Closing the gap in linear bilevel optimization: a new valid primal-dual inequality

Kleinert, Thomas; Plein, Fränk; Schmidt, Martin

doi:10.1007/s11590-020-01660-6

Cited by 19 publications

(13 citation statements)

References 24 publications

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“…Note that these inequalities can be seen as a special case of the valid inequalities discussed in [14] for bilevel optimization.…”

Section: Valid Inequalitiesmentioning

confidence: 99%

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

Cattaruzza,

Labbé,

Petris

et al. 2024

INFORMS Journal on Computing

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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. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [CRC TRR 154], Fonds De La Recherche Scientifique [PDR T0098.18], and Bundesministerium für Bildung und Forschung. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0105 .

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“…Note that these inequalities can be seen as a special case of the valid inequalities discussed in [14] for bilevel optimization.…”

Section: Valid Inequalitiesmentioning

confidence: 99%

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

Cattaruzza,

Labbé,

Petris

et al. 2024

INFORMS Journal on Computing

Self Cite

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“…This reformulation is practical for solving bilevel problems, but the choice of the big‐ M term should be applied with care. Checking big‐ M term validity can be as difficult as solving the original bilevel problem (Kleinert et al., 2020, 2021), and if the choice of big‐ M term is too small it can result in suboptimal solutions of the bilevel problem (Pineda and Morales, 2019).…”

Section: Bilevel Optimizationmentioning

confidence: 99%

Coordinating harvest planning and scheduling in an agricultural supply chain through a stochastic bilevel programming

Albornoz

Vera

2022

Int Trans Operational Res

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This paper addresses a selective harvest planning problem in the context of a hierarchical agricultural supply chain, which integrates the definition of management zones for harvest planning, and the coordination between the producer and the wholesaler. The problem is represented through a stochastic bilevel program that allows the representation of the hierarchy between the producer (leader) and a wholesaler (follower). The producer decides planning and scheduling of the selective harvest for each homogeneous management zone into the resulting partition, and the wholesaler decides the amount to be acquired to satisfy demand requirements. At each decision level, a stochastic optimization model is proposed for representing the uncertainty in future crop yields, prices, and demands, using a finite set of scenarios. A reformulation of the bilevel model into a mixed‐integer linear program is provided using Karush–Kuhn–Tucker conditions and replacing the nonlinear complementary constraints allowing for the introduction of auxiliary binary variables and a big‐M term. This model was applied in a case study for selective harvesting of grapes with data collected from a farm located in the south central zone of Chile. Our research shows valuable results of the proposed methodology from a set of instances representing the behavior of both decision makers under uncertainty.

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“…However, this approach may require a substantial amount of branching on complementary conditions which may be impractical on large problems. Recently, Kleinert et al (2020a) derived valid inequalities for LBP by exploiting the SD conditions of the follower-level problem, which proves to be very effective in closing the gap for some instances.…”

Section: Solution Approaches Of Bilevel Programming Problemmentioning

confidence: 99%

Single-leader multi-follower games for the regulation of two-sided Mobility-as-a-Service markets

Xi¹,

Aussel²,

Liu³

et al. 2021

Preprint

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Closing the gap in linear bilevel optimization: a new valid primal-dual inequality

Cited by 19 publications

References 24 publications

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

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

Coordinating harvest planning and scheduling in an agricultural supply chain through a stochastic bilevel programming

Single-leader multi-follower games for the regulation of two-sided Mobility-as-a-Service markets

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