Details
| Original language | English |
|---|---|
| Pages (from-to) | 975-1003 |
| Number of pages | 29 |
| Journal | OPTIMIZATION |
| Volume | 67 |
| Issue number | 7 |
| Publication status | Published - 20 May 2018 |
| Externally published | Yes |
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.
Keywords
- Graef-Younes reduction method, Partially ordered space, cone-monotone function, domination property, minimal element, multiobjective subdivision technique
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Decision Sciences(all)
- Management Science and Operations Research
- Mathematics(all)
- Applied Mathematics
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In: OPTIMIZATION, Vol. 67, No. 7, 20.05.2018, p. 975-1003.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - New algorithms for discrete vector optimization based on the Graef-Younes method and cone-monotone sorting functions
AU - Günther, Christian
AU - Popovici, Nicolae
N1 - Funding information: 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.
PY - 2018/5/20
Y1 - 2018/5/20
N2 - 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.
AB - 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.
KW - Graef-Younes reduction method
KW - Partially ordered space
KW - cone-monotone function
KW - domination property
KW - minimal element
KW - multiobjective subdivision technique
UR - http://www.scopus.com/inward/record.url?scp=85047147179&partnerID=8YFLogxK
U2 - 10.1080/02331934.2018.1474469
DO - 10.1080/02331934.2018.1474469
M3 - Article
VL - 67
SP - 975
EP - 1003
JO - OPTIMIZATION
JF - OPTIMIZATION
SN - 0323-3898
IS - 7
ER -