Approaches to approximate the efficient set and Pareto set of multiobjective programs are reviewed. Special attention is given to approximating structures, methods generating Pareto points, and approximation quality. ...
详细信息
Approaches to approximate the efficient set and Pareto set of multiobjective programs are reviewed. Special attention is given to approximating structures, methods generating Pareto points, and approximation quality. The survey covers more than 50 articles published since 1975.
In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modi...
详细信息
In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, an F-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of a saddle point are given.
In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak ...
详细信息
In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-invex functions in Antczak [Europ. J. Oper. Res. 137 (2002) 28] and univex functions in Bector et al. [Univex functions and univex nonlinear programming, Proc. Admin. Sci. Assoc. Canada, 1992, p. 115]. By utilizing the new concepts, we derive a Karush-Kuhn-Tucker sufficient optimality condition and establish Mond-Weir type and general Mond-Weir type duality results for the nondifferentiable multiobjective programming problem. (C) 2003 Elsevier B.V. All rights reserved.
The aim of the present paper is to propose a novel version of the well known multicriteria method PROMETHEE that deals with segmentation constraints and is also suitable for group decision making. The motivation for t...
详细信息
The aim of the present paper is to propose a novel version of the well known multicriteria method PROMETHEE that deals with segmentation constraints and is also suitable for group decision making. The motivation for the development of the method was a real case study concerning the selection of students for a postgraduate program. The proposed method, named PROMETHEE V2, is based on the principles of PROMETHEE V but uses the results of PROMETHEE I (instead of PROMETHEE II) and exploits the information provided by the leaving and entering flows in order to formulate a bi-objective Integer programming problem. The solution of the latter produces the Pareto optimal solutions which are usually more than one. Due to its structure, the whole decision process is especially suitable for group decision *** article a un double objectif, d'un point de vue méthodologique, on propose une nouvelle version de la méthode multicritère PROMETHEE en présence de contraintes de segmentation qui peut aussi être un outil d'aide adapté à la décision de groupes. La méthode proposée est mise en oeuvre dans le cas de sélection des étudiants candidats pour un diplôme 3e cycle. La méthode proposée, appelée PROMETHEE V2, est basée sur les principes du PROMETHEE V, néanmoins on utilise les résultats de PROMETHEE I (pas ceux de PROMETHEE II) et on valorise l’information fournie par les flux d'entrée et de sortie afin de formuler un modèle en variables entières bi-objectif. La solution de ce problème génère plus d'une solution Pareto optimale. En raison de sa structure, le processus global de décision est particulièrement approprié pour la décision de groupe.
In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak ...
详细信息
In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-invex functions in Antczak [Europ. J. Oper. Res. 137 (2002) 28] and univex functions in Bector et al. [Univex functions and univex nonlinear programming, Proc. Admin. Sci. Assoc. Canada, 1992, p. 115]. By utilizing the new concepts, we derive a Karush-Kuhn-Tucker sufficient optimality condition and establish Mond-Weir type and general Mond-Weir type duality results for the nondifferentiable multiobjective programming problem. (C) 2003 Elsevier B.V. All rights reserved.
The aim of the present paper is to propose a novel version of the well known multicriteria method PROMETHEE that deals with segmentation constraints and is also suitable for group decision making. The motivation for t...
详细信息
The aim of the present paper is to propose a novel version of the well known multicriteria method PROMETHEE that deals with segmentation constraints and is also suitable for group decision making. The motivation for the development of the method was a real case study concerning the selection of students for a postgraduate program. The proposed method, named PROMETHEE V2, is based on the principles of PROMETHEE V but uses the results of PROMETHEE I (instead of PROMETHEE II) and exploits the information provided by the leaving and entering flows in order to formulate a bi-objective Integer programming problem. The solution of the latter produces the Pareto optimal solutions which are usually more than one. Due to its structure, the whole decision process is especially suitable for group decision making.
In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modif...
详细信息
In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective ***, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.
MOPEN is a computational package designed as a global tool for Linear multiobjective and Goal programming problems with continuous and/or integer variables. The main existing techniques for these problems have been in...
详细信息
MOPEN is a computational package designed as a global tool for Linear multiobjective and Goal programming problems with continuous and/or integer variables. The main existing techniques for these problems have been included in this package. That is, it is possible to generate or approximate the efficient set using Generating Methods, to obtain Compromise solutions or to use Goal programming or reference Point approaches. As will be described, many advanced options have been implemented with every method. MOPEN has been implemented under a Windows environment;thus, it is easy to build and handle the data entry files and the result layout files. The behavior of MOPEN-in terms of CPU time used to solve large problems-can be considered as good;therefore, this package is a powerful tool to handle the previously mentioned problems. (c) 2004 Elsevier B.V. All rights reserved.
In this paper, we point out some inconsistencies in the earlier work of Ahmad and Husain (Appl. Math. Lett. 18, 721-728, 2005), and present the correct forms of their strong and converse duality theorems.
In this paper, we point out some inconsistencies in the earlier work of Ahmad and Husain (Appl. Math. Lett. 18, 721-728, 2005), and present the correct forms of their strong and converse duality theorems.
暂无评论