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Exact generation of epsilon-efficient solutions in multiple objective programming

OR SPECTRUM 2007年第2期29卷 335-350页

作者： Engau, Alexander Wiecek, Margaret M. Clemson Univ Dept Math Sci Clemson SC 29634 USA

It is a common characteristic of many multiple objective programming problems that the efficient solution set can only be identified in approximation: as this set often contains an infinite number of points, only a discrete representation can be computed, and due to numerical difficulties, each of these points itself might, in general, be only approximate to some efficient point. From among the various approximation concepts, this paper considers the notion of epsilon-efficient solutions and proposes several new methods for their generation. Supporting theoretical results are established and a numerical example is provided.

关键词： multiple objective programming epsilon-efficient solutions epsilon-Pareto outcomes approximation

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Cone characterizations of approximate solutions in real vector optimization

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2007年第3期134卷 499-513页

作者： Engau, A. Wiecek, M. M. Clemson Univ Dept Math Sci Clemson SC 29634 USA

Approximate nondominated solutions of real vector optimization problems are characterized using the concept of translated cones. Relationships between these solutions and Pareto nondominated points are examined, and t... 详细信息

关键词： approximate solutions epsilon-efficient solutions epsilon-minimal elements translated cones

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Generating ε-efficient solutions in multiobjective programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期177卷 1566-1579页

作者： Engau, Alexander Wiecek, Margaret M. Clemson Univ Dept Math Sci Clemson SC 29634 USA

Scalarization approaches to purposely generating e-efficient solutions of multiobjective programs are investigated and a generic procedure for computing these solutions is proposed and illustrated with an example. Real-life decision making situations in which the solutions are of significance are described. (c) 2005 Elsevier B.V. All rights reserved.

关键词： multiobjective programs epsilon-efficient solutions epsilon-Pareto outcomes epsilon-non-dominated outcomes scalarizations epsilon-optimality

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A parametric characterization of mean-variance efficient solutions for general feasible action sets

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Journal of Multi-Criteria Decision Analysis 1998年第2期7卷 109-119页

作者： White, D.J. Department of Decision Theory University of Manchester Manchester United Kingdom

In this paper we show how the mean-variance efficient solution problem may be converted to a parametric efficient solution problem with objective functions affine in the mean and second moment of the random variable of concern. Some potential uses are considered, the relationship with some other work is examined and two potential applications are given. © 1998 John Wiley & Sons, Ltd.

关键词： efficient solutions epsilon-efficient solutions Mean-variance Parametric programming

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