Marie-christine Costa - Academia.edu (original) (raw)
Uploads
Papers by Marie-christine Costa
Electronic Notes in Discrete Mathematics
We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph ... more We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G = (V, E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a minimum cost subset E ′ ⊂ E, covering T and r, such that the network induced by E ′ is (k+1)-survivable: after the removal of any k edges, there still exists a feasible flow from r to T. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set, a flow and a bi-level formulation where the second-level is a min-max problem (with an attacker and a defender). We propose algorithms for each problem formulation and compare their efficiency.
European Journal of Operational Research, 2016
This paper deals with the optimal design of a stand-alone hybrid system composed of wind turbines... more This paper deals with the optimal design of a stand-alone hybrid system composed of wind turbines, solar photovoltaic panels and batteries. To compensate for a possible lack of energy from these sources, an auxiliary fuel generator guarantees to meet the demand in every case but its use induces important costs. We have chosen a two-stage robust approach to take account of the stochastic behavior of the solar and wind energy production and also of the demand. We seek to determine the optimal system, i.e. the one that generates a minimum total cost when the worst case scenario relating to this system occurs. We use a constraint generation algorithm where each sub-problem (the recourse problem) can be reformulated by a mixed-integer linear program and hence solved by a standard solver. We also propose a polynomial time dynamic programming algorithm for the recourse problem and show that, in some cases, this algorithm is much more efficient than mixed-integer linear programming. Finally, we report computational experiments on instances constructed from real data, that show the efficiency of the proposed approach and we study the addition of constraints linking the uncertainty in consecutive time periods.
In a graph G = (V, E) a subset F of V is a d-extensible set if for any stable set S of F with |S|... more In a graph G = (V, E) a subset F of V is a d-extensible set if for any stable set S of F with |S|= d it exists a stable set S' of V-F F such that SUS' is a maximum stable set of G. We say that S can be extended to a maximum stable set with vertices outside of F, shortly S can be extended. We present a characterization of the d-extensible sets for the class of bipartite graphs and we determine, for some values of d, the maximum cardinality of a d-extensible set. We also determine the maximum cardinality of a d-extensible set for a subclass of arborescences where any vertex x of V belongs to a maximum stable set. This problem has some applications in reliability where we consider vertex failures in the graph G : a d-extensible set is the set of vertices that are not protected.
Due to the recent increase in bandwidth requirements, telecommunication operators have to support... more Due to the recent increase in bandwidth requirements, telecommunication operators have to support it with the deployment of optical fiber networks through Fiber-To-The-Home Gigabit Passive Optical Network technology (FTTH GPON). One great challenge, in a deregulated context, is to design this network while not knowing who and where the future subscribers will be. We focus on the problem of the robust optical fiber network deployment under demand uncertainty. A two-stage robust optimization model is proposed for this problem, as well as two robust solution methods extending classical results from Ben-Tal et al. and Babonneau et al. in order to be compliant with our uncertainty set
This paper deals with the optimization of cable layout, which is a problem encountered by Electri... more This paper deals with the optimization of cable layout, which is a problem encountered by Electricité de France (EDF) in power plant design. The problem consists in finding optimized cable routes connecting a set of pairs of facilities, respecting shelves' capacities and a number of other constraints. We show that the problem is equivalent to optimizing the cost of multiple
Abstract Given a graph G, the Shortest Capacitated Paths Problem (SCPP) consists of determining a... more Abstract Given a graph G, the Shortest Capacitated Paths Problem (SCPP) consists of determining a set of paths of least total length, linking given pairs of vertices in G, and satisfying capacity constraints on the arcs of G. We formulate the SCPP as a 0-1 linear program and study two Lagrangian relaxations for getting lower bounds on the optimal value.
Lecture Notes in Computer Science, 2008
We study the problem of reconstructing hv-convex binary matrices from few projections. We solve a... more We study the problem of reconstructing hv-convex binary matrices from few projections. We solve a polynomial time case and we determine some properties of the hv-convex matrices. Since the problem is NP-complete, we provide an iterative approximation based on a longest path and a min-cost/max-flow model. The experimental results show that the reconstruction algorithm performs quite well.
Lecture Notes in Computer Science, 2005
Abstract. This paper deals with the reconstruction of an alternate pe-riodical binary matrix from... more Abstract. This paper deals with the reconstruction of an alternate pe-riodical binary matrix from its orthogonal projections. For a fixed vector (p, q), a binary matrix A is alternate periodical when Ai,j +Ai+p,j+q = 1. For vectors (p = 1, q = 1), (p, 0) and (0,q) we propose polynomial time ...
Page 1. A BIBLIOGRAPHY ON MULTICUT AND INTEGER MULTIFLOW PROBLEMS CÉDRIC BENTZ1, MARIE-CHRISTINE ... more Page 1. A BIBLIOGRAPHY ON MULTICUT AND INTEGER MULTIFLOW PROBLEMS CÉDRIC BENTZ1, MARIE-CHRISTINE COSTA1, LUCAS LÉTOCART2 AND FRÉDÉRIC ROUPIN3 ... [80] R. Easley and D. Hartvigsen. Crossing Properties of Multiterminal Cuts. ...
Operations Research Letters, 2003
Operations Research Letters, 1994
Let G = (U, V, E) be an undirected bipartite graph. We specify some procedures that allow us to m... more Let G = (U, V, E) be an undirected bipartite graph. We specify some procedures that allow us to make efficiently the following 3-partition of the set E: E 1 is the set of edges belonging to all the maximum matchings (1-persistent edges); E o is the set of edges belonging to no maximum matching (0-persistent edges); E w is the set of edges belonging to at least one maximum matching but not to all of them (weakly presistent edges).
Operations Research Letters, 2006
Electronic Notes in Discrete Mathematics
We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph ... more We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G = (V, E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a minimum cost subset E ′ ⊂ E, covering T and r, such that the network induced by E ′ is (k+1)-survivable: after the removal of any k edges, there still exists a feasible flow from r to T. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set, a flow and a bi-level formulation where the second-level is a min-max problem (with an attacker and a defender). We propose algorithms for each problem formulation and compare their efficiency.
European Journal of Operational Research, 2016
This paper deals with the optimal design of a stand-alone hybrid system composed of wind turbines... more This paper deals with the optimal design of a stand-alone hybrid system composed of wind turbines, solar photovoltaic panels and batteries. To compensate for a possible lack of energy from these sources, an auxiliary fuel generator guarantees to meet the demand in every case but its use induces important costs. We have chosen a two-stage robust approach to take account of the stochastic behavior of the solar and wind energy production and also of the demand. We seek to determine the optimal system, i.e. the one that generates a minimum total cost when the worst case scenario relating to this system occurs. We use a constraint generation algorithm where each sub-problem (the recourse problem) can be reformulated by a mixed-integer linear program and hence solved by a standard solver. We also propose a polynomial time dynamic programming algorithm for the recourse problem and show that, in some cases, this algorithm is much more efficient than mixed-integer linear programming. Finally, we report computational experiments on instances constructed from real data, that show the efficiency of the proposed approach and we study the addition of constraints linking the uncertainty in consecutive time periods.
In a graph G = (V, E) a subset F of V is a d-extensible set if for any stable set S of F with |S|... more In a graph G = (V, E) a subset F of V is a d-extensible set if for any stable set S of F with |S|= d it exists a stable set S' of V-F F such that SUS' is a maximum stable set of G. We say that S can be extended to a maximum stable set with vertices outside of F, shortly S can be extended. We present a characterization of the d-extensible sets for the class of bipartite graphs and we determine, for some values of d, the maximum cardinality of a d-extensible set. We also determine the maximum cardinality of a d-extensible set for a subclass of arborescences where any vertex x of V belongs to a maximum stable set. This problem has some applications in reliability where we consider vertex failures in the graph G : a d-extensible set is the set of vertices that are not protected.
Due to the recent increase in bandwidth requirements, telecommunication operators have to support... more Due to the recent increase in bandwidth requirements, telecommunication operators have to support it with the deployment of optical fiber networks through Fiber-To-The-Home Gigabit Passive Optical Network technology (FTTH GPON). One great challenge, in a deregulated context, is to design this network while not knowing who and where the future subscribers will be. We focus on the problem of the robust optical fiber network deployment under demand uncertainty. A two-stage robust optimization model is proposed for this problem, as well as two robust solution methods extending classical results from Ben-Tal et al. and Babonneau et al. in order to be compliant with our uncertainty set
This paper deals with the optimization of cable layout, which is a problem encountered by Electri... more This paper deals with the optimization of cable layout, which is a problem encountered by Electricité de France (EDF) in power plant design. The problem consists in finding optimized cable routes connecting a set of pairs of facilities, respecting shelves' capacities and a number of other constraints. We show that the problem is equivalent to optimizing the cost of multiple
Abstract Given a graph G, the Shortest Capacitated Paths Problem (SCPP) consists of determining a... more Abstract Given a graph G, the Shortest Capacitated Paths Problem (SCPP) consists of determining a set of paths of least total length, linking given pairs of vertices in G, and satisfying capacity constraints on the arcs of G. We formulate the SCPP as a 0-1 linear program and study two Lagrangian relaxations for getting lower bounds on the optimal value.
Lecture Notes in Computer Science, 2008
We study the problem of reconstructing hv-convex binary matrices from few projections. We solve a... more We study the problem of reconstructing hv-convex binary matrices from few projections. We solve a polynomial time case and we determine some properties of the hv-convex matrices. Since the problem is NP-complete, we provide an iterative approximation based on a longest path and a min-cost/max-flow model. The experimental results show that the reconstruction algorithm performs quite well.
Lecture Notes in Computer Science, 2005
Abstract. This paper deals with the reconstruction of an alternate pe-riodical binary matrix from... more Abstract. This paper deals with the reconstruction of an alternate pe-riodical binary matrix from its orthogonal projections. For a fixed vector (p, q), a binary matrix A is alternate periodical when Ai,j +Ai+p,j+q = 1. For vectors (p = 1, q = 1), (p, 0) and (0,q) we propose polynomial time ...
Page 1. A BIBLIOGRAPHY ON MULTICUT AND INTEGER MULTIFLOW PROBLEMS CÉDRIC BENTZ1, MARIE-CHRISTINE ... more Page 1. A BIBLIOGRAPHY ON MULTICUT AND INTEGER MULTIFLOW PROBLEMS CÉDRIC BENTZ1, MARIE-CHRISTINE COSTA1, LUCAS LÉTOCART2 AND FRÉDÉRIC ROUPIN3 ... [80] R. Easley and D. Hartvigsen. Crossing Properties of Multiterminal Cuts. ...
Operations Research Letters, 2003
Operations Research Letters, 1994
Let G = (U, V, E) be an undirected bipartite graph. We specify some procedures that allow us to m... more Let G = (U, V, E) be an undirected bipartite graph. We specify some procedures that allow us to make efficiently the following 3-partition of the set E: E 1 is the set of edges belonging to all the maximum matchings (1-persistent edges); E o is the set of edges belonging to no maximum matching (0-persistent edges); E w is the set of edges belonging to at least one maximum matching but not to all of them (weakly presistent edges).
Operations Research Letters, 2006