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frFri, 10 Mar 2017 17:33:41 +0100https://cedric.cnam.fr/index.php/publis/article/view?id=3904
https://cedric.cnam.fr/index.php/publis/article/view?id=3904
Reformulation and solution approach for non-separable integer quadratic programsWe consider quadratic programs with pure general integer variables. The objective function is quadratic and convex and the constraints are linear. An exact solution approach is proposed. It is decomposed into two phases. In the first phase, the initial problem is reformulated into an equivalent problem with a separable objective function. This is done by use of a Gauss decomposition of the Hessian matrix of the initial problem and requires the addition of some continuous variables and constraints. In the second phase, the reformulated problem is linearized by an approximation of each squared term by a set of K linear functions that correspond to the tangents of a hyperbola in K points. We give a proof of the intuitive property that when K is large enough, the optimal value of the obtained linear program is very close to optimal value of the two previous problems, the initial problem and the reformulated separable problem. The reminder is dedicated to the implementation of a branch-and-bound algorithm for the solution of linearized problem, and its application to a set of instances. Several points are considered among which choice of the right value for parameter K and the implementation of a sophisticated heuristic solution algorithm. The numerical comparison is done with CPLEX 12.2 since, in this case, the initial problem as well as the problem reformulated by the first step can be solved by CPLEX. We show that with our approach, the total CPU time is divided by a factor ranging from 1.2 to 131.6 for instances with 40–60 variables.Fri, 10 Mar 2017 17:33:41 +0100OCPaperhttps://cedric.cnam.fr/index.php/labo/membre/colombier
https://cedric.cnam.fr/index.php/labo/membre/colombier
Kevin ColombieraWed, 01 Mar 2017 15:52:27 +0100OCJobhttps://cedric.cnam.fr/index.php/labo/membre/milliet
https://cedric.cnam.fr/index.php/labo/membre/milliet
Marie Milliet de FavergesaWed, 01 Mar 2017 15:21:56 +0100OCJobhttps://cedric.cnam.fr/index.php/publis/article/view?id=3826
https://cedric.cnam.fr/index.php/publis/article/view?id=3826
Optimisation de programmes polynomiaux en variables 0-1 et sans contraintesOptimisation de programmes polynomiaux en variables 0-1 et sans contraintesThu, 16 Feb 2017 15:05:23 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3825
https://cedric.cnam.fr/index.php/publis/article/view?id=3825
Optimisation du maillage électrique du parc éoliennes off-shore – projet StationisOptimisation du maillage électrique du parc éoliennes off-shore – projet StationisThu, 16 Feb 2017 14:58:30 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3815
https://cedric.cnam.fr/index.php/publis/article/view?id=3815
Entretien avec ...Entretien personnel invité sur la recherche opérationnelle.Sun, 12 Feb 2017 10:29:52 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3814
https://cedric.cnam.fr/index.php/publis/article/view?id=3814
d-extensibles de stables dans les graphes bipartisConsidérons un système dans lequel des composants peuvent tomber en panne. Il est possible
de maintenir des éléments pour éviter les pannes mais cela a un coût. Pour que le bon
fonctionnement ne soit pas affecté en cas de défaillance, on souhaite maintenir une partie aussi
petite que possible du système pour qu’en cas de panne dans l’autre partie, le système puisse
toujours opérer dans de bonnes conditions.
Supposons que le système puisse être modélisé par un graphe G = (V,E) dans lequel les
sommets sont les composants et tel que le système ne fonctionne que si ces sommets forment
un ensemble stable. Le système fonctionne tant qu’il existe un stable de cardinal maximal
alpha(G). Soit d un entier tel que 0 Sun, 12 Feb 2017 10:17:12 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3813
https://cedric.cnam.fr/index.php/publis/article/view?id=3813
Formulations for designing robust networks. An application to wind power collection.
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' of 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.Sun, 12 Feb 2017 08:57:52 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3810
https://cedric.cnam.fr/index.php/publis/article/view?id=3810
Reformulation Quadratique Convexe Pour l'Optimisation des Flux de PuissanceReformulation Quadratique Convexe Pour l'Optimisation des Flux de PuissanceWed, 08 Feb 2017 11:34:16 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3804
https://cedric.cnam.fr/index.php/publis/article/view?id=3804
Atabu search approach for the reconstruction
of binary images without empty interior regionIn this paper, we are concerned with a discrete tomography problem. We
seek to reconstruct a binary image from its orthogonal projections, i.e, its horizontal
and vertical line sums without interior black holes. We provide a tabu search
approach to minimize the number of holes while satisfying the projections. We test
our approach on some random binary images. Computational results show that the
algorithm proposed produces near-optimal solutions for all test problems.
Sat, 21 Jan 2017 17:14:03 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3803
https://cedric.cnam.fr/index.php/publis/article/view?id=3803
Blocking Independent Sets for H-free graphs via Edge Contractions and Vertex DeletionsLet d and k be two given integers, and let G be a graph. Can we reduce the independence number of G by at least d via at most k graph operations from some fixed set S? This problem belongs to a class of so-called blocker problems. It is known to be co-NP-hard even if S consists of either an edge contraction or a vertex deletion. We further investigate its computational complexity under these two settings:
– we give a sufficient condition on a graph class for the vertex variant to be computationally hard even if d = k = 1;
– in addition we prove that the vertex deletion variant is co-NP-hard for triangle-free graphs even if d = k = 1;
– we prove that the contraction variant is NP-complete for bipartite graphs but linear-time solvable for trees.
By combining our new results with known ones we are able to give full complexity classifications for both variants restricted to H-free graphs.Mon, 16 Jan 2017 14:17:58 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3802
https://cedric.cnam.fr/index.php/publis/article/view?id=3802
Blocking Independent Sets for H-free graphs via Edge Contractions and Vertex DeletionsLet $d$ and $k$ be two given integers, and let $G$ be a graph. Can we reduce the independence number of $G$ by at least $d$ via at most $k$ graph operations from some fixed set $S$? This problem belongs to a class of so-called blocker problems. It is known to be co-\NP-hard even if $S$ consists of either an edge contraction or a vertex deletion. We further investigate its computational complexity under these two settings:
-we give a sufficient condition on a graph class for the vertex variant to be computationally hard even if $d=k=1$;
-in addition we prove that the vertex deletion variant is co-\NP-hard for triangle-free graphs even if $d=k=1$;
-we prove that the contraction variant is \NP-complete for bipartite graphs but linear-time solvable for trees.
By combining our new results with known ones we are able to give full complexity classifications for both variants restricted to $H$-free graphs. Mon, 16 Jan 2017 14:09:44 +0100OCPaperhttps://cedric.cnam.fr/index.php/labo/membre/lucas
https://cedric.cnam.fr/index.php/labo/membre/lucas
Rémi LucasaFri, 06 Jan 2017 14:42:26 +0100OCJobhttps://cedric.cnam.fr/index.php/labo/membre/godard
https://cedric.cnam.fr/index.php/labo/membre/godard
Hadrien GodardaFri, 16 Dec 2016 09:16:06 +0100OCJobhttps://cedric.cnam.fr/index.php/labo/membre/lazare
https://cedric.cnam.fr/index.php/labo/membre/lazare
Arnaud LazareaFri, 09 Dec 2016 14:57:17 +0100OCJobhttps://cedric.cnam.fr/index.php/publis/article/view?id=3770
https://cedric.cnam.fr/index.php/publis/article/view?id=3770
On the edge capacitated Steiner tree problemWe 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' of E$, covering T and r, such that the network induced by E' is k-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. Fri, 09 Dec 2016 14:36:27 +0100OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3747
https://cedric.cnam.fr/index.php/publis/article/view?id=3747
Comparison of Quadratic Convex Reformulations to solve the Quadratic Assignment ProblemWe consider the $(QAP)$ that consists in minimizing a quadra\-tic function subject to assignment constraints where the variables are binary. In this paper, we build two families of equivalent quadratic convex formulations of $(QAP)$. The continuous relaxation of each equivalent formulation is then a convex problem and can be used within a B\& B. In this work, we focus on finding the "best" equivalent formulation within each family, and we prove that it can be computed using semidefinite programming. Finally, we get two convex formulations of $(QAP)$ that differ from their sizes and from the tightness of their continuous relaxation bound. We present computational experiments that prove the practical usefulness of using quadratic convex formulation to solve instances of $(QAP)$ of medium sizes.
Thu, 29 Sep 2016 12:01:07 +0200OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3704
https://cedric.cnam.fr/index.php/publis/article/view?id=3704
Using a conic bundle method to accelerate both phases of a quadratic convex reformulationWe present algorithm MIQCR-CB that is an advancement of method MIQCR (Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving mixed-integer quadratic programs and works in two phases: the first phase determines an equivalent quadratic formulation with a convex objective function by solving a semidefinite problem (SDP ), and, in the second phase, the equivalent formulation is solved by a standard solver. As the reformulation relies on the solution of a large-scale semidefinite program, it is not tractable by existing semidefinite solvers, already for medium sized problems. To surmount this difficulty, we present in MIQCR-CB a subgradient algorithm within a Lagrangian duality framework for solving (SDP ) that substantially speeds up the first phase. Moreover, this algorithm leads to a reformulated problem of smaller size than the one obtained by the original MIQCR method which results in a shorter time for solving the second phase. We present extensive computational results to show the efficiency of our algorithm. First, we apply MIQCR-CB to the k-cluster problem that can be formulated by a binary quadratic program. As an illustration of the efficiency of our new algorithm, for instances of size 80 and of density 25%, MIQCR-CB is on average 78 times faster for Phase 1 and 24 times faster for Phase 2 than the origi-
nal MIQCR. We also compare MIQCR-CB with QCR (Billionnet, Elloumi and Plateau, 2009) and with BiqCrunch (Krislock, Malick and Roupin, 2013)
two methods devoted to binary quadratic programming. We show that MIQCR-CB is able to solve most of the 225 considered instances within 3
hours of cpu time. We also present experiments on two classes of general integer instances where we compare MIQCR-CB with MIQCR, Couenne
and Cplex12.6. We demonstrate the significant improvement over the original MIQCR approach. Finally, we show that MIQCR-CB is able to solve
almost all of the considered instances while Couenne and Cplex12.6 are not able to solve half out of them.Mon, 05 Sep 2016 17:25:14 +0200OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3690
https://cedric.cnam.fr/index.php/publis/article/view?id=3690
Arc-Routing via Column Generation and Iterated Local Search in a Permutation Set-Covering FrameworkThe CARP problem is projected in a space of permutations, ie., any permutation can be decoded in a set of CARP routes.Tue, 09 Aug 2016 15:45:45 +0200OCPaperhttps://cedric.cnam.fr/index.php/default/event/view?id=241
https://cedric.cnam.fr/index.php/default/event/view?id=241
JFRO : programmation quadratique http://www.lamsade.dauphine.fr/~jfro/Wed, 22 Jun 2016 14:17:59 +0200OCEventhttps://cedric.cnam.fr/index.php/publis/article/view?id=3654
https://cedric.cnam.fr/index.php/publis/article/view?id=3654
Constraint Aggregation in Column Generation Models for Resource-Constrained Covering ProblemsWe propose an aggregation method to reduce the size of column generation (CG) models for covering
problems in which the feasible subsets depend on a resource constraint. The aggregation relies on a correlation
between the resource consumption of the elements and the corresponding optimal dual values. The resulting
aggregated dual model is a restriction of the original one, and it can be rapidly optimized to obtain a feasible dual solution. A primal bound can also be obtained by restricting the set of columns to those saturated by
the dual feasible solution obtained by aggregation. The convergence is realized by iterative disaggregation
until the gap is closed by the bounds. Computational results show the usefulness of our method for different
cutting-stock problems. An important advantage is the fact that it can produce high-quality dual bounds
much faster than the traditional lagrangian bound used in stabilized column generation.Thu, 16 Jun 2016 18:39:08 +0200OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3645
https://cedric.cnam.fr/index.php/publis/article/view?id=3645
The Maximum Matrix Contraction problem : AppendixThis document contains the appendix of a paper accepted at the conference ISCO 2016, entitled The Maximum Matrix Contraction problem, this appendix could not be added to the camera-ready version due to lack of space. In the paper, we introduce the {\it Maximum Matrix Contraction problem}, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem. Especially, we prove this problem to be NP-Complete and that every algorithm solving this problem is at most an 2 * sqrt(n)-approximation algorithm where $n$ is the number of ones in the matrix. We focused on three heuristics to solve the problem. In this appendix, we prove that, in the worst case, each algorithm returns an solution such that the ratio between an optimal density and the density of the returned solution is O(sqrt(n)).Thu, 02 Jun 2016 15:38:03 +0200OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3644
https://cedric.cnam.fr/index.php/publis/article/view?id=3644
Robust optimal sizing of a hybrid energy stand-alone systemThis 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.Wed, 25 May 2016 10:11:21 +0200OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3636
https://cedric.cnam.fr/index.php/publis/article/view?id=3636
The Maximum Matrix Contraction problemIn this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem. Especially, we prove this problem to be NP-Complete and that every algorithm solving this problem is at most an sqrt(n)-approximation algorithm where n is the number of ones in the matrix. We then focus on efficients algorithm to solve the problem: a linear program and three heuristics.Wed, 04 May 2016 18:45:12 +0200OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3626
https://cedric.cnam.fr/index.php/publis/article/view?id=3626
Reducing the clique and chromatic number via edge contractions and vertex deletionsWe consider the following problem: can a certain graph pa- rameter of some given graph G be reduced by at least d, for some inte- ger d, via at most k graph operations from some specified set S, for some given integer k? As graph parameters we take the chromatic number and the clique number. We let the set S consist of either an edge contraction or a vertex deletion. As all these problems are NP-complete for general graphs even if d is fixed, we restrict the input graph G to some special graph class. We continue a line of research that considers these problems for subclasses of perfect graphs, but our main results are full classifica- tions, from a computational complexity point of view, for graph classes characterized by forbidding a single induced connected subgraph H.Wed, 20 Apr 2016 12:01:51 +0200OCPaperhttps://cedric.cnam.fr/index.php/publis/article/view?id=3621
https://cedric.cnam.fr/index.php/publis/article/view?id=3621
Mutualisation de taxis avec partage de coût : modélisation, complexité et linéarisation du problème.
On se propose dans cette présentation d’étudier une variante du problème Dial-A-Ride (DARP). Dans, le problème original, on cherche a optimiser les routes de véhicules chargés de transporter des personnes depuis leurs origines respectives vers leurs destinations respectives, tout en respectant des contraintes de fenêtre de temps et des contraintes de capacités (nombre de places dans le véhicule). Ce modèle est généralement utilisé pour optimiser des chemins pour des taxis. Nous nous penchons sur une variante de ce problème dans laquelle les clients partagent le coût des trajets (ou des parties de trajets) qu'ils effectuent avec d'autres clients. Nous étudions dans un premier temps la complexité de ce problème. Puis, nous présentons un modèle linéaire en variable mixte et des règles de réduction de l'instance. La présentation se termine par une présentation des résultats de tests numériques.
Mon, 28 Mar 2016 10:48:29 +0200OCPaperhttp://cedric.cnam.fr/index.php/publis/article/view?id=3598
http://cedric.cnam.fr/index.php/publis/article/view?id=3598
Du sous-problème de séparation vers celui d'intersection: nouvelles bornes duales dans la génération de colonnesCet article porte sur le sous-problème d'intersection suivant: étant donné le programme dual d'un modèle de génération de colonnes et une direction duale y in R^n, trouver le maximum t tel que ty soit duale-réalisable. Ce sous-problème peut enrichir la CG classique de plusieurs façons:
- une preuve alternative de la borne duale de Farley (une spécialisation de la borne Lagrangienne pour le cas des coûts de colonnes unitaires).
- une borne duale qui peut être calculée pour des coûts non-unitaires.Fri, 05 Feb 2016 21:40:37 +0100OCPaperhttp://cedric.cnam.fr/index.php/publis/article/view?id=3597
http://cedric.cnam.fr/index.php/publis/article/view?id=3597
d-contraction optimale d'arêtes d'un grapheNous considéerons le problème suivant : peut-on diminuer un certain paramètre d'un graphe donné
$G$ d'au moins $d$ unités, pour un entier $d$,
via au plus $k$ contractions d'arêtes, pour un entier donné$k$?
Comme paramètre du graphe nous considérons le nombre chromatique, le nombre de stabilité et la taille de la plus grande clique.
Fri, 05 Feb 2016 15:55:03 +0100OCPaperhttp://cedric.cnam.fr/index.php/publis/article/view?id=3596
http://cedric.cnam.fr/index.php/publis/article/view?id=3596
Conception de câblages robustes dans les parcs éoliens : recherche d’une Arborescence de Steiner "robuste"Le problème de l'arborescence de Steiner consiste a trouver une arborescence de coût minimal sur un graphe G = (V;E) telle que cette arborescence couvre impérativement un sous-ensemble de sommets T inclus dans V. Notre problème ici consiste a trouver une solution "robuste". La robustesse évoquée ici consiste a minimiser le nombre d'éoliennes déconnectées de la station dans le cas d'une panne sur un câble dans le pire des cas. Plusieurs modèles sont étudiés, permettant une optimisation du pire des cas ou du cas moyen. Fri, 05 Feb 2016 15:46:45 +0100OCPaperhttp://cedric.cnam.fr/index.php/publis/article/view?id=3595
http://cedric.cnam.fr/index.php/publis/article/view?id=3595
On a robust inventory problem
In this paper we address the problem of optimizing multi-period inventory in the
case of uncertain demands. At each time period, the company produces a certain
quantity of goods which is used to serve a client demand. The unit selling price
was fixed in advance by contract for the time horizon and an expected value of the
quantity to deliver at each time period is known. In case of overproduction, goods
are added to the stock. In case of underproduction the missing goods are either
taken from the stock or bought on the international market. In addition at each
time period the manager can decide to buy more goods and add them to the stock
or to sell a part of the goods in stock, on the international market. The unit price
of purchase (or sale) of these goods on the international market are estimated in
advance for every period, according to the previous years.
But in fact, the demand and the purchasing costs on the international market
are uncertain and may differ from their expected values. Following the Betsimas
and Thiele approach, we assume that there is no known probabilistic distribution
of these values, but each one may vary in a given interval. We also assume that the
variation of the purchasing or selling costs is small, while the real demand can be
far enough from its expected value. Then the prices on the international market can
be approximate in the following way: the unit purchasing cost is set to its expected
value plus the maximum possible gap and the unit selling cost is set to its expected
value minus the maximum possible gap. Doing so, we guarantee a lower bound on
the profits.
The manager takes decisions in two stages: first he before discovering the actual
value taken by the demand, second once uncertainty has been revealed.
In this paper we address the problem of optimizing multi-period inventory in
the case of uncertain demands. We consider a wholesaler who purchases goods
on the international market and stocks them in a warehouse before selling them to
local customers. To serve the demand he can either demand at each time period,
the manager decides the quantity to buy His decisions are made in two stages: first
before discovering the actual value taken by the demand, second once uncertainty
has been revealed.
Fri, 05 Feb 2016 15:24:47 +0100OCPaper