Sylvie Borne - Academia.edu (original) (raw)
Papers by Sylvie Borne
Discrete Optimization, Aug 31, 2015
In this paper, we describe the circuit polytope on series-parallel graphs. We first show the exis... more In this paper, we describe the circuit polytope on series-parallel graphs. We first show the existence of a compact extended formulation. Though not being explicit, its construction process helps us to inductively provide the description in the original space. As a consequence, using the link between bonds and circuits in planar graphs, we also describe the bond polytope on series-parallel graphs.
The paper deals with a problem motivated by survivability issues in multilayer IP-over-WDM teleco... more The paper deals with a problem motivated by survivability issues in multilayer IP-over-WDM telecommunication networks. Given a set of traffic demands for which we know a survivable routing in the IP layer, our purpose is to look for the corresponding survivable topology in the WDM layer. The problem amounts to Multiple Steiner TSPs with order constraints. We propose an integer linear programming formulation for the problem and investigate the associated polytope. We also present new valid inequalities and discuss their facial aspect. Based on this, we devise a Branch-and-cut algorithm and present preliminary computational results.
ABSTRACT Telecommunication networks can be seen as the stacking of several layers like, for insta... more ABSTRACT Telecommunication networks can be seen as the stacking of several layers like, for instance, IP-over-Optical networks. This infrastructure has to be sufficiently survivable to restore the traffic in the event of a failure. Moreover, it should have adequate capacities so that the demands can be routed between the origin-destinations. In this paper we consider the Multilayer Capacitated Survivable IP Network Design problem. We study two variants of this problem with simple and multiple capacities. We give two multicommodity flow formulations for each variant of this problem and describe some valid inequalities. In particular, we characterize valid inequalities obtained using Chvatal-Gomory procedure from the well known Cutset inequalities. We show that some of these inequalities are facet defining. We discuss separation routines for all the valid inequalities. Using these results, we develop a Branch-and-Cut algorithm and a Branch-and-Cut-and-Price algorithm for each variant and present extensive computational results.
ABSTRACT With the explosive growth of traffic data, telecommunication networks have evolved towar... more ABSTRACT With the explosive growth of traffic data, telecommunication networks have evolved toward a multilayer architecture with high-speed routers interconnected by intelligent optical core networks. This architecture must be sufficiently survivable so that network services can be restored in the event of a catastrophic failure. In this paper, we consider the following survivable IPover- optical network design problem. Given a set of traffic demands and two node-disjoint paths routing each demand in the IP layer, the problem is to find for each demand two node-disjoint paths in the optical layer going through the optical switches corresponding to the routers visited in the paths of the IP layer and respecting the same order. We give two integer programming formulations for the problem. The first one uses the cut constraints and the second is a path-based formulation. We discuss the pricing problem for the latter and present some preliminary computational results. We also discuss the polyhedron associated with the cut formulation. oui
Lecture Notes in Computer Science, 2012
In the uncapacitated asymmetric traveling salesman with multiple stacks, we perform a hamiltonian... more In the uncapacitated asymmetric traveling salesman with multiple stacks, we perform a hamiltonian circuit to pick up n items, storing them in a vehicle with k stacks satisfying last-in-first-out constraints, and then we deliver every item by performing a hamiltonian circuit. We are interested in the convex hull of the (arc-)incidence vectors of such couples of hamiltonian circuits. For the general case, we determine the dimension of this polytope, and show that every facet of the asymmetric traveling salesman polytope defines one of its facets. For the special case with two stacks, we provide an integer linear programming formulation whose linear relaxation is polynomial-time solvable, and we propose new families of valid inequalities to reinforce this linear relaxation.
Electronic Notes in Discrete Mathematics, 2013
ABSTRACT We deal with a Home Health Care Problem (HHCP) which objective consists in constructing ... more ABSTRACT We deal with a Home Health Care Problem (HHCP) which objective consists in constructing the optimal routes and rosters for the health care staffs. The challenge lies in combining aspects of vehicle routing and staff rostering which are two well known hard combinatorial optimization problems. To solve this problem, we initially propose an integer linear programming formulation (ILP) and we tested this model on small instances. To deal with larger instances we develop a matheuristic based on the decomposition of the ILP formulation into two problems. The first one is a set partitioning like problem and it represents the rostering part. The second problem consists in the routing part. This latter is equivalent to a Multi-depot Traveling Salesman Problem with Time Windows (MTSPTW).
Annals of Operations Research, 2006
In the past years, telecommunications networks have seen an important evolution with the advances... more In the past years, telecommunications networks have seen an important evolution with the advances in optical technologies and the explosive growth of the Internet. Several optical systems allow a very large transport capacity, and data traffic has dramatically increased. Telecommunications networks are now moving towards a model of high-speed routers interconnected by intelligent optical core networks. Moreover, there is a general consensus that the control plan of the optical networks should utilize IP-based protocols for dynamic provisioning and restoration of lightpaths. The interaction of the IP routers with the optical core networks permits to achieve end-to-end connections, and the lightpaths of the optical networks define the topology of the IP network. This new infrastructure has to be sufficiently survivable, so that network services can be restored in the event of a catastrophic failure. In this paper we consider a multilayer survivable network design problem that may be of practical interest for IP-over-optical neworks. We give an integer programming formulation for this problem and discuss the associated polytope. We describe some valid inequalities and study when these are facet defining. We discuss separation algorithms for these inequalities S. Borne ( ) and introduce some reduction operations. We develop a Branch-and-Cut algorithm based on these results and present extensive computational results.
Discrete Optimization, Aug 31, 2015
In this paper, we describe the circuit polytope on series-parallel graphs. We first show the exis... more In this paper, we describe the circuit polytope on series-parallel graphs. We first show the existence of a compact extended formulation. Though not being explicit, its construction process helps us to inductively provide the description in the original space. As a consequence, using the link between bonds and circuits in planar graphs, we also describe the bond polytope on series-parallel graphs.
The paper deals with a problem motivated by survivability issues in multilayer IP-over-WDM teleco... more The paper deals with a problem motivated by survivability issues in multilayer IP-over-WDM telecommunication networks. Given a set of traffic demands for which we know a survivable routing in the IP layer, our purpose is to look for the corresponding survivable topology in the WDM layer. The problem amounts to Multiple Steiner TSPs with order constraints. We propose an integer linear programming formulation for the problem and investigate the associated polytope. We also present new valid inequalities and discuss their facial aspect. Based on this, we devise a Branch-and-cut algorithm and present preliminary computational results.
ABSTRACT Telecommunication networks can be seen as the stacking of several layers like, for insta... more ABSTRACT Telecommunication networks can be seen as the stacking of several layers like, for instance, IP-over-Optical networks. This infrastructure has to be sufficiently survivable to restore the traffic in the event of a failure. Moreover, it should have adequate capacities so that the demands can be routed between the origin-destinations. In this paper we consider the Multilayer Capacitated Survivable IP Network Design problem. We study two variants of this problem with simple and multiple capacities. We give two multicommodity flow formulations for each variant of this problem and describe some valid inequalities. In particular, we characterize valid inequalities obtained using Chvatal-Gomory procedure from the well known Cutset inequalities. We show that some of these inequalities are facet defining. We discuss separation routines for all the valid inequalities. Using these results, we develop a Branch-and-Cut algorithm and a Branch-and-Cut-and-Price algorithm for each variant and present extensive computational results.
ABSTRACT With the explosive growth of traffic data, telecommunication networks have evolved towar... more ABSTRACT With the explosive growth of traffic data, telecommunication networks have evolved toward a multilayer architecture with high-speed routers interconnected by intelligent optical core networks. This architecture must be sufficiently survivable so that network services can be restored in the event of a catastrophic failure. In this paper, we consider the following survivable IPover- optical network design problem. Given a set of traffic demands and two node-disjoint paths routing each demand in the IP layer, the problem is to find for each demand two node-disjoint paths in the optical layer going through the optical switches corresponding to the routers visited in the paths of the IP layer and respecting the same order. We give two integer programming formulations for the problem. The first one uses the cut constraints and the second is a path-based formulation. We discuss the pricing problem for the latter and present some preliminary computational results. We also discuss the polyhedron associated with the cut formulation. oui
Lecture Notes in Computer Science, 2012
In the uncapacitated asymmetric traveling salesman with multiple stacks, we perform a hamiltonian... more In the uncapacitated asymmetric traveling salesman with multiple stacks, we perform a hamiltonian circuit to pick up n items, storing them in a vehicle with k stacks satisfying last-in-first-out constraints, and then we deliver every item by performing a hamiltonian circuit. We are interested in the convex hull of the (arc-)incidence vectors of such couples of hamiltonian circuits. For the general case, we determine the dimension of this polytope, and show that every facet of the asymmetric traveling salesman polytope defines one of its facets. For the special case with two stacks, we provide an integer linear programming formulation whose linear relaxation is polynomial-time solvable, and we propose new families of valid inequalities to reinforce this linear relaxation.
Electronic Notes in Discrete Mathematics, 2013
ABSTRACT We deal with a Home Health Care Problem (HHCP) which objective consists in constructing ... more ABSTRACT We deal with a Home Health Care Problem (HHCP) which objective consists in constructing the optimal routes and rosters for the health care staffs. The challenge lies in combining aspects of vehicle routing and staff rostering which are two well known hard combinatorial optimization problems. To solve this problem, we initially propose an integer linear programming formulation (ILP) and we tested this model on small instances. To deal with larger instances we develop a matheuristic based on the decomposition of the ILP formulation into two problems. The first one is a set partitioning like problem and it represents the rostering part. The second problem consists in the routing part. This latter is equivalent to a Multi-depot Traveling Salesman Problem with Time Windows (MTSPTW).
Annals of Operations Research, 2006
In the past years, telecommunications networks have seen an important evolution with the advances... more In the past years, telecommunications networks have seen an important evolution with the advances in optical technologies and the explosive growth of the Internet. Several optical systems allow a very large transport capacity, and data traffic has dramatically increased. Telecommunications networks are now moving towards a model of high-speed routers interconnected by intelligent optical core networks. Moreover, there is a general consensus that the control plan of the optical networks should utilize IP-based protocols for dynamic provisioning and restoration of lightpaths. The interaction of the IP routers with the optical core networks permits to achieve end-to-end connections, and the lightpaths of the optical networks define the topology of the IP network. This new infrastructure has to be sufficiently survivable, so that network services can be restored in the event of a catastrophic failure. In this paper we consider a multilayer survivable network design problem that may be of practical interest for IP-over-optical neworks. We give an integer programming formulation for this problem and discuss the associated polytope. We describe some valid inequalities and study when these are facet defining. We discuss separation algorithms for these inequalities S. Borne ( ) and introduce some reduction operations. We develop a Branch-and-Cut algorithm based on these results and present extensive computational results.