Approximate solutions for the capacitated arc routing problem

The capacitated arc routing problem (CARP), is a capacitated variation of the arc routing problems in which there is a capacity constraint associated with each vehicle. Due to the computational complexity of the problem, recent research has focussed on developing and testing heuristic algorithms which solve the CARP approximately. In this paper, we review some of the existing solution procedures, analyze their complexity, and present two modifications of the existing methods to obtain near-optimal solutions for the CARP. Extensive computational results are presented and analyzed.     

Exploiting sparsity in pricing routines for the capacitated arc routing problem

The capacitated arc routing problem (CARP) is a well-known and fundamental vehicle routing problem. A promising exact solution approach to the CARP is to model it as a set covering problem and solve it via branch-cut-and-price. The bottleneck in this approach is the pricing (column generation) routine. In this paper, we note that most CARP instances arising in practical applications are defined on sparse graphs. We show how to exploit this sparsity to yield faster pricing routines. Extensive computational results are given.     

An improved heuristic for the capacitated arc routing problem

The capacitated arc routing problem (CARP) is an important and practical problem in the OR literature. In short, the problem is to identify routes to service (e.g., pickup or deliver) demand located along the edges of a network such that the total cost of the routes is minimized. In general, a single route cannot satisfy the entire demand due to capacity constraints on the vehicles. CARP belongs to the set of NP-hard problems; consequently numerous heuristic and metaheuristic solution approaches have been developed to solve it. In this paper an “ellipse rule” based heuristic is proposed for the CARP. This approach is based on the path-scanning heuristic, one of the mostly used greedy-add heuristics for this problem. The innovation consists basically of selecting edges only inside ellipses when the vehicle is near the end of each route. This new approach was implemented and tested on three standard datasets and the solutions are compared against: (i) the original path-scanning heuristic; (ii) two other path-scanning heuristics and (iii) the three best known metaheuristics. The results indicate that the “ellipse rule” approach lead to improvements over the three path-scanning heuristics, reducing the average distance to the lower bound in the test problems by about 44%.     

Capacitated arc routing problem with deadheading demands

Capacitated arc routing problem (CARP) is the determination of vehicle tours that serve all positive-demand edges (required edge) exactly once without exceeding vehicle capacity while minimizing sum of all tour costs. In CARP, total demand of a tour is calculated by means of all required edges on the tour. In this study, a new CARP variation is introduced, which considers not only required edges but also traversed edges while calculating total demand of the tour. The traversing demand occurs when the traversed edge is either servicing or non-servicing (deadheading). Since the new CARP formulation incurs deadheading edge demands it is called CARP with deadheading demands. An integer linear model is given for the problem which is used to solve small-sized instances, optimally. A constructive heuristic is presented to solve the problem which is a modified version of a well-known CARP heuristic. Furthermore, two post-optimization procedures are presented to improve the solution of the heuristic algorithm. The effectiveness of the proposed methods is shown on test problems, which are obtained by modifying CARP test instances.     

Lower and upper bounds for the mixed capacitated arc routing problem

This paper presents a linear formulation, valid inequalities, and a lower bounding procedure for the mixed capacitated arc routing problem (MCARP). Moreover, three constructive heuristics and a memetic algorithm are described. Lower and upper bounds have been compared on two sets of randomly generated instances. Computational results show that the average gaps between lower and upper bounds are 0.51% and 0.33%, respectively.     

A deterministic tabu search algorithm for the capacitated arc routing problem

The capacitated arc routing problem (CARP) is a difficult optimisation problem in vehicle routing with applications where a service must be provided by a set of vehicles on specified roads. A heuristic algorithm based on tabu search is proposed and tested on various sets of benchmark instances. The computational results show that the proposed algorithm produces high quality results within a reasonable computing time. Some new best solutions are reported for a set of test problems used in the literature.     

On Making a Distinguished Vertex of Minimum Degree by Vertex Deletion

For directed and undirected graphs, we study how to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-hard when parameterized by the graph’s feedback arc set number, whereas it becomes fixed-parameter tractable when combining the parameters “feedback vertex set number” and “number of vertices to delete”. For the so far unstudied undirected case, we show that the problem is NP-hard and W[1]-hard when parameterized by the “number of vertices to delete”. On the positive side, we show fixed-parameter tractability for several parameterizations measuring tree-likeness. In particular, we provide a dynamic programming algorithm for graphs of bounded treewidth and a vertex-linear problem kernel with respect to the parameter “feedback edge set number”. On the contrary, we show a non-existence result concerning polynomial-size problem kernels for the combined parameter “vertex cover number and number of vertices to delete”, implying corresponding non-existence results when replacing vertex cover number by treewidth or feedback vertex set number.     

Location-arc routing problem: Heuristic approaches and test instances

Location-routing is a branch of locational analysis that takes into account distribution aspects. The location-arc routing problem (LARP) considers scenarios where the demand is on the edges rather than being on the nodes of a network (usually a road network is assumed). Examples of such scenarios include locating facilities for postal delivery, garbage collection, road maintenance, winter gritting and street sweeping. This paper presents some heuristic approaches to tackle the LARP, as well as some proposals for benchmark instances (and corresponding results). New constructive and improvement methods are presented and used within different metaheuristic frameworks. Test instances were obtained from the capacitated arc routing problem (CARP) literature and adapted to address the LARP.     

Joint gateway selection,transmission slot assignment,routing and power control for wireless mesh networks

Wireless mesh networks (WMNs) provide cost effective solutions for setting up a communications network over a certain geographic area. In this paper, we study strategic problems of WMNs such as selecting the gateway nodes along with several operational problems such as routing, power control, and transmission slot assignment. Under the assumptions of the physical interference model and the tree-based routing restriction for traffic flow, a mixed integer linear programming (MILP) formulation is presented, in which the objective is to maximize the minimum service level provided at the nodes. A set of valid inequalities is derived and added to the model in an attempt to improve the solution quality. Since the MILP formulation becomes computationally infeasible for larger instances, we propose a heuristic method that is aimed at solving the problem in two stages. In the first stage, we devise a simple MILP problem that is concerned only with the selection of gateway nodes. In the second stage, the MILP problem in the original formulation is solved by fixing the gateway nodes from the first stage. Computational experiments are provided to evaluate the proposed models and the heuristic method.     

Network Characterizations for Excluding Braess’s Paradox

Braess’s paradox exposes a counterintuitive phenomenon that when travelers selfishly choose their routes in a network, removing links can improve the overall network performance. Under the model of nonatomic selfish routing, we characterize the topologies of k-commodity undirected and directed networks in which Braess’s paradox never occurs. Our results strengthen Milchtaich’s series-parallel characterization (Milchtaich, Games Econom. Behav. 57(2), 321–346 (2006)) for the single-commodity undirected case.     

Wavelength Conversion in All-Optical Networks with Shortest-Path Routing

We consider all-optical networks with shortest-path routing that use wavelength-division multiplexing and employ wavelength conversion at specific nodes in order to maximize their capacity usage. We present efficient algorithms for deciding whether a placement of wavelength converters allows the network to run at maximum capacity, and for finding an optimal wavelength assignment when such a placement of converters is known. Our algorithms apply to both undirected and directed networks. Furthermore, we show that the problem of designing such networks, i.e., finding an optimal placement of converters, is MAX SNP-hard in both the undirected and the directed case. Finally, we give a linear-time algorithm for finding an optimal placement of converters in undirected triangle-free networks, and show that the problem remains NP-hard in bidirected triangle-free planar networks.     

基于广义共同邻居的有向网络链路预测方法

链路预测利用已知网络节点及结构等信息预测网络未知连接或未来连接。现有主流方法多应用于无向网络,而且部分有向链路预测方法忽视了共同邻居在有向网络下的多样异构特征。针对上述问题,提出了一种广义共同邻居算法。该方法首先对有向网络定义了广义共同邻居,通过网络中有向邻居异构体的连边概率衡量不同结构对连边贡献程度,然后利用该定义对现有的局部相似性指标进行了优化,重定义8种基于广义共同邻居的有向相似性指标。在 12 个数据集上的实验表明,所提方法在两个衡量指标下普遍提升了现有预测指标性能。     

A genetic algorithm for a bi-objective capacitated arc routing problem

The capacitated arc routing problem (CARP) is a very hard vehicle routing problem for which the objective—in its classical form—is the minimization of the total cost of the routes. In addition, one can seek to minimize also the cost of the longest trip.In this paper, a multi-objective genetic algorithm is presented for this more realistic CARP. Inspired by the second version of the Non-dominated sorted genetic algorithm framework, the procedure is improved by using good constructive heuristics to seed the initial population and by including a local search procedure. The new framework and its different flavour is appraised on three sets of classical CARP instances comprising 81 files.Yet designed for a bi-objective problem, the best versions are competitive with state-of-the-art metaheuristics for the single objective CARP, both in terms of solution quality and computational efficiency: indeed, they retrieve a majority of proven optima and improve two best-known solutions.     

Memetic Algorithm With Extended Neighborhood Search for Capacitated Arc Routing Problems

The capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NP-hard and exact methods are only applicable to small instances, heuristic and metaheuristic methods are widely adopted when solving CARP. In this paper, we propose a memetic algorithm, namely memetic algorithm with extended neighborhood search (MAENS), for CARP. MAENS is distinct from existing approaches in the utilization of a novel local search operator, namely Merge-Split (MS). The MS operator is capable of searching using large step sizes, and thus has the potential to search the solution space more efficiently and is less likely to be trapped in local optima. Experimental results show that MAENS is superior to a number of state-of-the-art algorithms, and the advanced performance of MAENS is mainly due to the MS operator. The application of the MS operator is not limited to MAENS. It can be easily generalized to other approaches.     

A Global Repair Operator for Capacitated Arc Routing Problem

Capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NP-hard and exact methods are only applicable for small instances, heuristics and metaheuristic methods are widely adopted when solving CARP. This paper demonstrates one major disadvantage encountered by traditional search algorithms and proposes a novel operator named global repair operator (GRO) to address it. We further embed GRO in a recently proposed tabu search algorithm (TSA) and apply the resultant repair-based tabu search (RTS) algorithm to five well-known benchmark test sets. Empirical results suggest that RTS not only outperforms TSA in terms of quality of solutions but also converges to the solutions faster. Moreover, RTS is also competitive with a number of state-of-the-art approaches for CARP. The efficacy of GRO is thereby justified. More importantly, since GRO is not specifically designed for the referred TSA, it might be a potential tool for improving any existing method that adopts the same solution representation.     

An application of a computational ecology model to a routing methodin computer networks

The paper proposes a network routing method based on a computational ecology model. The computational ecology model is a mathematical model proposed by B.A. Huberman and T. Hogg (1988), which represents a macro action of multi-agent systems. We formulate routing on a computer network as a resource allocation problem, where packets and links are regarded as agents and resources, respectively. Then, we apply an extended computational ecology model for this problem. Agents conflict so as to get more payoffs from links. As a result, they get the same payoffs, and a good resource allocation is achieved. In each node, each packet selects a link according to the selection rate decided through conflicts, and routing is accomplished autonomously with adaptability on the computer network. Moreover, we improve fault-tolerance of the system by local information exchanges. Finally, we examine the efficiency of the proposed method by computer simulation.     

Solving capacitated arc routing problems using a transformation to the CVRP

A well-known transformation by Pearn, Assad and Golden reduces a capacitated arc routing problem (CARP) into an equivalent capacitated vehicle routing problem (CVRP). However, that transformation is regarded as unpractical, since an original instance with r   required edges is turned into a CVRP over a complete graph with 3r+1$3r+1$ vertices. We propose a similar transformation that reduces this graph to 2r+1$2r+1$ vertices, with the additional restriction that a previously known set of r pairwise disconnected edges must belong to every solution. Using a recent branch-and-cut-and-price algorithm for the CVRP, we observed that it yields an effective way of attacking the CARP, being significantly better than the exact methods created specifically for that problem. Computational experiments obtained improved lower bounds for almost all open instances from the literature. Several such instances could be solved to optimality.     

Scale-free network modles with accelerating growth

Complex networks are everywhere. A typical example is software network. Basing on analyzing evolutive structure of the software networks, we consider accelerating growth of network as power-law growth, which can be more easily generalized to real systems than linear growth. For accelerating growth via a power law and scale-free state with preferential linking, we focus on exploring the generic property of complex networks. Generally, two scenarios are possible. In one of them, the links are undirected. In the other scenario, the links are directed. We propose two models that can predict the emergence of power-law growth and scale-free state in good agreement with these two scenarios and can simulate much more real systems than existing scale-free network models. Moreover, we use the obtained predictions to fit accelerating growth and the connectivity distribution of software networks describing scale-free structure. The combined analytical and numerical results indicate the emergence of a novel set of models that considerably enhance our ability to understand and characterize complex networks, whose applicability reaches far beyond the quoted examples.     

Scale-free network models with accelerating growth

Complex networks are everywhere. A typical example is software network. Basing on analyzing evolutive structure of the software networks, we consider accelerating growth of network as power-law growth, which can be more easily generalized to real systems than linear growth. For accelerating growth via a power law and scale-free state with preferential linking, we focus on exploring the generic property of complex networks. Generally, two scenarios are possible. In one of them, the links are undirected. In the other scenario, the links are directed. We propose two models that can predict the emergence of power-law growth and scale-free state in good agreement with these two scenarios and can simulate much more real systems than existing scale-free network models. Moreover, we use the obtained predictions to fit accelerating growth and the connectivity distribution of software networks describing scale-free structure. The combined analytical and numerical results indicate the emergence of a novel set of models that considerably enhance our ability to understand and characterize complex networks, whose applicability reaches far beyond the quoted examples.     

MPLS流量工程仿真

在通信网络中,负载不均衡或部分网络失效常常会引起网络拥塞问题,导致业务的服务质量下降.相对于传统的动态路由协议解决此类问题所具有的局限性,MPLS流量工程是解决问题的一种有效途径.在计算机网络仿真平台上,设计了动态路由协议和MPLS流量工程仿真实例,通过运行仿真,获取了它们的网络性能及业务服务质量数据.通过对仿真结果进行比较和分析,可以看出,MPLS流量工程通过更为灵活的方式在多条链路上实现负载分担,可以改进网络资源利用率,当链路或节点失效时,能够提供快速的恢复机制.