Integer Programming Duality in Multiple Objective Programming

The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria intege...

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Bibliographic Details
Published in:Journal of global optimization Vol. 29; no. 1; pp. 1 - 18
Main Authors: Klamroth, Kathrin, Tind, Jørgen, Zust, Sibylle
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.05.2004
Subjects:
Algorithms
Integer programming
Linear programming
Mathematical functions
Optimization
Studies
Utility functions
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria integer programming. However, in this case one may apply the more general e-constraint approach, resulting in particular single-criteria integer programming problems to generate efficient solutions. We show how this approach implies a more general, composite utility function of the criteria yielding a unified treatment of multiple criteria optimization with and without integrality constraints. Moreover, any efficient solution can be found using appropriate composite functions. The functions may be generated by the classical solution methods such as cutting plane and branch and bound algorithms.
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ISSN:0925-5001
1573-2916
DOI:10.1023/B:JOGO.0000035000.06101.07