Quasi-Newton methods for multiobjective optimization problems

Vahid Morovati (), Hadi Basirzadeh and Latif Pourkarimi
Additional contact information
Vahid Morovati: Shahid Chamran University of Ahvaz
Hadi Basirzadeh: Shahid Chamran University of Ahvaz
Latif Pourkarimi: Razi University

4OR, 2018, vol. 16, issue 3, No 2, 294 pages

Abstract: Abstract This work is an attempt to develop multiobjective versions of some well-known single objective quasi-Newton methods, including BFGS, self-scaling BFGS (SS-BFGS), and the Huang BFGS (H-BFGS). A comprehensive and comparative study of these methods is presented in this paper. The Armijo line search is used for the implementation of these methods. The numerical results show that the Armijo rule does not work the same way for the multiobjective case as for the single objective case, because, in this case, it imposes a large computational effort and significantly decreases the speed of convergence in contrast to the single objective case. Hence, we consider two cases of all multi-objective versions of quasi-Newton methods: in the presence of the Armijo line search and in the absence of any line search. Moreover, the convergence of these methods without using any line search under some mild conditions is shown. Also, by introducing a multiobjective subproblem for finding the quasi-Newton multiobjective search direction, a simple representation of the Karush–Kuhn–Tucker conditions is derived. The H-BFGS quasi-Newton multiobjective optimization method provides a higher-order accuracy in approximating the second order curvature of the problem functions than the BFGS and SS-BFGS methods. Thus, this method has some benefits compared to the other methods as shown in the numerical results. All mentioned methods proposed in this paper are evaluated and compared with each other in different aspects. To do so, some well-known test problems and performance assessment criteria are employed. Moreover, these methods are compared with each other with regard to the expended CPU time, the number of iterations, and the number of function evaluations.

Keywords: Quasi-Newton methods; Multiobjective optimization; Nonparametric methods; Nondominated points; Performance profiles; 90C29; 90C30; 90C53 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10288-017-0363-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:aqjoor:v:16:y:2018:i:3:d:10.1007_s10288-017-0363-1

Ordering information: This journal article can be ordered from
https://www.springer ... ch/journal/10288/PSE

DOI: 10.1007/s10288-017-0363-1

Access Statistics for this article

4OR is currently edited by Yves Crama, Michel Grabisch and Silvano Martello

More articles in 4OR from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().