On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach

Benjamin Martin (), Alexandre Goldsztejn (), Laurent Granvilliers () and Christophe Jermann ()

Journal of Global Optimization, 2016, vol. 64, issue 1, 3-16

Abstract: The global resolution of constrained non-linear bi-objective optimization problems (NLBOO) aims at covering their Pareto-optimal front which is in general a one-manifold in $$\mathbb {R}^2$$ R 2 . Continuation methods can help in this context as they can follow a continuous component of this front once an initial point on it is provided. They constitute somehow a generalization of the classical scalarization framework which transforms the bi-objective problem into a parametric single-objective problem. Recent works have shown that they can play a key role in global algorithms dedicated to bi-objective problems, e.g. population based algorithms, where they allow discovering large portions of locally Pareto optimal vectors, which turns out to strongly support diversification. The contribution of this paper is twofold: we first provide a survey on continuation techniques in global optimization methods for NLBOO, identifying relations between several work and usual limitations, among which the ability to handle inequality constraints. We then propose a rigorous active set management strategy on top of a continuation method based on interval analysis, certified with respect to feasibility, local optimality and connectivity. This allows overcoming the latter limitation as illustrated on a representative bi-objective problem. Copyright Springer Science+Business Media New York 2016

Keywords: Non-linear bi-objective optimization; Continuation; Interval analysis; Constraints activity (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10898-014-0201-3 (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:jglopt:v:64:y:2016:i:1:p:3-16

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

DOI: 10.1007/s10898-014-0201-3

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 ().