Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems

Diego Cattaruzza (), Martine Labbé (), Matteo Petris (), Marius Roland () and Martin Schmidt ()
Additional contact information
Diego Cattaruzza: University Lille, CNRS, Centrale Lille, Inria, UMR 9189-CRIStAL, Lille, France
Martine Labbé: Department of Computer Science, Université Libre de Bruxelles, 1050 Brussels, Belgium; Parc Scientifique de la Haute Borne, Inria Lille-Nord Europe, 59650 Villeneuve d’Ascq, France
Matteo Petris: University Lille, CNRS, Centrale Lille, Inria, UMR 9189-CRIStAL, Lille, France
Marius Roland: Department of Mathematics, Trier University, 54296 Trier, Germany
Martin Schmidt: Department of Mathematics, Trier University, 54296 Trier, Germany

INFORMS Journal on Computing, 2024, vol. 36, issue 4, 1084-1107

Abstract: We consider mixed-integer linear quantile minimization problems that yield large-scale problems that are very hard to solve for real-world instances. We motivate the study of this problem class by two important real-world problems: a maintenance planning problem for electricity networks and a quantile-based variant of the classic portfolio optimization problem. For these problems, we develop valid inequalities and present an overlapping alternating direction method. Moreover, we discuss an adaptive scenario clustering method for which we prove that it terminates after a finite number of iterations with a global optimal solution. We study the computational impact of all presented techniques and finally show that their combination leads to an overall method that can solve the maintenance planning problem on large-scale real-world instances provided by the ROADEF/EURO challenge 2020 1 and that they also lead to significant improvements when solving a quantile-version of the classic portfolio optimization problem.

Keywords: quantile minimization; value-at-risk (VaR); mixed-integer optimization; valid inequalities; adaptive clustering (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/ijoc.2022.0105 (application/pdf)

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:inm:orijoc:v:36:y:2024:i:4:p:1084-1107

Access Statistics for this article

More articles in INFORMS Journal on Computing from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().