Determining the optimal double-component assignment for a stochastic computer network

This study determines the optimal double-component assignment based on the system reliability criterion for a computer system, in which the computer system is represented as a network with a set of links and a set of vertices. The double-component assignment is to assign a set of transmission lines (resp. facilities) to the links (resp. vertices) of the network, in which each transmission line (resp. facility) has multiple states due to maintenance or failure. Thus, the computer system according to any double-component assignment is called a stochastic computer network. The system reliability is the probability that the specific units of data are successfully transmitted through the stochastic computer network. An optimization algorithm which integrates the genetic algorithm, minimal paths, and Recursive Sum of Disjoint Products is utilized to find the optimal double-component assignment with maximal system reliability. Several computer networks are utilized to demonstrate the efficiency of the proposed algorithm compared with other algorithms. By solving this problem, data can be more reliably transmitted and thus the organization operation is executed more smoothly.     

Optimization of loss-balanced multicast in all-optical WDM networks

In wavelength-division multiplexing (WDM) optical networks, multicast is implemented by constructing a light-forest, which is a set of light-trees with each light-tree rooted from the multicast source and terminated at a partition subset of the destination nodes. Multicast routing scenario has considerable impact on the quality of optical signal received at each destination. To guarantee the fairness of signal quality at different destinations in a multicast session, it is desirable to construct a loss-balanced light-forest to deliver the multicast traffic. A loss-balanced light-forest is composed of a set of light-trees bounded in size (number of destinations per multicast tree), in size variation (difference in the number of destinations among different multicast trees), and in dimension (maximum source-to-destination distance on each multicast tree). This paper investigates the multicast routing and wavelength assignment (MC-RWA) problem under the loss-balance constraint. The problem is formulated as an optimization model using integer linear programming (ILP). Numerical solutions to the optimization model can supply useful performance benchmarks for loss-balance-constrained optical multicast in WDM networks. This work was supported by the NSF under Grant OCI-0225642 and by the U.S. DoE under Grant DE-FG02–03ER25566.     

Approximation algorithms for multicast routing in ad hoc wireless networks

Energy efficient multicast problem is one of important issues in ad hoc networks. In this paper, we address the energy efficient multicast problem for discrete power levels in ad hoc wireless networks. The problem of our concern is: given n nodes deployed over 2-D plane and each node v has l(v) transmission power levels and a multicast request (s,D) (clearly, when D is V∖{s}, the multicast request is a broadcast request), how to find a multicast tree rooted at s and spanning all destinations in D such that the total energy cost of the multicast tree is minimized. We first prove that this problem is NP-hard and it is unlikely to have an approximation algorithm with performance ratio ρlnn(ρ<1). Then, we propose a general algorithm for the multicast/broadcast tree problem. And based on the general algorithm, we propose an approximation algorithm and a heuristics for multicast tree problem. Especially, we also propose an efficient heuristic for broadcast tree problem. Simulations ensure our algorithms are efficient.     

Finding disjoint paths with related path costs

We consider routing in survivable networks that provide protection against node or link failures. In these networks resilience against failures is provided by routing connections on pairs of disjoint paths called primary and backup paths. The primary path of a connection carries its traffic under normal circumstances and in the eventuality of a network failure effecting the primary path the connection traffic (all or some portion of it) is rerouted over its backup path. In an online setting as connection requests arrive a pair of disjoint primary and backup paths of least total cost (under some link cost metric) are selected to route the connections. In many situations the cost metric used for the primary path differs from the cost metric used for the backup path. Also in many realistic settings these two cost metrics are related to each other. In this paper we study the problem of finding a pair of edge or node disjoint paths of least total cost where the cost of the primary path is the total cost of its links while the cost for the backup path is α times the sum of the cost of its links, for some given α < 1. We show that the problem is hard to approximate to within a factor for any positive . In addition we show that the problem is complete for a set of hard to approximate problems. On the positive side we show that a simple algorithm achieves an approximation ratio of for the problem.     

随机网络瓶颈容量扩张相关机会规划模型

文章研究的问题为,在不确定环境中,怎样去增加网络中一组边的容量到一个指定的容量,以至于网络瓶颈扩张的费用不超过给定的总费用上限的概率尽可能的大.本文假定每一条边的单位扩张费用Wi是一个随机的变量,它服从一定的概率分布.带有随机单位扩张费用W的网络瓶颈容量扩张问题可以根据一些规则,列出它的相关机会规划模型的通用表达式.随后,本文将网络瓶颈容量算法、随机模拟方法和遗传算法合成在一起,设计出该问题的混合智能通用算法.最后,给出数值算例.     

Directed Steiner trees with diffusion costs

Given a directed arc-weighted graph G with n nodes, a root r and k terminals, the directed steiner tree problem (DST) consists in finding a minimum-weight tree rooted at r and spanning all the terminals. If this problem has several applications in multicast routing in packet switching networks, the modeling is not adapted anymore in networks based upon the circuit switching principle in which some nodes, called non diffusing nodes, are unable to duplicate packets. We define a more general problem, namely the directed steiner tree with a limited number of diffusing nodes (DSTLD), that enables us to model multicast in a network containing at most d diffusing nodes. We show that DSTLD is XP with respect to d, and use this result to build a \(\left\lceil \frac{k-1}{d} \right\rceil \)-approximation algorithm for DST that is XP in d. We deduce from that result a strong inapproximability property. In particular, we prove that, under the assumption that NP \(\not \subseteq \) ZTIME \([n^{\log ^{O(1)}n}]\), there is no polynomial-time approximation algorithm for DSTLD with ratio \(\varOmega \left( \frac{k}{d}\right) \). We finally give an evaluation of performances of an exact algorithm dedicated to the case \(d \le 3\).     

多级供应链系统成本分析随机网络模型及算法研究

供应链成本管理是企业战略管理的核心组成部分。为研究多级供应链网络系统的成本组成及其分布特征、分析各节点企业的成本管理对多级供应链网络系统的影响、找到供应链系统成本管理中的薄弱环节和关键企业,本文构建了多级供应链系统成本的随机网络分析模型。首先研究了模型的结构性质特征,给出成本分布特征的解析算法。然后扩展模型,分别从系统成本类型构成(生产成本、库存成本和物流成本)和系统对企业成本波动的灵敏度两个角度深入研究多级供应链网络成本问题。数值算例分析结果说明了多级供应链网络系统成本分析模型和相关算法的有效性和实用性。     

Reliable Ad Hoc Routing Based on Mobility Prediction

Reliability is a very important issue in Mobile Ad hoc NETworks (MANETs). Shortest paths are usually used to route packets in MANETs. However, a shortest path may fail quickly, because some of the wireless links along a shortest path may be broken shortly after the path is established due to mobility of mobile nodes. Rediscovering routes may result in substantial data loss and message exchange overhead. In this paper, we study reliable ad hoc routing in the urban environment. Specifically, we formulate and study two optimization problems. In the minimum Cost Duration-bounded Path (CDP) routing problem, we seek a minimum cost source to destination path with duration no less than a given threshold. In the maximum Duration Cost-bounded Path (DCP) routing problem, we seek a maximum duration source to destination path with cost no greater than a given threshold. We use a waypoint graph to model the working area of a MANET and present an offline algorithm to compute a duration prediction table for the given waypoint graph. An entry in the duration prediction table contains the guaranteed worst-case duration of the corresponding wireless link. We then present an efficient algorithm which computes a minimum cost duration-bounded path, using the information provided in the duration prediction table. We also present a heuristic algorithm for the DCP routing problem. In addition, we show that the proposed prediction and routing schemes can be easily applied for designing reliable ad hoc routing protocols. Simulation results show that our mobility prediction based routing algorithms lead to higher network throughput and longer average path duration, compared with the shortest path routing. This research was supported in part by ARO grant W911NF-04-1-0385 and NSF grant CCF-0431167. The information reported here does not reflect the position or the policy of the federal government.     

Design Improvements for Message Propagation in Malleable Social Networks

This study presents the formal problem definition and computational analysis of the network design improvements for idea and message propagation in both enterprise and consumer social networks (ESN and CSN, respectively). Message propagation in social networks is impacted by how messages are seeded in the network, and by propagation characteristics of the network topology itself. It has been recognized that the propagation properties of these networks can be actively influenced by network design interventions, such as the deliberate creation of new connections. We address the problem of finding cost‐effective message seeding, and identifying potential new network connections that allow improved propagation in social networks with cascade propagation. We use the hop‐constrained minimum spanning tree (HMST) model to find the seeds and possible new connections that result in networks with improved propagation properties. Moreover, we present new heuristic algorithms that substantially improve the solution quality for the HMST problem. Computational results posit that the design improvements proposed by the HMST approach can greatly improve cascade propagation performance of the networks at low cost.     

Designing survivable resilient networks: A stochastic hybrid genetic algorithm approach

As high-speed networks have proliferated across the globe, their topologies have become sparser due to the increased reliability of components and cost considerations. Reliability has been a traditional goal within network design optimization. An alternative design consideration, network resilience, has not been studied or incorporated into network designs nearly as much. The authors propose a methodology for the difficult estimation of traffic efficiency (TE), a measure of network resilience, and a hybrid genetic algorithm to design networks using this measure.     

A branch-and-price algorithm for production routing problems with carbon cap-and-trade

This study presents a model for a pollution production-routing problem under carbon cap-and-trade. The aim is to incorporate carbon emissions into production inventory and routing decisions. The model is characterized by an additional flow-related cost structure, which generalizes models for pollution-routing problems and production inventory and routing problems. Correspondingly, we develop a branch-and-price heuristic by incorporating a column-generation formulation based on the Dantzig–Wolfe decomposition. In addition, we design an ad hoc label-setting algorithm to deal with time-slice networks in pricing subproblems. Computational results allow us to provide managerial insights concerning reduction of carbon emissions in supply chains. We prove that the model has the potential to reduce emission levels of carbon dioxide and operational costs.     

多油品供给受限下多油库被动配送车辆路径问题研究

成品油供给不足将导致加油站油品订单无法完全满足,如何安排有限油品的合理配送对保障能源供给安全至关重要。为此,本文考虑有限供给下不同客户配送的优先次序,开展配送计划、车辆调度和路径优化等油品配送网络规划活动,对多油品供给受限情况下多油库被动配送车辆路径问题（Multiple Depot Vehicle Routing Problem,MDVRP）进行深入研究。首先,文章构建了考虑需求优先等级和配送成本的多油品多油库车辆路径规划多目标优化模型。其次,采用多目标粒子群优化算法（Multi-Objective Particle Swarm Optimization,MOPSO）对模型进行求解,以实现车辆高效调度和油品配送路径优化。最后,基于CNPC在青岛市部分油库和加油站点的数据信息,构建油品配送网络进行实证检验。算例结果显示,配送车辆路径经过优化后,生成Pareto非劣解集,配送成本显著降低,配送满足率明显提高,这也进一步验证了该模型及相关算法的可行性和有效性。     

Exact and heuristic algorithms for solving the generalized minimum filter placement problem

We consider a problem of placing route-based filters in a communication network to limit the number of forged address attacks to a prescribed level. Nodes in the network communicate by exchanging packets along arcs, and the originating node embeds the origin and destination addresses within each packet that it sends. In the absence of a validation mechanism, one node can send packets to another node using a forged origin address to launch an attack against that node. Route-based filters can be established at various nodes on the communication network to protect against these attacks. A route-based filter examines each packet arriving at a node, and determines whether or not the origin address could be legitimate, based on the arc on which the packet arrives, the routing information, and possibly the destination. The problem we consider seeks to find a minimum cardinality subset of nodes to filter so that the prescribed level of security is achieved. We formulate a mixed-integer programming model for the problem and derive valid inequalities for this model by identifying polynomially-solvable subgraphs of the communication network. We also present three heuristics for solving the filter placement problem and evaluate their performance against the optimal solution provided by the mixed-integer programming model. The authors gratefully acknowledge the comments of two anonymous referees, whose input led to an improved version of this paper. Dr. Smith gratefully acknowledges the support of the Office of Naval Research under Grant #N00014-03-1-0510 and the Defense Advanced Research Projects Agency under Grant #N66001-01-1-8925.     

An Improved Approximation Algorithm for Multicast <Emphasis Type="Italic">k</Emphasis>-Tree Routing

An improved approximation algorithm is presented in this paper for the multicast k-tree routing problem. The algorithm has a worst case performance ratio of (2.4 + ρ), where ρ is the best approximation ratio for the metric Steiner tree problem (and is about 1.55 so far). The previous best approximation algorithm for the multicast k-tree routing problem has a performance ratio of 4. Two techniques, weight averaging and tree partitioning, are developed to facilitate the algorithm design and analysis.Research supported by AICML, CFI, NSERC, PENCE, a Startup Grant from the University of Alberta, and NNSF Grant 60373012.     

一类网络扩张的机会约束模型与算法

在不确定环境中的机会约束下,怎样去增加一组边的容量到一个指定的瓶颈容量,而使网络瓶颈扩张的费用最小.带有随机单位扩张费用的网络瓶颈容量扩张问题,可以根据一些概率机会约束规则,列出它的机会约束规划模型的通用表达式.将网络瓶颈容量算法、随机模拟方法和遗传算法合成在一起,设计出该问题的混合智能通用算法.最后,给出数值案例.     

Reliable Supply Chain Network Design

Risk management in supply chains has been receiving increased attention in the past few years. In this article, we present formulations for the strategic supply chain network design problem with dual objectives, which usually conflict with each other: minimizing cost and maximizing reliability. Quantifying the total reliability of a network design is not as straightforward as total cost calculation. We use reliability indices and develop analytical formulations that model the impact of upstream supply chain on individual entities’ reliability to quantify the total reliability of a network. The resulting multiobjective nonlinear model is solved using a novel hybrid algorithm that utilizes a genetic algorithm for network design and linear programming for network flow optimization. We demonstrate the application of our approach through illustrative examples in establishing tradeoffs between cost and reliability in network design and present managerial implications.     

直接配送下随机需求库存-路径问题最优平稳策略及其算法

直接配送策略下随机需求库存-路径问题（Stochastic Demand Inventory Routing Problem with Direct Deliveries, SDIRPDD）由于其需求的不确定性、决策的长期性以及其最优策略形式对求解其他库存-路径问题（IRP）的参考价值,使得对SDIPRDD问题的研究成为物流、供应链优化领域研究的一个热点。文章首先证明了无约束SDIRPDD的最优平稳策略为（s,S）形式,并通过分析车辆数约束对客户单阶段期望成本函数的影响,给出了存在车辆数和客户库存容量约束时SDIRPDD问题的最优平稳策略形式,进而提出了一种求解有约束SDIRPDD问题最优平稳策略的近似算法。最后,通过数值算例验证了算法的有效性并分析了结果的现实意义。     

Stochastic Measures of Network Resilience: Applications to Waterway Commodity Flows

Given the ubiquitous nature of infrastructure networks in today's society, there is a global need to understand, quantify, and plan for the resilience of these networks to disruptions. This work defines network resilience along dimensions of reliability, vulnerability, survivability, and recoverability, and quantifies network resilience as a function of component and network performance. The treatment of vulnerability and recoverability as random variables leads to stochastic measures of resilience, including time to total system restoration, time to full system service resilience, and time to a specific α% resilience. Ultimately, a means to optimize network resilience strategies is discussed, primarily through an adaption of the Copeland Score for nonparametric stochastic ranking. The measures of resilience and optimization techniques are applied to inland waterway networks, an important mode in the larger multimodal transportation network upon which we rely for the flow of commodities. We provide a case study analyzing and planning for the resilience of commodity flows along the Mississippi River Navigation System to illustrate the usefulness of the proposed metrics.     

越库配送下考虑时空距离的库门分配与车辆调度优化

针对越库配送下考虑时空距离的库门分配与车辆路径问题,建立以车辆派遣成本、运输成本、时间惩罚成本、越库内部操作成本总和最小化为目标的库门分配与车辆路径优化模型。根据问题的特征设计改进的自适应遗传算法,并根据时空距离生成初始解。通过对不同规模的算例进行对比和分析,验证了模型的正确性和算法的有效性,结果表明,所得出的库门分配和车辆调度优化方案可以有效降低越库配送中心的运营成本。研究成果拓展和丰富了越库配送下的车辆路径问题研究,能为物流企业优化配送方案提供理论依据。     

含有连续型随机参数的回收物流网络优化设计

考虑到设计参数的不确定性,建立了单一产品、有处理能力约束的回收物流网络优化设计的二阶段随机规划模型.该模型借助于抽样技术给出了连续型随机参数的有限离散数值,利用混合遗传算法计算并比较了不同网络的建设和运营费用,从而避免了网络设施数量和随机向量维数对模型求解效率的影响.为得到稳健的回收物流网络,利用大样本对计算获得的可行网络进行了评价.考虑到样本随机性的影响,给出了基于随机模型的回收物流网络优化设计步骤.另外,通过算例说明了随机模型的有效性,证实了确定性模型近似处理随机规划问题的不适用性.