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Análisis interactivo de las soluciones del problema lineal múltiple ordenado.

Eduardo Conde Sánchez, Francisco Ramón Fernández García, Justo Puerto Albandoz (1994)

Qüestiió

En este trabajo se estudian procedimientos para la elección entre las soluciones eficientes del Problema de Programación Lineal con Objetivos Múltiples, cuando el decisor manifiesta preferencias sobre ciertas ordenaciones de las valoraciones de las funciones objetivo, utilizándose como criterio de valoración global funciones basadas en el k-ésimo valor del vector de los objetivos ordenado en cada punto.Se desarrollan procedimientos para generar ordenaciones compatibles con la información del decisor....

Analyse de récession et résultats de stabilité d’une convergence variationnelle, application à la théorie de la dualité en programmation mathématique

Driss Mentagui (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Soit X un espace de Banach de dual topologique X ' . 𝒞 X (resp. 𝒞 X ' ) désigne l’ensemble des parties non vides convexes fermées de X (resp. w * -fermées de X ' ) muni de la topologie de la convergence uniforme sur les bornés des fonctions distances. Cette topologie se réduit à celle de la métrique de Hausdorff sur les convexes fermés bornés [16] et admet en général une représentation en terme de cette dernière [11]. De plus, la métrique qui lui est associée s’est révélée très adéquate pour l’étude quantitative...

Analyse de récession et résultats de stabilité d'une convergence variationnelle, application à la théorie de la dualité en programmation mathématique

Driss Mentagui (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Let X be a Banach space and X' its continuous dual. C(X) (resp. C(X')) denotes the set of nonempty convex closed subsets of X (resp. ω*-closed subsets of X') endowed with the topology of uniform convergence of distance functions on bounded sets. This topology reduces to the Hausdorff metric topology on the closed and bounded convex sets [16] and in general has a Hausdorff-like presentation [11]. Moreover, this topology is well suited for estimations and constructive approximations [6-9]. We...

Analyse de sensibilité pour les problèmes linéaires en variables 0-1

Babacar Thiongane, Anass Nagih, Gérad Plateau (2003)

RAIRO - Operations Research - Recherche Opérationnelle

Cet article est un travail de synthèse autour de l’analyse de sensibilité pour les problèmes linéaires en variables 0-1. De nombreux aspects sont ainsi abordés : historique et formes d’analyse de sensibilité, exemples d’application, complexité, conditions d’optimalité, algorithmes et approches. Nous dressons par ailleurs quelques perspectives de recherche actuelles dans ce domaine.

Analyse de sensibilité pour les problèmes linéaires en variables 0-1

Babacar Thiongane, Anass Nagih, Gérad Plateau (2010)

RAIRO - Operations Research

Cet article est un travail de synthèse autour de l'analyse de sensibilité pour les problèmes linéaires en variables 0-1. De nombreux aspects sont ainsi abordés : historique et formes d'analyse de sensibilité, exemples d'application, complexité, conditions d'optimalité, algorithmes et approches. Nous dressons par ailleurs quelques perspectives de recherche actuelles dans ce domaine.

Analysis of a near-metric TSP approximation algorithm

Sacha Krug (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The traveling salesman problem (TSP) is one of the most fundamental optimization problems. We consider the β-metric traveling salesman problem (Δβ-TSP), i.e., the TSP restricted to graphs satisfying the β-triangle inequality c({v,w}) ≤ β(c({v,u}) + c({u,w})), for some cost function c and any three vertices u,v,w. The well-known path matching Christofides algorithm (PMCA) guarantees an approximation ratio of 3β2/2 and is the best known algorithm for the Δβ-TSP, for 1 ≤ β ≤ 2. We provide a complete...

Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming

Jingyong Tang, Li Dong, Liang Fang, Li Sun (2015)

Applications of Mathematics

The smoothing-type algorithm is a powerful tool for solving the second-order cone programming (SOCP), which is in general designed based on a monotone line search. In this paper, we propose a smoothing-type algorithm for solving the SOCP with a non-monotone line search. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results are also reported which indicate...

Analysis of an isopetype dual algorithm for optimizing control and nonlinear optimization

Wojciech Tadej, Piotr Tatjewski (2001)

International Journal of Applied Mathematics and Computer Science

First results concerning important theoretical properties of the dual ISOPE (Integrated System Optimization and Parameter Estimation) algorithm are presented. The algorithm applies to on-line set-point optimization in control structures with uncertainty in process models and disturbance estimates, as well as to difficult nonlinear constrained optimization problems. Properties of the conditioned (dualized) set of problem constraints are investigated, showing its structure and feasibility properties...

Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market

René Henrion, Jiří Outrata, Thomas Surowiec (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an equilibrium problem with equilibrium constraints (EPEC) arising from the modeling of competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This first requires a structural analysis of the problem, e.g., verifying constraint qualifications. Second, the calmness property of a certain multifunction has to be verified in order to justify using M-stationarity conditions. Third,...

Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market∗

René Henrion, Jiří Outrata, Thomas Surowiec (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an equilibrium problem with equilibrium constraints (EPEC) arising from the modeling of competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This first requires a structural analysis of the problem, e.g., verifying constraint qualifications. Second, the calmness property of a certain multifunction has to be verified in order...

Analysis of the best-worst ant system and its variants on the TSP.

Oscar Cordón, Iñaki Fernández de Viana, Francisco Herrera (2002)

Mathware and Soft Computing

In this contribution, we will study the influence of the three main components of Best-Worst Ant System: the best-worst pheromone trail update rule, the pheromone trail mutation and the restart. Both the importance of each of them and the fact whether all of them are necessary will be analyzed. The performance of different variants of this algorithm will be tested when solving different instances of the TSP.

Another set of verifiable conditions for average Markov decision processes with Borel spaces

Xiaolong Zou, Xianping Guo (2015)

Kybernetika

In this paper we give a new set of verifiable conditions for the existence of average optimal stationary policies in discrete-time Markov decision processes with Borel spaces and unbounded reward/cost functions. More precisely, we provide another set of conditions, which only consists of a Lyapunov-type condition and the common continuity-compactness conditions. These conditions are imposed on the primitive data of the model of Markov decision processes and thus easy to verify. We also give two...

Ant algorithm for flow assignment in connection-oriented networks

Krzysztof Walkowiak (2005)

International Journal of Applied Mathematics and Computer Science

This work introduces ANB (bf Ant Algorithm for bf Non-bf Bifurcated Flows), a novel approach to capacitated static optimization of flows in connection-oriented computer networks. The problem considered arises naturally from several optimization problems that have recently received significant attention. The proposed ANB is an ant algorithm motivated by recent works on the application of the ant algorithm to solving various problems related to computer networks. However, few works concern the use...

Ant Colony Optimisation: models and applications.

Oscar Cordón, Francisco Herrera, Thomas Stützle (2002)

Mathware and Soft Computing

Ant Colony Optimization (ACO) is a metaheuristic that is inspired by the shortest path searching behavior of various ant species [1,2]. The initial work of Dorigo, Maniezzo and Colorni [3,4] who proposed the first ACO algorithm called Ant System, has stimulated a still strongly increasing number of researchers to develop more sophisticated and better performing ACO algorithms that are used to successfully solve a large number of hard combinatorial optimization problems such as the traveling salesman...

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