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Finding non dominated points for multiobjective integer convex programs with linear constraints

JOURNAL OF GLOBAL OPTIMIZATION 2022年第1期84卷 95-117页

作者： Zerfa, Lamia Chergui, Mohamed El-Amine Univ Alger 1 Fac Sci 02 Rue Didouche Mourad Algiers Algeria USTFIB Fac Math RECITS Lab PO 32 El Alia Algiers 16111 Algeria

In this paper, we present a branch-and-bound based algorithm to generate all non dominated points for a multiobjective integer programming problem with convex objective functions and linear constraints (MOICP). The principle is to solve a single objective program (P) defined from the original MOICP program with relaxed integrality constraints. Whenever an integer solution is found through the branching process, a node is created in the search tree for each criterion. That is, by adding a cutting plane that locally approximates the criterion, as to exclude a subset of dominated points. The nodes are traversed according to the depth-first strategy and the same process is repeated for the obtained programs as (P). Finally, as to illustrate the efficiency of the suggested algorithm, we present an experimental study, where we assess its efficiency using randomly generated quadratic multiobjective integer problems with linear constraints.

关键词： multiobjective convex programming Non dominated point multiobjective quadratic programming Branch-and-bound

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On fuzzy random multiobjective quadratic programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第2期193卷 329-341页

作者： Ammar, E. E. Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, a multiobjective quadratic programming problem having fuzzy random coefficients matrix in the objective and constraints and the decision vector are fuzzy pseudorandom variables is considered. First, we show that the efficient solutions of fuzzy quadratic multiobjective programming problems are resolved into series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are proved to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. At the end, numerical examples are illustrated in the support of the obtained results. (C) 2007 Elsevier B.V. All rights reserved.

关键词： multiobjective quadratic programming Fuzzy programming Fuzzy numbers Fuzzy random variables Interval analysis

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On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem

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INFORMATION SCIENCES 2008年第2期178卷 468-484页

作者： Ammar, E. E. Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, a multiobjective quadratic programming problem fuzzy random coefficients matrix in the objectives and constraints and the decision vector are fuzzy variables is considered. First, we show that the efficient solutions fuzzy quadratic multiobjective programming problems series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. An application fuzzy portfolio optimization problem as a convex quadratic programming approach is discussed and an acceptable solution to such problem is given. At the end, numerical examples are illustrated in the support of the obtained results. (c) 2007 Published by Elsevier Inc.

关键词： multiobjective quadratic programming portfolio problem fuzzy programming fuzzy numbers fuzzy random variables interval analysis

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