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An interactive graphic presentation for multiobjective linear programming

APPLIED MATHEMATICS AND COMPUTATION 2001年第2期123卷 229-248页

作者： Anderson, RK Dror, M Univ Arizona Coll Business & Publ Adm MIS Dept Tucson AZ 85721 USA Utah Valley State Coll Comp Sci & Informat Syst Orem UT 84058 USA

In this paper we examine the design and implementation issues relating to the search process for a solution to an interactive multiobjective linear optimization problem (MOLP). A solution methodology proposed by Dror and Gass is employed. The primary objective of the design process is to investigate the advantages of using interactive graphics in the presentation of alternative solutions and to direct the solution search. We find several features useful, including three-dimensional perspective views, graph animation, interactive highlighting, and interactive detail inspection. (C) 2001 Elsevier Science Inc. All rights reserved.

关键词： multiobjective linear programming multi-criteria decision making presentation graphics decision support

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A fuzzy satisficing method for large-scale multiobjective linear programming problems with block angular structure

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FUZZY SETS AND SYSTEMS 1996年第3期78卷 279-288页

作者： Sakawa, M Inuiguchi, M Sawada, K MATSUSHITEA ELECT WORKS LTD INFORMAT SYST CTROSAKA 571JAPAN

In this paper, we focus on large-scale multiobjective linear programming problems with the block angular structure. By considering the imprecise nature of human judgements, we assume that the decision maker may have a fuzzy goal for each of the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, we adopt the fuzzy decision for aggregating them. Then it is shown that the formulated problem can be reduced to one master problem and a number of linear subproblems and the satisficing solution for the decision maker can be obtained by directly applying the Dantzig-Wolfe decomposition method.

关键词： large-scale linear programming multiobjective linear programming block angular structure fuzzy goals fuzzy decision fuzzy satisficing method

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FUZZY-programming IN multiobjective linear-programming - A PARAMETRIC APPROACH

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FUZZY SETS AND SYSTEMS 1989年第3期29卷 303-313页

作者： CHANAS, S Institute of Production Engineering and Management Technical University of Wrocław Wyb. Wyspiańskiego 27 50-370 Wrocław Poland

Zimmermann's fuzzy approach to the compromise solution concept in the multi-objective linear programming problem is considered. It is shown that given a class of membership functions of fuzzy goals assigned to objective functions in the problem, wider than primarily proposed by Zimmermann, the use of classical linear programming methods to solve and analyse the problem is also possible. As a result of application of the method based on the parametric programming technique, one can obtain a fuzzy solution of the problem. This solution is a certain fuzzy subset of the set of weakly efficient solutions of the problem. The solution which belongs to this set to the highest degree is a maximizing one (in Bellman and Zadeh's terminology). It may also be obtained by use of the usual non-parametric simplex method.

关键词： multiobjective linear programming compromise solution fuzzy programming parametric programming

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Range sets for weak efficiency in multiobjective linear programming and a parametric polytopes intersection problem

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OPTIMIZATION 2019年第2-3期68卷 645-666页

作者： Hladik, Milan Rada, Miroslav Sitarz, Sebastian Garajova, Elif Charles Univ Prague Dept Appl Math Fac Math & Phys Prague Czech Republic Univ Econ Dept Financial Accounting & Auditing Prague Czech Republic Univ Silesia Inst Math Dept Math Methods Econ & Finance Katowice Poland

The aim of this paper is to obtain the range set for a given multiobjective linear programming problem and a weakly efficient solution. The range set is the set of all values of a parameter such that a given weakly efficient solution remains efficient when the objective coefficients vary in a given direction. The problem was originally formulated by Benson in 1985 and left to be solved. We formulate an algorithm for determining the range set, based on some hard optimization problems. Due to toughness of these optimization problems, we propose also lower and upper bound approximation techniques. In the second part, we focus on topological properties of the range set. In particular, we prove that a range set is formed by a finite union of intervals and we propose upper bounds on the number of intervals. Our approach to tackle the range set problem is via the intersection problem of parametric polytopes. Thus, our results have much wider area of applicability since the intersection (and separability) problem of convex polyhedra is important in many fields of optimization.

关键词： multiobjective linear programming efficient solution sensitivity analysis range set

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Determining maximal efficient faces in multiobjective linear programming problem

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2009年第1期354卷 234-248页

作者： Pourkarimi, L. Yaghoobi, M. A. Mashinchi, M. Shahid Bahonar Univ Kerman Fac Math & Comp Sci Dept Math Kerman Iran Shahid Bahonar Univ Kerman Fac Math & Comp Sci Dept Stat Kerman Iran

Finding an efficient or weakly efficient solution in a multiobjective linear programming (MOLP) problem is not a difficult task. The difficulty lies in finding all these solutions and representing their structures. Since there are many convenient approaches that obtain all of the (weakly) efficient extreme points and (weakly) efficient extreme rays in an MOLP, this paper develops an algorithm which effectively finds all of the (weakly) efficient maximal faces in an MOLP using all of the (weakly) efficient extreme points and extreme rays. The proposed algorithm avoids the degeneration problem, which is the major problem of the most of previous algorithms and gives an explicit structure for maximal efficient (weak efficient) faces. Consequently, it gives a convenient representation of efficient (weak efficient) set using maximal efficient (weak efficient) faces. The proposed algorithm is based oil two facts. Firstly, the efficiency and weak efficiency property of a face is determined using a relative interior point of it. Secondly, the relative interior point is achieved using some affine independent points. Indeed, the affine independent property enable us to obtain an efficient relative interior point rapidly. (c) 2008 Elsevier Inc. All rights reserved.

关键词： multiobjective linear programming Maximal efficient face Minimal index set Efficiency

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FINDING ALL MAXIMAL EFFICIENT FACES IN multiobjective linear-programming

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MATHEMATICAL programming 1993年第3期61卷 357-375页

作者： ARMAND, P 1. Département de Mathématiques Faculté des Sciences Université de Limoges 123 avenue Albert Thomas 87060 Limoges Cédex France

An algorithm for finding the whole efficient set of a multiobjective linear program is proposed. From the set of efficient edges incident to a vertex, a characterization of maximal efficient faces containing the vertex is given. By means of the lexicographic selection rule of Dantzig, Orden and Wolfe, a connectedness property of the set of dual optimal bases associated to a degenerate vertex is proved. An application of this to the problem of enumerating all the efficient edges incident to a degenerate vertex is proposed. Our method is illustrated with numerical examples and comparisons with Armand-Malivert's algorithm show that this new algorithm uses less computer time.

关键词： multiobjective linear programming EFFICIENT SET DEGENERACY SIMPLEX ALGORITHM

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AN INTERACTIVE FUZZY SATISFICING METHOD FOR GENERALIZED multiobjective linear-programming PROBLEMS WITH FUZZY PARAMETERS

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FUZZY SETS AND SYSTEMS 1990年第2期35卷 125-142页

作者： SAKAWA, M YANO, H KAGAWA UNIV COLL ECONDEPT INFORMAT SCITAKAMATSUKAGAWA 760JAPAN

A new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed. In general, two types of fuzziness of human judgements should be incorporated in multiobjective programming problems. One is the experts' ambiguous understanding of the nature of the parameters in the problem-formulation process, and the other is the fuzzy goals of the decision maker for each of the objective functions. In order to cope with both types of fuzziness, multiobjective linear programming problems with fuzzy parameters which reflect the experts' ambiguous understanding in the problem-formulation are formulated and the concept of generalized α-multiobjective linear programming and M-α-Pareto optimality is introduced. In our interactive fuzzy satisficing method, the satisficing solution of the decision maker is derived efficiently from among M-α-Pareto optimal solutions. On the basis of the proposed method, an interactive computer program is written to implement man-machine interactive procedures. Finally, an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs.

关键词： multiobjective linear programming interactive fuzzy satisficing method fuzzy parameters M-α-Pareto optimality satisficing solution

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Computing the tolerances in multiobjective linear programming

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OPTIMIZATION METHODS & SOFTWARE 2008年第5期23卷 731-739页

作者： Hladik, Milan Charles Univ Prague Dept Appl Math CR-11800 Prague Czech Republic

We consider a multiobjective linear program and the coefficients of the multiobjective function are supposed to be uncertain. Let x* be an efficient point. We propose a procedure computing a tolerance for each objective function coefficient, such that all these coefficients may simultaneously and independently vary within their tolerances while preserving the efficiency of x*. If x* is a non-degenerate basic solution, then the procedure runs in a polynomial time. Our method is also applicable for the intervals of multiobjective linear programming for checking the necessary efficiency of x*, i.e. whether x* is efficient for all the realizations of interval values.

关键词： multiobjective linear programming interval matrix efficient point sensitivity analysis tolerance analysis

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Fuzzy-efficient solutions for the multiobjective linear programming problems with mixed fuzzy-stochastic resources

Fuzzy-efficient solutions for the multiobjective linear prog...

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International Conference on Intelligent Mechatronics and Automation

作者： Song, YX Wu, XP Fei, J USN Dept Basic Courses Wuhan 430033 Peoples R China

ISBN: (纸本)0780387481

This paper presents a novel method for solving the multi-objective linear programming problems with mixed fuzzy-stochastic resources. A fuzzifying technique is first proposed to treat the stochastic resources constraints as fuzzified chance constraints, as a result of this, the stochastic constraints are treated in a fuzzy environment. Then, based on the max-min operator, an improve approach is presented to solve all the fuzzy-efficient solutions for the multiobjective fuzzy-stochastic linear programming problems. The proposed method pursues not only the highest membership degree in the objective but also a better utilization of each constrained resource. Finally, a numerical example is given to illustrate the method.

关键词： multiobjective linear programming fuzzy-stochastic resources fuzzy-efficient solutions

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Computing the tolerances in multiobjective linear programming

Computing the tolerances in multiobjective linear programmin...

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2nd International Conference on Optimization Methods and Software/6th EUROPT Workshop on Advances in Continuous Optimization

作者： Hladik, Milan Charles Univ Prague Dept Appl Math CR-11800 Prague Czech Republic

关键词： multiobjective linear programming interval matrix efficient point sensitivity analysis tolerance analysis

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