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Original Articles

New algorithms for discrete vector optimization based on the Graef-Younes method and cone-monotone sorting functions

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Pages 975-1003 | Received 16 Jun 2017, Accepted 04 May 2018, Published online: 20 May 2018
 

Abstract

The well-known Jahn-Graef-Younes algorithm, proposed by Jahn in 2006, generates all minimal elements of a finite set with respect to an ordering cone. It consists of two Graef-Younes procedures, namely the forward iteration, which eliminates a part of the non-minimal elements, followed by the backward iteration, which is applied to the reduced set generated by the previous iteration. Without using the backward iteration, we develop new algorithms that also compute all minimal elements of the initial set, by combining the forward iteration with certain sorting procedures based on cone-monotone functions. In particular, when the ordering cone is polyhedral, computational results obtained in MATLAB allow us to compare our algorithms with the Jahn-Graef-Younes algorithm, within a bi-objective optimization problem.

Acknowledgements

The authors are grateful to the anonymous referees for their valuable and constructive remarks.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

Dedicated to Professor Johannes Jahn in honor of his 65th birthday.

Additional information

Funding

Nicolae Popovici’s research was supported by a grant of the Romanian Ministry of Research and Innovation, CNCS-UEFISCDI [project number PN-III-P4-ID-PCE-2016-0190], within PNCDI III.

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