A Genetic Algorithm for the Weight Setting Problem in OSPF Routing

With the growth of the Internet, Internet Service Providers (ISPs) try to meet the increasing traffic demand with new technology and improved utilization of existing resources. Routing of data packets can affect network utilization. Packets are sent along network paths from source to destination following a protocol. Open Shortest Path First (OSPF) is the most commonly used intra-domain Internet routing protocol (IRP). Traffic flow is routed along shortest paths, splitting flow at nodes with several outgoing links on a shortest path to the destination IP address. Link weights are assigned by the network operator. A path length is the sum of the weights of the links in the path. The OSPF weight setting (OSPFWS) problem seeks a set of weights that optimizes network performance. We study the problem of optimizing OSPF weights, given a set of projected demands, with the objective of minimizing network congestion. The weight assignment problem is NP-hard. We present a genetic algorithm (GA) to solve the OSPFWS problem. We compare our results with the best known and commonly used heuristics for OSPF weight setting, as well as with a lower bound of the optimal multi-commodity flow routing, which is a linear programming relaxation of the OSPFWS problem. Computational experiments are made on the AT&T Worldnet backbone with projected demands, and on twelve instances of synthetic networks.     

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.     

Reliability evaluation of a multicast over coded packet networks

Network coding is a generalization of conventional routing methods that allows a network node to code information flows before forwarding them. While it has been theoretically proved that network coding can achieve maximum network throughput, theoretical results usually do not consider the stochastic nature in information processing and transmission, especially when the capacity of each arc becomes stochastic due to failure, attacks, or maintenance. Hence, the reliability measurement of network coding becomes an important issue to evaluate the performance of the network under various system settings. In this paper, we present analytical expressions to measure the reliability of multicast communications in coded networks, where network coding is most promising. We define the probability that a multicast rate can be transmitted through a coded packet network under a total transmission cost constraint as the reliability metric. To do this, we first introduce an exact mathematical formulation to construct multicast connections over coded packet networks under a limited transmission cost. We then propose an algorithm based on minimal paths to calculate the reliability measurement of multicast connections and analyze the complexity of the algorithm. Our results show that the reliability of multicast routing with network coding improved significantly compared to the case of multicast routing without network coding.     

Improvement of path analysis algorithm in social networks based on HBase

When social network has reached hundreds of million users, the analysis of data in social network services becomes very important. Understanding how nodes interconnect in large graphs is an essential problem in many fields. In order to find connecting nodes between two nodes or two groups of source nodes in huge graphs, we propose a parallelized data-mining algorithm to get the shortest path between nodes in a social network based on HBase distributed key/value store. Our algorithm can achieve the shortest path among different nodes in network under the parallel environment. We analyze the social network model by this algorithm first, and then optimize the output from cloud platform by using the intermediary degrees and degree central algorithm. Finally, with a simulated social network, we validate the efficiency of the proposed algorithm. The experiment results indicate that our algorithm can improve the efficiency of parallel breath-first search (BSF).     

基于改进蚁群算法的低碳车辆路径问题研究

全球气候恶化危及人类生存环境,物流运输过程中产生的大量温室气体则是祸源之一。本文考虑带有碳排放约束的车辆路径问题（VRP）,以车辆行驶里程最短和碳排放量最小为目标,构建了多目标的VRP非线性规划模型。提出了一种改进的蚁群系统算法对该模型进行求解,算法在更新路径上的蚂蚁信息素时引入了混沌扰动机制,此举能降低算法运行时陷入局部最优解的概率并有效提高算法的适应性。同时,对启发因子、状态转移概率、信息素更新等环节进行了优化设计,提高了最优路径的搜索效率。最后,数值仿真实验证明了该算法的求解表现优于同类研究常用的遗传算法和禁忌搜索算法,具有较强的全局寻优能力。在灵敏性和有效性的保证下,本研究所设计的改进蚁群算法能够较好地处理低碳车辆路径问题（LCVRP）。     

Optimizing trains movement on a railway network

Focusing on solving critically important train operation problems on a railway network, this paper investigates a mathematical model for finding optimal trains movements under the consideration of operational interactions. With the predetermined routing and traversing order plan, we explicitly consider the optimization of energy consumption and travel time as the objective based on the coasting control methods. To reduce the calculation difficulties, simulation-based methodologies are proposed to compute the energy consumption and traversing time through using specific performance of the involved trains. A genetic algorithm integrated with simulation is designed to seek the approximate optimal coasting control strategies on the railway network. The numerical experiments investigate the effectiveness of the proposed model and algorithm.     

基于Dijkstra-PD-ACO算法的大城市公交线路优化与评价方法研究

城市公交线路的布设受到诸多影响因素的作用,单纯的追求线路单一指标的"最优"在实际公交线路优化时往往难以取得满意的效果。首先针对传统公交线路优化算法在求解线路优化问题中存在的不足,基于蚁群优化算法的寻优特性,结合Dijkstra算法在局部路径寻优中的优点,提出了Dijkstra蚁群混合优化算法。其次对于线路优化所得到的可行备选方案集,基于分层聚类主成分分析评价法进行优化效能评价。最后以合肥市一环内公交线路优化为实例进行验证。结果表明, 本文提出的方法在兼顾客流密度最大、出行路径最短的同时给出了有效公交线路备选方案,优化结果也符合合肥市的实际情况。同时,该方法对我国大中城市公交线网优化问题的研究具有一定的借鉴意义。     

Minimum power assignment in wireless ad hoc networks with spanner property

Power assignment for wireless ad hoc networks is to assign a power for each wireless node such that the induced communication graph has some required properties. Recently research efforts have focused on finding the minimum power assignment to guarantee the connectivity or fault-tolerance of the network. In this paper, we study a new problem of finding the power assignment such that the induced communication graph is a spanner for the original communication graph when all nodes have the maximum power. Here, a spanner means that the length of the shortest path in the induced communication graph is at most a constant times of the length of the shortest path in the original communication graph. Polynomial time algorithm is given to minimize the maximum assigned power with spanner property. The algorithm also works for any other property that can be tested in polynomial time and is monotone. We then give a polynomial time approximation method to minimize the total transmission radius of all nodes. Finally, we propose two heuristics and conduct extensive simulations to study their performance when we aim to minimize the total assigned power of all nodes. The author is partially supported by NSF CCR-0311174.     

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.     

基于地心天际球面坐标的低轨卫星通信网络簇结构协同工作机制设计

低轨LEO（Low earth orbit）卫星通信网络系统星间链路结构与链接关系十分复杂，如何实现该系统的高度可靠、高效工作是一件十分复杂和困难的工作。传统路由算法多选择分布式路由，忽略了卫星内部的分簇管理，在一定程度上，大大增加了算法的时间复杂度和空间复杂度。针对此问题，本文从LEO卫星通信网络的特征出发，运用空间通信技术，分簇规划技术与排队图示评审技术Q-GERT（Queuing graphic evaluation review technique），首先构建LEO卫星通信网络的地心天际球面坐标体系，搭建具有分簇架构的多层次通信网络；其次基于网络综合效能最优化，设计能够实现高度分布式协同通信业务管理的路由模型与算法；最后通过案例研究，表明本文所提工作机制的实用性与有效性。     

OMEGa: an optimistic most energy gain method for minimum energy multicasting in wireless ad hoc networks

In wireless ad hoc networks where every device runs on its own battery, the energy consumption is critical to lengthen the network lifetime. The communication among devices in the network can be categorized as unicasting and multicasting (including broadcasting). For the case of unicasting, computing the energy optimal path between the two communicating nodes is polynomially solvable by computing the shortest path. But for the case of multicasting, shortest path or minimum spanning tree does not guarantee an energy optimal communication. In this paper, we present our novel approach, Optimistic Most Energy Gain (OMEGa) method, for the minimum energy multicasting in wireless ad hoc networks. OMEGa aims at maximum utilization of Wireless Multicast Advantage (WMA), which essentially means covering more nodes by using larger energy. Both theoretical and experimental analysis shows OMEGa method performs very well. Research is partially supported by NSF and Air Force grants.     

Integrated Ant Colony and Tabu Search approach for time dependent vehicle routing problems with simultaneous pickup and delivery

Today manufacturers have become much more concerned with the coordination of both manufacturing (of new products) and recycling (of reusable resources) operations. This requires simultaneous scheduling of both forward and reverse flows of goods over a supply chain network. This paper studies time dependent vehicle routing problems with simultaneous pickup and delivery (TD-VRPSPD). We formulate this problem as a mixed integer programming model, where the time step function is used to calculate the travel time. To efficiently solve this complex problem, we develop a hybrid algorithm that integrates both Ant Colony System (ACS) and Tabu Search (TS) algorithms. Our algorithm uses the pheromones, travel time and vehicle residual loading capacity as a factor structure according to the characteristics of TD-VRPSPD. In our computational experiments, 56 groups of benchmark instances are used to evaluate the performance of our hybrid algorithm. In addition, we compare the performance of our hybrid algorithm with those of individual ACS and TS algorithms. The computational results suggest that our hybrid algorithm outperform stand-alone ACS and the TS algorithms.     

Strategic and operational decision-making in expanding supply chains for LNG as a fuel

The European Union aims for a 40% reduction in greenhouse gas emissions by 2030, compared to 1990 levels, and recognizes the opportunities of Liquefied Natural Gas (LNG) as an alternative fuel for transportation to reach this goal. The lack of a mature supply chain for LNG as a fuel results in a need to invest in new (satellite) terminals, bunker barges and tanker trucks. This network design problem can be defined as a Two-Echelon Capacitated Location Routing Problem with Split Deliveries (2E-CLRPSP). An important feature of this problem is that direct deliveries are allowed from terminals, which makes the problem much harder to solve than the existing location routing literature suggests. In this paper, we improve the performance of a hybrid exact algorithm and apply our algorithm to a real-world network design problem related to the expansion of the European supply chain for LNG as a fuel. We show that satellite terminals and bunker barges become an interesting option when demand for LNG grows and occurs further away from the import terminal. In those situations, the large investments associated with LNG satellites and bunker barges are offset by reductions in operational costs of the LNG tanker trucks.     

基于图的广度搜索的进度生成机制

启发式算法是解决资源受限的项目调度问题的经典方法之一，通常用来生成元启发算法初始解，传统的串行（SSGS）和并行（PSGS）是生成项目调度方案的经典机制，本文基于图的广度优先搜索算法，提出了一种考虑任务节点位置因素的广度生成机制（BSSGS），并验证了算法的效果。借鉴广度搜索算法定义进度生成机制中的当前任务集合C、候选任务集合D以及阶段变量g等，对各任务节点进行层次划分并定义任务调度秩序；结合优先规则选择候选任务j^*并进行资源R_k（t）调度更新，进而生成完整的调度方案；案例分析表明新机制在满足优先规则和资源约束的同时兼顾了任务节点在网络中位置因素，拥有对于局部复杂网络不回避，对关键节点及时调度等明显优势；选择PSPLIB中算例，在不同优先规则下对新机制进行了测试，测试结果表明新的进度生成机制在LPT、SPT、MTS和MIS等优先规则下，在平均最短工期、平均资源利用率及最优调度方案率等方面优于串行和并行进度生成机制，且算法时间复杂度与传统机制相比并未增加，仍为O（J²，K）。     

Improving robustness of next-hop routing

A weakness of next-hop routing is that following a link or router failure there may be no routes between some source-destination pairs, or packets may get stuck in a routing loop as the protocol operates to establish new routes. In this article, we address these weaknesses by describing mechanisms to choose alternate next hops. Our first contribution is to model the scenario as the following tree augmentation problem. Consider a mixed graph where some edges are directed and some undirected. The directed edges form a spanning tree pointing towards the common destination node. Each directed edge represents the unique next hop in the routing protocol. Our goal is to direct the undirected edges so that the resulting graph remains acyclic and the number of nodes with outdegree two or more is maximized. These nodes represent those with alternative next hops in their routing paths. We show that tree augmentation is NP-hard in general and present a simple \(\frac{1}{2}\)-approximation algorithm. We also study 3 special cases. We give exact polynomial-time algorithms for when the input spanning tree consists of exactly 2 directed paths or when the input graph has bounded treewidth. For planar graphs, we present a polynomial-time approximation scheme when the input tree is a breadth-first search tree. To the best of our knowledge, tree augmentation has not been previously studied.     

Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios

We consider the design of a multicommodity flow network, in which point-to-point demands are routed across the network subject to link capacity restrictions. Such a design must build enough capacity and diverse routing paths through the network to ensure that feasible multicommodity flows continue to exist, even when components of the network fail. In this paper, we examine several methodologies to optimally design a minimum-cost survivable network that continues to support a multicommodity flow under any of a given set of failure scenarios, where each failure scenario consists of the simultaneous failure of multiple arcs. We begin by providing a single extensive form mixed-integer programming formulation for this problem, along with a Benders decomposition algorithm as an alternative to the extensive form approach. We next investigate strategies to improve the performance of the algorithm by augmenting the master problem with several valid inequalities such as cover constraints, connectivity constraints, and path constraints. For the smallest instances (eight nodes, 10 origin–destination pairs, and 10 failure scenarios), the Benders implementation consumes only 10% of the time required by the mixed-integer programming formulation, and our best augmentation strategy reduces the solution time by another 50%. For medium- and large-sized instances, the extensive form problem fails to terminate within 2 h on any instance, while our decomposition algorithms provide optimal solutions on all but two problem instances.     

Best routes selection in multimodal networks using multi-objective genetic algorithm

In this study, we propose a bi-level multi-objective Taguchi genetic algorithm for a multimodal routing problem with time windows. The mathematic model is constructed, which is featured by two optimal objectives, multiple available transportation manners and different demanded delivery times. After thoroughly analyzing the characteristics of the formulated model, a corresponding bi-level multi-objective Taguchi genetic algorithm is designed to find the Pareto-optimal front. At the upper level, a genetic multi-objective algorithm simultaneously searches the Pareto-optimal front and provides the most feasible routing path choices for the lower level. After generalizing the matrices of costs and time in a multimodal transportation network, the \(k\) -shortest path algorithm is applied to providing some potential feasible paths. A multi-objective genetic algorithm is proposed at the lower level to determine the local optimal combination of transportation manners for these potential feasible paths. To make the genetic algorithm more robust, sounder and faster, the Taguchi (orthogonal) experimental design method is adopted in generating the initial population and the crossover operator. The case study shows that the proposed algorithm can effectively find the Pareto-optimal front solutions and offer series of transportation routes with best combinations of transportation manners. The shipper can easily select the required shipping schemes with specified demands.     

用混合遗传算法求解物流配送路径优化问题的研究

论文建立了物流配送路径优化问题的数学模型,并针对遗传算法在局部搜索能力方面的不足,提出将爬山算法与遗传算法相结合,从而构造了求解物流配送路径优化问题的混合遗传算法,并进行了实验计算。计算结果表明,用混合遗传算法求解物流配送路径优化问题,可以在一定程度上克服遗传算法在局部搜索能力方面的不足和爬山算法在全局搜索能力方面的不足,从而得到质量较高的解。     

Broadcast Routing with Minimum Wavelength Conversion in WDM Optical Networks

We consider dynamic routing of broadcast connections in WDM optical networks. Given the current network state, we want to find a minimum set of network nodes S such that a broadcast routing using only the nodes in S as wavelength conversion nodes can be found. This ensures that the average conversion delay from the source to all destinations is minimized. We refer to the problem as Broadcast Conversion Node Selection (BCNS) problem. We prove that BCNS has no polynomial-time approximation with performance ratio ln n for < 1 unless NPDTIME(n^{O(log log n)}) where n is the number of vertices in the input graph. We present a greedy approximation algorithm for BCNS that achieves approximation ratio 2+ln n. Simulation results show that the algorithm performs very well in practice, obtaining optimal solutions in most of the cases.     

车辆路径问题的禁忌搜索算法研究

论文在对车辆路径问题进行简单描述的基础上,通过设计一种新的解的表示方法构造了求解该问题的一种新的禁忌搜索算法,并进行了实验计算。计算结果表明,用本文设计的禁忌搜索算法求解车辆路径问题,不仅可以取得很好的计算结果,而且算法的计算效率较高,收敛速度较快,计算结果也较稳定。