm is presented.     

Finding the Kth shortest path in a time‐schedule network

We consider the problem of finding the Kth shortest path for a time‐schedule network, where each node in the network has a list of prespecified departure times, and departure from the node can take place only at one of these departure times. We develop a polynomial time algorithm independent of K for finding the Kth shortest path. The proposed algorithm constructs a map structure at each node in the network, using which we can directly find the Kth shortest path without having to enumerate the first K − 1 paths. Since the same map structure is used for different K values, it is not necessary to reconstruct the table for additional paths. Consequently, the algorithm is suitable for directly finding multiple shortest paths in the same network. Furthermore, the algorithm is modified slightly for enumerating the first K shortest paths and is shown to have the lowest possible time complexity under a condition that holds for most practical networks. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

交互网络上任意节点对的最短路径集解法

搜索交互网络中的最短路径是研究网络结构的重要内容,在常见的Dijkstr和Floyd算法中,只能获取一条最短路径.在交互网络上任意节点对之间的最短路径不止一条的情况下,运用Floyd算法对已知加权交互网络的最短路径进行求解,对获得最短路径后的每一个节点对,在其中插入已知交互网络中的其余所有节点,并计算此时的节点对之间的...     

Ripples,complements, and substitutes in generalized networks

We extend the qualitative theory of sensitivity analysis for minimum-cost pure network flows of Granot and Veinott [17] to generalized network flow problems, that is, network flow problems where the amount of flow picked up by an arc is multiplied by a (positive) gain while traversing the arc. Three main results are presented. The ripple theorem gives upper bounds on the absolute value of optimal-flow variations as a function of variations in the problem parameter(s). The theory of substitutes and complements provides necessary and sufficient conditions for optimal-flow changes to consistently have the same (or the opposite) sign(s) in two given arcs, whereas the monotonicity theorem links changes in the value of the parameters to changes in optimal arc flows. Bounds on the rates of changes are also discussed. Compared with pure networks, the presence of gains makes qualitative sensitivity analysis here a much harder task. We show the profound effect on computational issues caused by the departure from the pure network structure. © 1996 John Wiley & Sons, Inc.     

网络图的自动生成算法及其系统实现

研究了网络自动生成的实现算法和系统实现技术。该算法按路线来画结点 ,将其区分为不同的层 ,再绘制路径。先画出所有关键路 ,确定关键节点的坐标 ;然后对于未确定坐标的结点 ,寻找其由关键结点出发再回到关键结点的最短路径 ,将该路径上的结点画为一层 ,按不同的路线分为不同的层次进行绘制 ,直到所有结点均确定坐标。然后确定路线的层次 ,最后统一协调规整。以此算法开发的软件系统可节省时间 ,并可保证生成规范的网络图。     

基于分簇理论的信息流优化算法研究

将导弹防御指控网络看作变拓扑结构网络,引入小世界网络中"簇"的概念,以最短作战响应时间为优化指标,提出了一种基于平均连接度自适应分簇算法的信息流优化算法。仿真结果表明,该算法在保证信息优裕度的前提下,提高了信息可达度和信息交互质量,提高了指控网络遭受打击时的重构能力。     

Minimum-cost flows in convex-cost networks

An algorithm is given for solving minimum-cost flow problems where the shipping cost over an arc is a convex function of the number of units shipped along that arc. This provides a unified way of looking at many seemingly unrelated problems in different areas. In particular, it is shown how problems associated with electrical networks, with increasing the capacity of a network under a fixed budget, with Laplace equations, and with the Max-Flow Min-Cut Theorem may all be formulated into minimum-cost flow problems in convex-cost networks.     

The constrained shortest path problem

The shortest path problem between two specified nodes in a general network possesses the unimodularity property and, therefore, can be solved by efficient labelling algorithms. However, the introduction of an additional linear constraint would, in general, destroy this property and the existing algorithms are not applicable in this case. This paper presents a parametric approach for solving this problem. The algorithm presented would require, on the average, a number of iterations which is polynomially bounded. The similarity of this approach to that of the generalized Lagrange multiplier technique is demonstrated and a numerical example is presented.     

Detection of minimal forecast horizons in dynamic programs with multiple indicators of the future

Many sequential planning problems can be represented as a shortest path problem in an acyclic network. This includes all deterministic dynamic programs as well as certain stochastic sequential decision problems. In this article, we identify a large class of shortest path problems for which a general efficient algorithm for the simultaneous solution and detection of minimal forecast horizons is developed. Detection of a such minimal forecast horizons is essential when accurate information regarding various relevant parameters is obtained progressively, i.e., when the initial information is restricted to a limited horizon of “future” stages only. We describe five classes of planning problems which can be efficiently addressed by the general algorithm. These classes deal with multi-item joint replenishment systems, combined inventory and routing problems, machine scheduling issues, single item stochastic inventory settings and routing problems in the plane and in space. © 1996 John Wiley & Sons, Inc.     

LEO 卫星网络路径选择策略研究

路由算法在选择路径时,主要考虑传输延迟和跳数这两个因素,分别选取最短延迟路径(Least Delay Path, LDP)或最少跳数路径( Least Hops Path, LHP)。在卫星网络中,基于LHP选径策略实现更加简单,但其应用在LEO卫星网络中合理性的研究成果不多。本文对极轨道LEO卫星网络中,LDP和LHP之间关系进行详细的理论分析,验证了LHP选径策略的合理性。并在此基础上,提出一种基于横向传输优先级（Horizontal Transmitting Priority, HTP）的LHP最短路径选择策略,利用横向链路长短特性简化路径决策流程。通过仿真,该方法能够快速寻找到最短LHP路径,为LEO卫星网络路由算法提供一定的研究基础。     

一种基于节点资源利用率的无标度网络路由策略

本文研究了节点负载处理能力异质条件下的无标度网络交通动力学过程,提出了一种基于节点资源利用率的全局动态路由策略。该策略利用网络中节点资源利用率构建了一种全局代价函数,选择使该代价函数最小的路径来传输负载。实验结果表明该路由策略在略微增加平均路径长度的情况下成倍地提高了网络负载传输能力,与有效路由策略的比较进一步验证了该策略的有效性。     

Decomposition algorithms for finding the shortest path between a source node and a sink node of a network

Decomposition algorithms for finding a shortest path between a source node and a sink node of an arbitrary distance network are developed. Different decomposition algorithms are proposed for different network topologies. Since Shier's algorithm compares very favorably with other decomposition algorithms in all the network topologies, we compare our algorithms against Shier's algorithm. It is shown that the efficiency of the proposed algorithms compares very favorably with Shier's algorithm. For special types of networks the computational requirements of the proposed algorithm is a polynomial of O(n²).     

分段线性凸费用网络流的两个算法

本文讨论了分段线性凸费用网络流问题,推广了线性费用网络流中的负回路方法和最小费用路方法,从而得到了求分段线性凸费用网络的最小费用流的两个算法。