Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems
| Autor: | Cattaruzza, Diego, Labbé, Martine, Petris, Matteo, Roland, Marius, Schmidt, Martin |
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| Přispěvatelé: | Integrated Optimization with Complex Structure (INOCS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Université libre de Bruxelles (ULB), Trier University, Cattaruzza, Diego |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Quantile Minimization [INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO] Value-at-Risk (VaR) [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] Mixed-Integer Optimization Valid Inequalities [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO] Adaptive Clustering |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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