Integer programming duality in multiple objective programming

Integer programming duality in multiple objective programming

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Article ID: iaor2005391
Country: Netherlands
Volume: 29
Issue: 1
Start Page Number: 1
End Page Number: 18
Publication Date: May 2004
Journal: Journal of Global Optimization
Authors: , ,
Keywords: programming: multiple criteria
Abstract:

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 maker's 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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