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The Polytope of m-Subspaces of a Finite Affine Space

Julie Christophe, Jean-Paul Doignon (2007)

RAIRO - Operations Research

The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the...

The traveling salesman problem and harmonic analysis.

Peter W. Jones (1991)

Publicacions Matemàtiques

In this paper we propose to discuss some relationships between the classical Traveling Salesman Problem (TSP), Litlewood-Paley theory, and harmonic measure. This circle of ideas is also closely related to the theory of Cauchy integrals on Lipschitz graphs, and this aspect is discussed more fully in the paper of David and Semmes [2] in this proceedings. The main differences between the subjects in [2] and this paper are that the results here are valid for one dimensional sets, whereas [2] treats...

Three tabu search methods for the MI-FAP applied to 802.11 networks

Sacha Varone, Nicolas Zufferey (2008)

RAIRO - Operations Research - Recherche Opérationnelle

Wireless LAN using IEEE 802.11 networks are now widely deployed at home by residential users or in hot spots by telecommunication operators. A hot spot is a place where a set of access points (APs) are located nearby each other and can serve many users. Since perturbations can degrade the quality of the signal, a careful channel assignment to each AP has to be done. Channel assignment of APs at hot spots, and more generally setup configuration and management, is still often done manually. In this...

Three tabu search methods for the MI-FAP applied to 802.11 networks

Sacha Varone, Nicolas Zufferey (2009)

RAIRO - Operations Research

Wireless LAN using IEEE 802.11 networks are now widely deployed at home by residential users or in hot spots by telecommunication operators. A hot spot is a place where a set of access points (APs) are located nearby each other and can serve many users. Since perturbations can degrade the quality of the signal, a careful channel assignment to each AP has to be done. Channel assignment of APs at hot spots, and more generally setup configuration and management, is still often done manually. In this...

Towards a theory of practice in metaheuristics design: A machine learning perspective

Mauro Birattari, Mark Zlochin, Marco Dorigo (2006)

RAIRO - Theoretical Informatics and Applications

A number of methodological papers published during the last years testify that a need for a thorough revision of the research methodology is felt by the operations research community – see, for example, [Barr et al., J. Heuristics1 (1995) 9–32; Eiben and Jelasity, Proceedings of the 2002 Congress on Evolutionary Computation (CEC'2002) 582–587; Hooker, J. Heuristics1 (1995) 33–42; Rardin and Uzsoy, J. Heuristics7 (2001) 261–304]. In particular, the performance evaluation of nondeterministic methods,...

Two-stage robust optimization, state-space representable uncertainty and applications

Michel Minoux (2014)

RAIRO - Operations Research - Recherche Opérationnelle

The present paper addresses the class of two-stage robust optimization problems which can be formulated as mathematical programs with uncertainty on the right-hand side coefficients (RHS uncertainty). The wide variety of applications and the fact that many problems in the class have been shown to be NP-hard, motivates the search for efficiently solvable special cases. Accordingly, the first objective of the paper is to provide an overview of the most important applications and of various polynomial...

Un algorithme pour la bipartition d’un graphe en sous-graphes de cardinalité fixée

Philippe Michelon, Stéphanie Ripeau, Nelson Maculan (2001)

RAIRO - Operations Research - Recherche Opérationnelle

Nous présentons une méthode de Séparation et Évaluation Progressive pour la bipartition d’un graphe en 2 sous-ensembles ayant une cardinalité fixée. À chaque nœud de l’arbre de recherche, nous calculons une borne inférieure en dualisant les contraintes d’intégralité et en approximant le domaine réalisable par un ellipsoïde. Une borne supérieure est également calculée par la méthode Tabou. Des résultats numériques sont présentés et commentés.

Un Algorithme pour la Bipartition d'un Graphe en Sous-graphes de Cardinalité Fixée

Philippe Michelon, Stéphanie Ripeau, Nelson Maculan (2010)

RAIRO - Operations Research

A branch-and-bound method for solving the min cut with size constraint problem is presented. At each node of the branch-and-bound tree the feasible set is approximated by an ellipsoid and a lower bound is computed by minimizing the quadratic objective function over this ellipsoid. An upper bound is also obtained by a Tabu search method. Numerical results will be presented.

Un algoritmo para el problema de biflujo máximo simétrico no dirigido.

Antonio Sedeño Noda, Carlos González Martín (2002)

Qüestiió

En este trabajo proponemos un algoritmo de O(nmlogU) para resolver el problema de biflujo máximo simétrico en una red no dirigida. Para resolver este problema se introduce un cambio de variable que permite dividir el problema original en dos problemas de flujo máximo. De esta manera se obtiene un algoritmo sencillo y eficiente donde se utilizan las herramientas computacionales propias de la resolución del clásico problema de maximizar un único flujo.

Valeurs extrémales d'un problème d'optimisation combinatoire et approximation polynomiale

Marc Demange, Vangelis Th. Paschos (1996)

Mathématiques et Sciences Humaines

A la suite de quelques-uns de nos travaux antérieurs sur la théorie de la complexité et de l'approximation polynomiale, nous présentons quelques nouvelles réflexions et arguments sur les valeurs (et solutions) extrérmales, (optimale et pire), des problèmes d'optirnisation combinatoire. Cette discussion nous conduit à considérer la limite entre constructibilité et non-constructibilité, source constante de contradiction en théorie de la complexité. En effet, cette théorie, telle qu'on la connaît et...

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