Piecewise w ∞-equitable efficiency in multiobjective programming

Piecewise w ∞-equitable efficiency in multiobjective programming In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objectives. To solve this problem in this paper, the original problem is decomposed into a collection of smaller subproblems, according to the decision maker, and the subproblems are solved by the concept of w r -equitable efficiency, where w ∈ R + m is a weight vector. First some theoretical and practical aspects of Pw r -equitably efficient solutions are discussed and by using the concept of Pw r -equitable efficiency one model is presented to coordinate weakly w r -equitable efficient solutions of subproblems. Then the concept of Pw ∞-equitable is introduced to generate subsets of equitably efficient solutions, which aims to offer a limited number of representative solutions to the decision maker. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Piecewise w ∞-equitable efficiency in multiobjective programming

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
10.1007/s10255-017-0686-x
Publisher site
See Article on Publisher Site

Abstract

In equitable multiobjective optimization all the objectives are uniformly optimized, but in some cases the decision maker believes that some of them should be uniformly optimized according to the importance of objectives. To solve this problem in this paper, the original problem is decomposed into a collection of smaller subproblems, according to the decision maker, and the subproblems are solved by the concept of w r -equitable efficiency, where w ∈ R + m is a weight vector. First some theoretical and practical aspects of Pw r -equitably efficient solutions are discussed and by using the concept of Pw r -equitable efficiency one model is presented to coordinate weakly w r -equitable efficient solutions of subproblems. Then the concept of Pw ∞-equitable is introduced to generate subsets of equitably efficient solutions, which aims to offer a limited number of representative solutions to the decision maker.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Aug 7, 2017

References

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