Bernard Fortz

Bernard Fortz
Université Libre de Bruxelles | ULB · Department of Informatics

About

83
Publications
11,199
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3,709
Citations
Citations since 2017
15 Research Items
880 Citations
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2017201820192020202120222023050100150
2017201820192020202120222023050100150
2017201820192020202120222023050100150

Publications

Publications (83)
Article
Full-text available
In blockchains, transactions fees are fixed by the users. The probability for a transaction to be processed quickly increases with the fee level. In this paper, we study the transactions fees optimization problem in Ethereum blockchain. This problem consists in determining the minimum price a user should pay in order that its transaction be process...
Article
We study the relation between the linear programming relaxation of two classes of models for the Steiner tree problem with hop constraints. One class is characterized by having hop-indexed arc variables. Although such models have proved to have a very strong linear programming bound, they are not easy to use because of the huge number of variables....
Article
We consider two covering variants of the network design problem. We are given a set of origin/destination pairs, called O/D pairs, and each such O/D pair is covered if there exists a path in the network from the origin to the destination whose length is not larger than a given threshold. In the first problem, called the Maximal Covering Network Des...
Chapter
This chapter studies models and techniques for long-term planning of networks for which clients demands are not known in advance. It this case, the objective is to build a network at minimum cost, considering only the fixed cost associated with opening a link. Capacity and routing costs are therefore ignored. Nevertheless, the network is subject to...
Preprint
Group testing is a screening strategy that involves dividing a population into several disjointed groups of subjects. In its simplest implementation, each group is tested with a single test in the first phase, while in the second phase only subjects in positive groups, if any, need to be tested again individually. In this paper, we address the prob...
Preprint
Full-text available
We consider two covering variants of the network design problem. We are given a set of origin/destination (O/D) pairs and each such O/D pair is covered if there exists a path in the network from the origin to the destination whose length is not larger than a given threshold. In the first problem, called the maximal covering network design problem,...
Article
In this paper, we analyze different mathematical formulations for general Stackelberg games (GSGs)and Stackelberg security games (SSGs). We consider GSGs in which a single leader commits to a utility maximizing strategy knowing that p possible followers optimize their own utility taking the leader's strategy into account. SSGs are a type of GSG tha...
Article
Full-text available
A point-interval \((I_v, p_v)\) is a pair constituted by an interval \(I_v\) of \({\mathbb {R}}\) and a point \(p_v \in I_v\). A graph \(G=(V,E)\) is a Max-Point-Tolerance (MPT) graph if each vertex \(v\in V\) can be mapped to a point-interval in such a way that (u, v) is an edge of G iff \(I_u \cap I_v \supseteq \{p_u, p_v\}\). MPT graphs constitu...
Article
Given an undirected graph, we study the problem of finding K edge-disjoint paths, each one containing at most L edges, between a given pair of nodes. We focus on the case of K = 2and L = 3. For this particular case, previous known compact formulations are valid only for the case with non-negative edge costs. We provide the first compact linear desc...
Article
In this paper, we consider multicommodity flow problems, with unsplittable flows and piecewise linear routing costs. We first focus on the case where the piecewise linear routing costs are convex. We show that this problem is NP-hard for the general case, but polynomially solvable when there is only one commodity. We then propose a strengthened mix...
Article
Full-text available
This paper considers a pricing problem on a network with connected toll arcs and proposes a Dantzig-Wolfe reformulation for it. First, the relaxation of this formulation is theoretically shown to be at least as good as the reference proposed in the literature. Then, we detail the particularities of the implementation of a branch-and-price algorithm...
Article
During the planning of communication networks, the routing decision process (distributed and online) often remains decoupled from the network design process, that is, resource installation and allocation-planning process (centralized and offline). To reconcile both processes and take into account demand variability, we generalize the capacitated mu...
Article
Switched Ethernet networks rely on the Spanning Tree Protocol (STP) to ensure a cycle-free connectivity between nodes, by reducing the topology of the network to a spanning tree. The Multiple Spanning Tree Protocol (MSTP) allows for the providers to partition the traffic in the network and assign it to different virtual local area networks, each sa...
Article
The distributed monitoring problem refers to the placement and configuration of passive monitoring points to jointly realize a task of monitoring traffic flows. Given a monitoring task, the objective consists in minimizing the total monitoring cost to realize this task. We formulate this problem as a mixed-integer program. This formulation can also...
Article
The Minimum Weighted Tree Reconstruction (MWTR) problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nodes is greater than or equal to a given distance between the considered pair of terminal nodes. This problem has applications in sever...
Conference Paper
The cooperative monitoring problem refers to the placement and configuration of passive monitoring points (or monitors) to jointly realize a task of monitoring time-varying traffic flows. Given a traffic monitoring task, e.g., monitor a traffic flow percentage, the objective consists in minimizing the total monitoring cost to realize this task. We...
Article
The capacitated fixed-charge network design (FCND) problem considers the simultaneous optimization of capacity installation and routing of traffic where a fixed cost is paid for opening a link and a linear routing cost is paid for sending traffic flow(s) on that link. The routing decisions must be performed such that the traffic flows remain bounde...
Conference Paper
In communication networks, the routing decision process (distributed and online) remains decoupled from the network design process, i.e., resource installation and allocation planning process (centralized and offline). To reconcile both processes, we ambition to design a distributed optimization technique aware of distributed nature of the routing...
Article
In this paper, we study the hop-constrained survivable network design problem with reliable edges. Given a graph with non-negative edge costs and node pairs Q, the hop-constrained survivable network design problem consists of constructing a minimum cost set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at...
Conference Paper
Full-text available
The distributed monitoring problem refers to the placement and configuration of passive monitoring points to jointly realize a task of monitoring traffic flows. Given a monitoring task, the objective consists in minimizing the total monitoring cost to realize this task. We formulate this problem as a mixed-integer program. This formulation can also...
Book
Telecommunications is an important area of application in combinatorial optimization. A large class of problems encountered by telecommunications operators are related to location theory. The aim of this chapter is to review recent developments in the application of location models for the design of (wired) telecommunications networks. In particula...
Article
The combined network design and (distributed) traffic routing problem can be formulated as a large-scale multi-period mixed integer optimization problem. This problem combines network design decisions and routing decisions, with time-dependent traffic demands. In this paper, we consider different branch-and-cut strategies for solving the problem wi...
Conference Paper
The combined network design and (distributed) traffic routing problem can be formulated as a large-scale multi-period mixed integer optimization problem. This problem combines network design decisions and routing decisions, with time-dependent demands. In [1], we proposed a compact formulation based on the aggregation of flows by destination. We ob...
Conference Paper
The capacitated Fixed-Charge Network Design (FCND) problem deals with the simultaneous optimization of capacity installation and routing of traffic, where a fixed cost is paid for opening a link and a linear routing cost is paid for sending traffic flow on a link. The routing decision must be performed such that flows remain bounded by the installe...
Conference Paper
In today’s communication networks, distributed control functions such as routing inherit their design driven by processing capacity and memory consumption. Henceforth, the routing protocol decision process (distributed and online) remains still decoupled from the routing optimization process (centralized and offline). Distributed optimization does...
Conference Paper
The Multiple Spanning Tree Protocol (MSTP), used in Ethernet networks, maintains a set of spanning trees that are used for routing the demands in the network. Each spanning tree is allocated to a pre-defined set of demands. In this paper we present two mixed integer programming models for the Traffic Engineering problem of optimally designing a net...
Article
Full-text available
This special double issue of the EURO Journal on Computational Optimization focuses on computational methods for network optimization problems. Network optimization is a key area of operational research. Significant research activities are produced in this topic, as attested by the success of conferences organized by the EURO working group “Europea...
Article
This paper considers a pricing problem on a network with connected toll arcs and proposes a Dantzig-Wolfe reformulation for it. The model is solved with column generation and the gap between the optimal integer value and the linear relaxation optimal value is shown to be at least as good as the one from the mixed-integer formulation proposed in the...
Article
Throughout the last decade, extensive deployment of popular intra-domain routing protocols such as open shortest path first and intermediate system–intermediate system, has drawn an ever increasing attention to Internet traffic engineering. This paper reviews optimization techniques that have been deployed for managing intra-domain routing in netwo...
Article
The ring spur assignment problem arises in the design of next-generation telecommunications networks and has applications in location-allocation problems. The aim is to identify a minimum cost set of interconnected ring spurs. We seek to connect all nodes of the network either on a set of bounded disjoint local rings or by a single spur edge connec...
Article
Full-text available
Given a graph with nonnegative edge weights and a set of pairs of nodes 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, we present the first formulation...
Article
The desire for configuring well-managed OSPF routes to handle the communication needs in the contemporary business world with larger networks and changing service requirements has opened the way to use traffic engineering tools with the OSPF protocol. Moreover, anticipating possible shifts in expected traffic demands while using network resources e...
Article
This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly ${\mathcal{N}\mathcal{P}}$ -hard in...
Article
Language of publication: en
Article
Intra-domain routing protocols are based on Shortest Path First (SPF) routing, where shortest paths are calculated between each pair of nodes (routers) using pre-assigned link weights, also referred to as link metric. These link weights can be modified by network administrators in accordance with the routing policies of the network operator. The op...
Article
Intra-domain routing protocols are based on shortest path first (SPF) routing, where shortest paths are calculated between each pair of nodes (routers) using pre-assigned link weights, also referred to as link metric. These link weights can be modified by network administrators in accordance with the routing policies of the network operator. The op...
Conference Paper
We present two complete integer programming formulations for the ring spur assignment problem. This problem arises in the design of next generation telecommunications networks. We analyse and compare the formulations in terms of compactness, the resulting LP bound and results from a branch and cut implementation. We present our conclusions with com...
Conference Paper
Full-text available
We consider the problem of designing a network for hazardous material transportation where the government can decide which roads have to be forbidden to hazmats and the carriers choose the routes on the network. We assume that the government is interested in minimizing the overall risk of the shipments whereas the carriers minimize the route costs....
Article
We show how we can linearize individual probabilistic linear constraints with binary variables when all coefficients are independently distributed according to either N(μi,λμi)N(μi,λμi), for some λ>0λ>0 and μi>0μi>0, or Γ(ki,θ)Γ(ki,θ) for some θ>0θ>0 and ki>0ki>0. The constraint can also be linearized when the coefficients are independent and ident...
Chapter
Full-text available
The Internet is a huge world-wide packet switching network comprised of more than 13,000 distinct subnetworks, referred to as Autonomous Systems (ASs) . They all rely on the Internet Protocol (IP) for transport of packets across the network. And most of them use shortest path routing protocols , such as OSPF or IS-IS, to control the routing of IP p...
Article
Benders decomposition has been widely used for solving network design problems. In this paper, we use a branch-and-cut algorithm to improve the separation procedure of Gabrel et al. and Knippel et al. for capacitated network design. We detail experiments on bi-layer networks, comparing with Knippel’s previous results.
Article
Full-text available
The main difficulty in two-stage Stochastic programming with real recourse is the number of scenarios to consider, resulting in a huge number of variables and constraints. In this work, we overcome this difficulty for the knapsack problem with penalty recourse by considering only gaussian random variables. Using their summation property, we can sim...
Article
Full-text available
Link weight optimization is shown to be a key issue in engineering of IGPs using shortest path first routing. The IGP weight optimization problem seeks a weight array resulting an optimal load distribution in the network based on the topology information and a traffic demand matrix. Several solution methods for various kinds of this problem have be...
Chapter
This paper describes the Park & Ride Integrated System, a new concept of demand-responsive transport system, and the underlying problems to be solved to manage this system. We first present its functionalities and its global architecture. The first feature we examine is the real-time aspects having to be dealt with. We then propose a routing algori...
Article
We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that the shortest cycle (a “ring”) to which each edge belongs, does not exceed a given length K. We identify a class of inequalities, called cycle inequalities, valid for the problem and show that these inequalities together with the...
Chapter
Full-text available
Long-term planning of backbone telephone networks has been an important area of application of combinatorial optimization over the last few years. In this chapter, we review polyhedral results for models related to these problems. In particular, we study classical survivability requirements in terms of k-connectivity of the network, then we extend...
Article
Shortest Path First (SPF) protocols such as Open Shortest Path First (OSPF) (7) or Intermediate System-Inter- mediate System (IS-IS) (4) are the most commonly used Interior Gateway Protocols (IGPs) today. Traffic is routed along shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the...
Article
Full-text available
Nowadays, survivability in telecommunication networks is a crucial problem in networks optimization. Given a set of requirements, which correspond to single or multicommodity flows, the survivable network de-sign problem (SNDP) consists in determining a minimum cost network topology and capacity assignment such that all traffic demands are sat-isfi...
Article
Full-text available
We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labbé and Maffioli (Operations Research, vol. 48, no. 6, pp. 866–877, 2000). In this paper, we compute a...
Article
Full-text available
In this paper, we adapt the heuristic of Fortz and Thorup for optimizing the weights of Shortest Path First protocols such as Open Shortest Path First (OSPF) or Intermediate System-Intermediate System (IS-IS), in order to take into account failure scenarios.
Article
We consider the problem of designing self-healing rings in order to protect the transmission of telecommunication demands in a zonal network. This problem stems from a real application with operational constraints such as dual homing and hop limit per ring. A modeling approach taking into account ring interactions is proposed as well as a tabu sear...
Article
We present a tabu search heuristic for a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a "ring") does not exceed a given length K.
Article
Full-text available
Traffic engineering involves adapting the routing of traffic to network conditions, with the joint goals of good user performance and efficient use of network resources. We describe an approach to intradomain traffic engineering that works within the existing deployed base of interior gateway protocols, such as Open Shortest Path First and Intermed...
Article
Full-text available
We study the polyhedron associated with a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a “ring”) does not exceed a given length K.¶We present here a new formulation of the problem and derive facet results for different classes of valid inequalit...
Article
Full-text available
A system of techniques is presented for optimizing open shortest path first (OSPF) or intermediate system-intermediate system (IS-IS) weights for intradomain routing in a changing world, the goal being to avoid overloaded links. We address predicted periodic changes in traffic as well as problems arising from link failures and emerging hot spots
Article
Full-text available
We study the problem of computing the reliability of a network operated using the OSPF protocol where links fail with given independent probabilities. Our measure of reliability is the expected lost demand in the network. Computing this measure is #P-complete, so we developed approximation methods based on related work for circuit-switched networks...
Article
Full-text available
We present a tabu search heuristic for a network design problem which consists in deter-mining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a "ring") does not exceed a given length K. Numerical results are provided for randomly generated graphs and graphs coming from real-world applications.
Article
Full-text available
Open Shortest Path First (OSPF) is the most commonly used intra-domain internet routing protocol. Traffic flow is routed along shortest paths, splitting flow at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the network operator. The weig...
Article
We study the problem of designing at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a "mesh") does not exceed a given lengthK. This problem arises in the design of fiber-optic-based backbone telecommunication networks. A Branch-and-Cut approach to this problem is presented for which we introduce severa...
Article
Full-text available
Open Shortest Path First (OSPF) is one of the most commonly used intra-domain internet routing protocol. Traffic flow is routed along shortest paths, splitting flow evenly at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the network oper...
Conference Paper
Full-text available
Open shortest path first (OSPF) is the most commonly used intra-domain Internet routing protocol. Traffic flow is routed along shortest paths, splitting flow at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the network operator. The weig...
Article
. We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle whose length does not exceed a given bound. This problem was first studied by Fortz, Labb'e and Maffioli [7]. Several classes of valid inequalities for this problem were proposed [5--7]. We study here the separation problems associated...
Article
Full-text available
This dissertation is the result of a project funded by Belgacom, the Belgian telecommunication operator, dealing with the development of new models and optimization techniques for the long-term planning of the backbone network. The minimum-cost two-connected spanning network problem consists in finding a network with minimal total cost for which th...
Article
Full-text available
: Network design problems are deceptively easy to describe, but are often very difficult to solve. Given a set of available (perhaps capacitated) edges, the problem seeks a least cost network, composed of both variable flow costs and edge fixed costs, that meets prescribed multicommodity flow requirements. Several decades ago, applied mathematician...
Chapter
We study the problem of designing at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a “mesh”) does not exceed a given length K. This problem arises in the design of fiber optics based backbone telecommunication networks. To keep closer to reality, we assume the triangle inequality holds. A Branch-and-C...
Article
. We study the polyhedron associated with a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a "ring") does not exceed a given length K. We present here a new formulation of the problem and derive facet results for different classes of valid inequal...
Article
Full-text available
In this paper, we present a mathematical model which integrates tactical-operational production and distribution decisions in a shared resources environment. More precisely, we integrate lot sizing production and distribution decisions with vehicle routing decisions. We obtain a global multi-period multi-item multi-vehicle model where a capacity co...
Article
Full-text available
We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labb e and Maaoli 6]. Structural results for this particular case are presented : we compute a lower bou...
Article
We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that the shortest cycle (a “ring”) to which each edge belongs, does not exceed a given length K. We identify a class of inequalities, called cycle inequalities, valid for the problem and show that these inequalities together with the...

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