Planning for optimal expansion of leased line communication networks

We report a new heuristic algorithm useful for developing least-cost expansion plans for leased telecommunications networks in which there is a hierarchy of possible transmission facilities. The problem combines network topology design and capacity expansion problems. Implemented on a PC, the algorithm has successfully developed topology growth plans for twenty periods on networks with up to 31 nodes.     

Two new algorithms for the Min-Power Broadcast problem in static ad hoc networks

In this paper we address the Min-Power Broadcast problem in wireless ad hoc networks. Given a network with an identified source node w, the Min-Power Broadcast (MPB) problem is to assign transmission range to each node such that communication from w to other nodes is possible and the total energy consumption is minimized.

As the problem is NP-Hard we first propose a simulated annealing algorithm for the MPB problem. Utilizing a special node selection mechanism in its neighborhood structure the algorithm is designed in a way enabling an efficient power consumption evaluation and search for neighboring solutions. We then combine the algorithm with a decomposition approach to enhance its performance. This is achieved by decomposing the master problem and performing metropolis chain of the simulated annealing only on the much smaller subproblems resulting from decomposition. Results from a comprehensive computational study indicate the efficiency and effectiveness of the proposed algorithms.     

A constraint generation scheme to probabilistic linear problems with an application to power system expansion planning

In this paper, we first describe a constraint generation scheme for probabilistic mixed integer programming problems. Next, we present a decomposition approach to the peak capacity expansion planning of interconnected hydrothermal generating systems, with bounds on the transmission capacity between the regions. The objective is to minimize investments in generating units and interconnection links, subject to constraints on supply reliability. The problem is formulated as a stochastic integer program. The constraint generation scheme, which is similar to Benders decomposition, is applied in the solution of the peak capacity expansion problem. The master problem in this decomposition scheme is an integer program, solved by implicit enumeration. The operating subproblem corresponds to a stochastic network flow problem, and is solved by a maximum flow algorithm and Monte Carlo simulation. The approach is illustrated through a case study involving the expansion of the system of the Brazilian Southeastern region.     

On capacity expansion planning under strategic and operational uncertainties based on stochastic dominance risk averse management

A new scheme for dealing with uncertainty in scenario trees is presented for dynamic mixed 0–1 optimization problems with strategic and operational stochastic parameters. Let us generically name this type of problems as capacity expansion planning (CEP) in a given system, e.g., supply chain, production, rapid transit network, energy generation and transmission network, etc. The strategic scenario tree is usually a multistage one, and the replicas of the strategic nodes root structures in the form of either a special scenario graph or a two-stage scenario tree, depending on the type of operational activity in the system. Those operational scenario structures impact in the constraints of the model and, thus, in the decomposition methodology for solving usually large-scale problems. This work presents the modeling framework for some of the risk neutral and risk averse measures to consider for CEP problem solving. Two types of risk averse measures are considered. The first one is a time-inconsistent mixture of the chance-constrained and second-order stochastic dominance (SSD) functionals of the value of a given set of functions up to the strategic nodes in selected stages along the time horizon, The second type is a strategic node-based time-consistent SSD functional for the set of operational scenarios in the strategic nodes at selected stages. A specialization of the nested stochastic decomposition methodology for that problem solving is outlined. Its advantages and drawbacks as well as the framework for some schemes to, at least, partially avoid those drawbacks are also presented.     

Minimum power multicasting in wireless networks under probabilistic node failures

In this paper we deal with a probabilistic extension of the minimum power multicast (MPM) problem for wireless networks. The deterministic MPM problem consists in assigning transmission powers to the nodes, so that a multihop connection can be established between a source and a given set of destination nodes and the total power required is minimized. We present an extension to the basic problem, where node failure probabilities for the transmission are explicitly considered. This model reflects the necessity of taking uncertainty into account in the availability of the hosts. The novelty of the probabilistic minimum power multicast (PMPM) problem treated in this paper consists in the minimization of the assigned transmission powers, imposing at the same time a global reliability level to the solution network. An integer linear programming formulation for the PMPM problem is presented. Furthermore, an exact algorithm based on an iterative row and column generation procedure, as well as a heuristic method are proposed. Computational experiments are finally presented.     

Virtual Path Design in Service-Specific ATM Networks

This paper addresses the problem of virtual path management in ATM networks, which is the problem of jointly selecting efficient virtual trunk routes and sizing them to meet end-to-end grade-of-service requirements. The problem is posed over capacitated networks and is formulated as a two-level multi-commodity network flow problem with linear side-constraints (physical layer capacity) and non-linear side constraints (end-to-end/link blocking). Through a variety of examples we show the method (i) generates solutions that agree with engineering judgement, (ii) can solve VP layout management for realistic size networks (of up to 200 nodes) in reasonable time and (iii) provides upper bounds on how far the solution strays from the mathematically optimal design.     

IP modeling of the survivable hop constrained connected facility location problem

We consider a generalized version of the rooted connected facility location problem which occurs in planning of telecommunication networks with both survivability and hop-length constraints. Given a set of client nodes, a set of potential facility nodes including one predetermined root facility, a set of optional Steiner nodes, and the set of the potential connections among these nodes, that task is to decide which facilities to open, how to assign the clients to the open facilities, and how to interconnect the open facilities in such a way, that the resulting network contains at least λ edge-disjoint paths, each containing at most H edges, between the root and each open facility and that the total cost for opening facilities and installing connections is minimal. We study two IP models for this problem and present a branch-and-cut algorithm based on Benders decomposition for finding its solution. Finally, we report computational results.     

Price-directive decomposition applied to routing in telecommunication networks

The telecommunication network design problem is considered to study the level of transmission network. A heuristic approach is defined to solve the combined routing-grouping problem, where the grouping one is solved by a heuristic approach. The routing problem is defined considering reliability constraints, supplementary circuits demands and a piecewise linear objective function to take into account the influence of the grouping. This last model is solved using a price-directive decomposition method, which has allowed us to solve real networks using an exact method.     

Benders Decomposition for a Location-Design Problem in Green Wireless Local Area Networks

We consider a problem arising in the design of green (or energy-saving) wireless local area networks (GWLANs). Decisions on both location and capacity dimensioning must be taken simultaneously. We model the problem as an integer program with nonlinear constraints and derive valid inequalities. We handle the nonlinearity of the formulation by developing a Benders decomposition algorithm. We propose various ways to improve the Benders master problem and the feasibility cuts.     

Capacity optimization through sensing threshold adaptation for cognitive radio networks

We propose capacity optimization through sensing threshold adaptation for sensing-based cognitive radio networks. The objective function of the proposed optimization is the maximization of the capacity at the secondary user subject to transmit power and sensing threshold constraints for protecting the primary user. After proving the concavity of capacity on sensing threshold, the problem is solved using the Lagrange duality decomposition method in conjunction with a subgradient iterative algorithm. The numerical results show that the proposed optimization can lead to significant capacity maximization for the secondary user as long as this is affordable to the primary user.     

On the semi-discretization of optimal control problems for networks of elastic strings: global optimality systems and domain decomposition

We consider a star-graph as an examplary network, with elastic strings stretched along the edges. The network is allowed to perform out-of-the plane displacements. We consider such networks as being controlled at its simple nodes via Dirichlet conditions. The objective is to steer given initial data to final target data in a given time T with minimal control costs. This problem is discussed in the continuous as well as in the discrete case. We discuss an iterative domain decomposition technique and its discrete analogue. We prove convergence and show some numerical results.     

A distributed approximation algorithm for the bottleneck connected dominating set problem

Some of the most popular routing protocols for wireless sensor networks require a virtual backbone for efficient communication between the sensors. Connected dominating sets (CDS) have been studied as a method of choosing nodes to be in the backbone. The traditional approach is to assume that the transmission range of each node is given and to minimize the number of nodes in the CDS representing the backbone. A recently introduced alternative strategy is based on the concept of k-bottleneck connected dominating set (k-BCDS), which, given a positive integer k, minimizes the transmission range of the nodes that ensures a CDS of size k exists in the network. This paper provides a 6-approximate distributed algorithm for the k-BCDS problem. The results of empirical evaluation of the proposed algorithm are also included.     

A self-tuning heuristic for the design of communication networks

This paper addresses the design of communication networks that has a large application area. The problem is to design a minimum cost network subject to a given reliability level. Complexity of the problem is twofold: (1) finding a minimum-cost network topology that every pair of nodes can communicate with each other and (2) computing overall reliability to provide the reliability constraint. Over the last two decades, metaheuristic algorithms have been widely applied to solve this problem due to its NP-hardness. In this study, a self-tuning heuristic (STH), which is a new approach free from parameter tuning, is applied to the design of communication networks. Extensive computational results confirm that STH generates superior solutions to the problem in comparison to some well-known local search metaheuristics, and also more sophisticated metaheuristics proposed in the literature. The practical advantage of STH lies in both its effectiveness and simplicity in application to the design problem.     

Dynamic Capacity Acquisition and Assignment under Uncertainty

Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-and-bound strategy for the problem. Encouraging preliminary computational results are provided.     

A robust optimization approach for multicast network coding under uncertain link costs

Network coding is a technique that can be used to improve the performance of communication networks by performing mathematical operations at intermediate nodes. An important problem in coding theory is that of finding an optimal coding subgraph for delivering network data from a source node throughout intermediate nodes to a set of destination nodes with the minimum transmission cost. However, in many real applications, it can be difficult to determine exact values or specific probability distributions of link costs. Establishing minimum-cost multicast connections based on erroneous link costs might exhibit poor performance when implemented. This paper considers the problem of minimum-cost multicast using network coding under uncertain link costs. We propose a robust optimization approach to obtain solutions that protect the system against the worst-case value of the uncertainty in a prespecified set. The simulation results show that a robust solution provides significant improvement in worst-case performance while incurring a small loss in optimality for specific instances of the uncertainty.     

Identifying influential spreaders by weight degree centrality in complex networks

The problem of identifying influential spreaders in complex networks has attracted much attention because of its great theoretical significance and wide application. In this paper, we propose a successful ranking method for identifying the influential spreaders. The proposed method measures the spreading ability of nodes based on their degree and their ability of spreading out. We also use a tuning weight parameter, which is always associated with the property of the networks such as the assortativity, to regulate the weight between the degree and the ability of spreading out. To test the effectiveness of the proposed method, we conduct the experiments on several synthetic networks and real-world networks. The results show that the proposed method outperforms the existing well-known ranking methods.     

A branch and price algorithm for the minimum power multicasting problem in wireless sensor networks

The Minimum Power Multicast Problem arises in wireless sensor networks and consists in assigning a transmission power to each node of a network in such a way that the total power consumption over the network is minimized, while a source node is connected to a set of destination nodes, toward which a message has to be sent periodically. A new mixed integer programming model for the problem, based on paths, is presented. A practical exact algorithm based on column generation and branch and price is derived from this model. A comparison with state-of-the-art exact methods is presented, and it is shown that the new approach compares favorably to other algorithms when the number of destination nodes is moderate. Under this condition, the proposed method is able to solve previously unmanageable instances.     

An introduction to dynamic generative networks: Minimum cost flow

What we are dealing with is a class of networks called dynamic generative network flows in which the flow commodity is dynamically generated at source nodes and dynamically consumed at sink nodes. As a basic assumption, the source nodes produce the flow according to time generative functions and the sink nodes absorb the flow according to time consumption functions. This paper tries to introduce these networks and formulate minimum cost dynamic flow problem for a pre-specified time horizon T. Finally, some simple, efficient approaches are developed to solve the dynamic problem, in the general form when the capacities and costs are time varying and some other special cases, as a minimum cost static flow problem.     

Calculation of minimal capacity vectors through k minimal paths under budget and time constraints

Reducing the transmission time is an important issue for a flow network to transmit a given amount of data from the source to the sink. The quickest path problem thus arises to find a single path with minimum transmission time. More specifically, the capacity of each arc is assumed to be deterministic. However, in many real-life networks such as computer networks and telecommunication networks, the capacity of each arc is stochastic due to failure, maintenance, etc. Hence, the minimum transmission time is not a fixed number. Such a network is named a stochastic-flow network. In order to reduce the transmission time, the network allows the data to be transmitted through k minimal paths simultaneously. Including the cost attribute, this paper evaluates the probability that d units of data can be transmitted under both time threshold T and budget B. Such a probability is called the system reliability. An efficient algorithm is proposed to generate all of lower boundary points for (d, T, B), the minimal capacity vectors satisfying the demand, time, and budget requirements. The system reliability can then be computed in terms of such points. Moreover, the optimal combination of k minimal paths with highest system reliability can be obtained.     

Reliability evaluation according to a routing scheme for multi-state computer networks under assured accuracy rate

In many real-time networks such as computer networks, each arc has stochastic capacity, lead time, and accuracy rate. Such a network is named a multi-state computer network (MSCN). Under the strict assumption that the capacity of each arc is deterministic, the quickest path (QP) problem is to find a path that sends a specific amount of data with minimum transmission time. From the viewpoint of internet quality, the transmission accuracy rate is one of critical performance indicators to assess internet network for system administrators and customers. Under both assured accuracy rate and time constraint, this paper extends the QP problem to discuss the flow assignment for a MSCN. An efficient algorithm is proposed to find the minimal capacity vector meeting such requirements. The system reliability, the probability to send \(d\) units of data through multiple minimal paths under both assured accuracy rate and time constraint, can subsequently be computed. Furthermore, two routing schemes with spare minimal paths are adopted to reinforce the system reliability. The enhanced system reliability according to the routing scheme is calculated as well. The computational complexity in both the worst case and average case are analyzed.