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

Cattaruzza, Diego; Labbé, Martine; Petris, Matteo; Roland, Marius; Schmidt, Martin

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

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

Author(s) :

Cattaruzza, Diego [Auteur]

Integrated Optimization with Complex Structure [INOCS]
Labbé, Martine [Auteur]
Integrated Optimization with Complex Structure [INOCS]
Université libre de Bruxelles [ULB]
Petris, Matteo [Auteur]
Integrated Optimization with Complex Structure [INOCS]
Roland, Marius [Auteur]
Trier University
Schmidt, Martin [Auteur]
Trier University

Journal title :

INFORMS Journal on Computing

Publisher :

Institute for Operations Research and the Management Sciences (INFORMS)

Publication date :

2024

ISSN :

1091-9856

English keyword(s) :

Quantile Minimization
Value-at-Risk (VaR)
Mixed-Integer Optimization
Valid Inequalities
Adaptive Clustering

HAL domain(s) :

Computer Science [cs]/Operations Research [math.OC]
Mathématiques [math]/Combinatoire [math.CO]

English abstract : [en]

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 realworld ...
Show more >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 realworld 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 EURO/ROADEF challenge 2020 1 and that they also lead to significant improvements when solving a quantile-version of the classic portfolio optimization problem.Show less >

Language :

Anglais

Popular science :

Non

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