Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations

Jonas Ide () and Elisabeth Köbis ()

Mathematical Methods of Operations Research, 2014, vol. 80, issue 1, 99-127

Abstract: In this paper we present new concepts of efficiency for uncertain multi-objective optimization problems. We analyze the connection between the concept of minmax robust efficiency presented by Ehrgott et al. (Eur J Oper Res, 2014 , doi: 10.1016/j.ejor.2014.03.013 ) and the upper set less order relation $$\preceq _s^u$$ ⪯ s u introduced by Kuroiwa ( 1998 , 1999 ). From this connection we derive new concepts of efficiency for uncertain multi-objective optimization problems by replacing the set ordering with other set orderings. Those are namely the lower set less ordering (see Kuroiwa 1998 , 1999 ), the set less ordering (see Nishnianidze in Soobshch Akad Nauk Gruzin SSR 114(3):489–491, 1984 ; Young in Math Ann 104(1):260–290, 1931 , doi: 10.1007/BF01457934 ; Eichfelder and Jahn in Vector Optimization. Springer, Berlin, 2012 ), the certainly less ordering (see Eichfelder and Jahn in Vector Optimization. Springer, Berlin, 2012 ), and the alternative set less ordering (see Ide et al. in Fixed Point Theory Appl, 2014 , doi: 10.1186/1687-1812-2014-83 ; Köbis 2014 ). We analyze the resulting concepts of efficiency and present numerical results on the occurrence of the various concepts. We conclude the paper with a short comparison between the concepts, and an outlook to further work. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Robustness; Multi-objective optimization; Set-valued optimization; Set order relations; Uncertainty; Scenarios (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (28)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-014-0471-z (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:80:y:2014:i:1:p:99-127

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-014-0471-z

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().