Pedro Patrício

Bio: Pedro Patrício is an academic researcher from University of Beira Interior. The author has contributed to research in topics: Path protection & Network planning and design. The author has an hindex of 4, co-authored 10 publications receiving 143 citations.

MPLS over WDM network design with packet level QoS constraints based on ILP models

Abstract: MPLS (multiprotocol label switching) over WDM (wavelength division multiplexing) networks are gaining significant attention due to the efficiency in resource utilization that can be achieved by jointly considering the two network layers. This paper addresses the design of MPLS over WDM networks, where some of the WDM nodes may not have packet switching capabilities. Given the WDM network topology and the offered traffic matrix, which includes the location of the edge LSRs (label switched routers), we jointly determine the location of the core LSRs (i.e. the core WDM nodes that also need to include packet switching capabilities) and the lightpath routes (which are terminated on the LSRs) that minimize the total network cost. We consider constraints both at the optical and packet layers: an MPLS hop constraint on the maximum number of LSRs traversed by each LSP (label switched path), which guarantees a given packet level QoS, and a WDM path constraint on the maximum length of lightpaths, which accommodates the optical transmission impairments. A novel integer linear programming (ILP) formulation based on an hop-indexed approach, which we call the HOP model, is proposed. A two-phase heuristic, derived from a decomposition of the HOP model in two simpler ILP models that are solved sequentially, is also developed. The computational results show that the heuristic is efficient and produces good quality solutions, as assessed by the lower bounds computed from the HOP model. In some cases, the optimal solution is obtained with the branch-and-bound method.

Hop-constrained node survivable network design : an application to MPLS over WDM

Abstract: In this paper, we address a hop-constrained node survivable network design problem that is defined in the context of multi-protocol label switching (MPLS) over wavelength division multiplexing (WDM) networks. At the lower WDM layer, we consider a maximum length constraint for optical connections between MPLS routers. At the upper MPLS layer, we consider survivability as well as maximum delay constraints. Survivability is guaranteed by routing each demand through D node-disjoint paths and maximum delay is guaranteed by constraining all paths to a maximum number of hops. An Integer Linear Programming model, based on the previous works by Gouveia et al. (Proc of IEEE INFOCOM, 2003, and Telecommunications network planning: innovations in pricing, network design and management, pp 167–180, 2006) is used to model the network design problem considering two different survivability mechanisms: path diversity (where each demand is equally split over the D paths) and path protection (where any D–1 out of the D paths have enough capacity to support the total demand). For both mechanisms, we use the NSFNet and EON real world networks to make a cost analysis of the design solutions for different values of D. In the path diversity mechanism, the results consistently show that greater values of D impose a cost penalty that is greater than the gain in the percentage of demand that is protected. In the path protection mechanism, where all traffic is totally protected, the results show that the network solutions obtained with D=3 node-disjoint paths have consistently lower costs than the network solutions obtained with D=2 node-disjoint paths. However, using values of D that are greater than 3 led to network solutions with larger costs.

Compact Models for Hop-Constrained Node Survivable Network Design: An Application to MPLS

Abstract: In this paper we discuss compact models for a hop-constrained node survivable network design problem. We discuss two models involving one set of variables associated to each path between each pair of demand nodes (a standard network flow model with additional cardinality constraints and a model with hop-indexed variables) and a third model involving one single set of hop-indexed variables for each demand pair. We show that the aggregated more compact hop-indexed model produces the same linear programming bound as the multi-path hop-indexed model. This work is given in the context of the following MPLS network design problem. Given the location of edge nodes, the candidate locations of core nodes and the pairs of locations that can be physically connected, the MPLS network design problem addressed in this paper is the determination of the physical network topology, i.e., the location of core nodes and the connections required between all nodes. The aim of the design task is to determine the least cost network. The physical network must support routing paths between all pairs of edge nodes fulfilling two types of path constraints. The first type is a MPLS hop constraint on the maximum number of edges traversed by each routing path, which guarantees a given packet level quality of service (QoS). The second type is the fault-tolerance constraint. An important component of providing QoS is the service reliability and a fault-tolerance scheme must be present in the network to deal efficiently with failure scenarios. We present computational results, taken from graphs with up to 50 nodes and slightly more than 400 edges.

Fratura proximal do fémur bilateral: Incidência e fatores de risco de fratura contralateral

Abstract: In patients with osteoporotic fractures of the proximal femur, little is known about the incidence and risk factors of contralateral fracture

Design of Survivable Networks: A survey

Abstract: For the past few decades, combinatorial optimization techniques have been shown to be powerful tools for formulating and solving optimization problems arising from practical situations. In particular, many network design problems have been formulated as combinatorial optimization problems. With the advances of optical technologies and the explosive growth of the Internet, telecommunication networks have seen an important evolution and therefore designing survivable networks has become a major objective for telecommunication operators. Over the past years, much research has been carried out to devise efficient methods for survivable network models, and particularly cutting plane based algorithms. In this paper, we attempt to survey some of these models and the optimization methods used for solving them. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(1), 1–21 2005

Benders Decomposition for the Hop-Constrained Survivable Network Design Problem

Abstract: Given a graph with nonnegative edge weights and node pairs Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia [Gouveia, L. 1998. Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints. INFORMS J. Comput.102 180--188], we present a formulation for the problem valid for any K, L ≥ 1. We use a Benders decomposition method to efficiently handle the large number of variables and constraints. We show that our Benders cuts contain constraints used in previous studies to formulate the problem for L = 2, 3, 4, as well as new inequalities when L ≥ 5. Whereas some recent works on Benders decomposition study the impact of the normalization constraint in the dual subproblem, we focus here on when to generate the Benders cuts. We present a thorough computational study of various branch-and-cut algorithms on a large set of instances including the real-based instances from SNDlib. Our best branch-and-cut algorithm combined with an efficient heuristic is able to solve the instances significantly faster than CPLEX 12 on the extended formulation.

The regenerator location problem

Abstract: In this article, we introduce the regenerator location problem (RLP), which deals with a constraint on the geographical extent of transmission in optical networks. Specifically, an optical signal can only travel a maximum distance of dmax before its quality deteriorates to the point that it must be regenerated by installing regenerators at nodes of the network. As the cost of a regenerator is high, we wish to deploy as few regenerators as possible in the network, while ensuring all nodes can communicate with each other. We show that the RLP is NP-Complete. We then devise three heuristics for the RLP. We show how to represent the RLP as a max leaf spanning tree problem (MLSTP) on a transformed graph. Using this fact, we model the RLP as a Steiner arborescence problem (SAP) with a unit degree constraint on the root node. We also devise a branch-and-cut procedure to the directed cut formulation for the SAP problem. In our computational results over 740 test instances, the heuristic procedures obtained the optimal solution in 454 instances, whereas the branch-and-cut procedure obtained the optimal solution in 536 instances. These results indicate the quality of the heuristic solutions are quite good, and the branch-and-cut approach is viable for the optimal solution of problems with up to 100 nodes. Our approaches are also directly applicable to the MLSTP indicating that both the heuristics and branch-and-cut approach are viable options for the MLSTP. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010

Risk approaches for delivering disaster relief supplies

Abstract: We consider the problem of designing the logistic system to assure adequate distribution of relief aid in a post-natural-disaster situation, when damages to infrastructure may disrupt the delivery of relief aid. The problem is formulated as a multi-objective optimization problem, encompassing three objective functions of central interest in such problems. The first objective function is a measure of risk (various forms of such risk are analyzed). The second objective function measures the coverage provided by the logistic system in the distribution of relief aid to disaster victims. The third objective function represents total travel time. We focus on the risk of delivery tours for relief supplies, where risk here captures the threat that potential tours become impassable after the natural hazard event. In order to cope with a range of different natural disasters and policy objectives, we develop five approaches emphasizing different measures of tour-dependent risk. To cover both earthquake and flood risks, we consider correlated as well as uncorrelated risk measures. We develop a two-phase solution approach to reflect the dictates of real-world disaster relief motivating this analysis. The first phase generates potentially Pareto-optimal solutions to the overall multi-objective logistic design problem with respect to three objectives. For any given risk measure, the first-phase design problem is formulated as a multi-objective integer program and a memetic algorithm is proposed as the solution approach. The second phase is an enrichment procedure to generate a broader range of potentially Pareto-optimal alternatives. The suggested approach is tested on real-world data from the province of Manabi in Ecuador and the results associated with the different risk measures are analyzed to illustrate the value of the proposed approach for the design of disaster relief networks.

Risk approaches for delivering disaster relief supplies

Abstract: We consider the problem of designing the logistic system to assure adequate distribution of relief aid in a post-natural-disaster situation, when damages to infrastructure may disrupt the delivery of relief aid. The problem is formulated as a multi-objective optimization problem, encompassing three objective functions of central interest in such problems. The first objective function is a measure of risk (various forms of such risk are analyzed). The second objective function measures the coverage provided by the logistic system in the distribution of relief aid to disaster victims. The third objective function represents total travel time. We focus on the risk of delivery tours for relief supplies, where risk here captures the threat that potential tours become impassable after the natural hazard event. In order to cope with a range of different natural disasters and policy objectives, we develop five approaches emphasizing different measures of tour-dependent risk. To cover both earthquake and flood risks, we consider correlated as well as uncorrelated risk measures. We develop a two-phase solution approach to reflect the dictates of real-world disaster relief motivating this analysis. The first phase generates potentially Pareto-optimal solutions to the overall multi-objective logistic design problem with respect to three objectives. For any given risk measure, the first-phase design problem is formulated as a multi-objective integer program and a memetic algorithm is proposed as the solution approach. The second phase is an enrichment procedure to generate a broader range of potentially Pareto-optimal alternatives. The suggested approach is tested on real-world data from the province of Manabi in Ecuador and the results associated with the different risk measures are analyzed to illustrate the value of the proposed approach for the design of disaster relief networks.