EconPapers    
Economics at your fingertips  
 

Extending interval branch-and-bound from two to few objectives in nonlinear multiobjective optimization

Ignacio Araya (), Victor Reyes () and Javier Montero ()
Additional contact information
Ignacio Araya: Pontificia Universidad Católica de Valparaíso
Victor Reyes: Universidad Diego Portales
Javier Montero: Pontificia Universidad Católica de Valparaíso

Journal of Global Optimization, 2025, vol. 92, issue 2, No 3, 295-320

Abstract: Abstract Nonlinear multiobjective optimization presents significant challenges, particularly when addressing problems with three or more objectives. Building on our previous work using Interval Branch and Bound (B&B) techniques for biobjective optimization, we extend these methods to handle the increased complexity of multiobjective scenarios. Interval B&B methods involve dividing the original problem into smaller subproblems and solving them recursively to achieve a desired level of accuracy. These methods offer the advantage of guaranteeing global optimality and providing rigorous bounds on solution quality. We introduce a refined representation of non-dominated regions using two sets of vectors: the non dominated feasible vectors found so far and its associated set of extreme vectors. To accurately define the feasible non-dominated region within each subspace, we adapt an “envelope constraint” from biobjective solvers. Additionally, we propose a novel method for computing the distance from a subspace to the dominated region, and enhance a peeling technique for contracting the subspace based on the dominated region and the envelope constraint. Our approach is evaluated on a set of benchmark problems, and our results show a significant improvement in solution quality and convergence speed compared to a basic approach. Specifically, our enhanced strategy achieves a 42% reduction in relative CPU time, with a remarkable average time reduction of 63% in problems with three objectives. The code of our solver can be found in our git repository ( https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop ).

Keywords: Interval methods; Branch and Bound; Multiobjective optimization (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-025-01479-4 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:jglopt:v:92:y:2025:i:2:d:10.1007_s10898-025-01479-4

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-025-01479-4

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2025-06-03
Handle: RePEc:spr:jglopt:v:92:y:2025:i:2:d:10.1007_s10898-025-01479-4