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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Diego Cattaruzza & Martine Labbé & Matteo Petris & Marius Roland & Martin Schmidt, 2024. "Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems," INFORMS Journal on Computing, INFORMS, vol. 36(4), pages 1084-1107, July.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:4:p:1084-1107
    DOI: 10.1287/ijoc.2022.0105
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    References listed on IDEAS

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    1. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    2. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
    3. QIU, Feng & AHMED, Shabbir & DEY, Santanu S & WOLSEY, Laurence A, 2014. "Covering linear programming with violations," LIDAM Reprints CORE 2618, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Benati, Stefano & Rizzi, Romeo, 2007. "A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 423-434, January.
    5. Tanner, Matthew W. & Ntaimo, Lewis, 2010. "IIS branch-and-cut for joint chance-constrained stochastic programs and application to optimal vaccine allocation," European Journal of Operational Research, Elsevier, vol. 207(1), pages 290-296, November.
    6. Feng Qiu & Shabbir Ahmed & Santanu S. Dey & Laurence A. Wolsey, 2014. "Covering Linear Programming with Violations," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 531-546, August.
    7. Björn Geißler & Antonio Morsi & Lars Schewe & Martin Schmidt, 2018. "Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 309-323, May.
    8. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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